# QB/d cp2.10

< QB

• Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
• At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
• Quizbank physics 1 (id 60675)
• Quizbank physics 2 (id 61712)
• Quizbank astronomy (id 63705)

The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.

See special:permalink/1895273 for a wikitext version of this quiz.

### LaTexMarkup begin

%[[File:Quizbankqb_{{SUBPAGENAME}}.pdf|thumb|See[[:File:Quizbankqb_{{SUBPAGENAME}}.pdf]]]]
%CurrentID: {{REVISIONID}}
%PDF: [[:File:Quizbankqb_{{SUBPAGENAME}}.pdf]]%Required images: [[file:Wikiversity-logo-en.svg|45px]][[File:DC circuit 3 resistors 1 voltage source.svg|45px]][[File:KirchhoffLaws simple.svg|45px]][[File:Kirchhoff loop w external current.svg|45px]][[File:RC_switch.svg|45px]]

%This code creates both the question and answer key using \newcommand\mytest
%%%    EDIT QUIZ INFO  HERE   %%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\quizname}{QB/d_cp2.10}

\newcommand{\quiztype}{numerical}%[[Category:QB/numerical]]
%%%%% PREAMBLE%%%%%%%%%%%%
\newif\ifkey %estabkishes Boolean ifkey to turn on and off endnotes

\documentclass[11pt]{exam}
\RequirePackage{amssymb, amsfonts, amsmath, latexsym, verbatim,
xspace, setspace,datetime}
\RequirePackage{tikz, pgflibraryplotmarks, hyperref}
\usepackage[left=.5in, right=.5in, bottom=.5in, top=.75in]{geometry}
\usepackage{endnotes, multicol,textgreek} %
\usepackage{graphicx} %
\singlespacing %OR \onehalfspacing OR \doublespacing
\parindent 0ex % Turns off paragraph indentation
% BEGIN DOCUMENT
\begin{document}
\title{d\_cp2.10}
\author{The LaTex code that creates this quiz is released to the Public Domain\\
Attribution for each question is documented in the Appendix}
\maketitle
\begin{center}
\includegraphics[width=0.15\textwidth]{666px-Wikiversity-logo-en.png}
\\Latex markup at\\
\end{center}
\begin{frame}{}
\begin{multicols}{3}
\tableofcontents
\end{multicols}
\end{frame}
\pagebreak\section{Quiz}
\keytrue
\begin{questions}
\question A given battery has a 12\,V emf and an internal resistance of 0.1\,\textOmega\ . If it is connected to a  0.5\,\textOmega\  resistor what is the power dissipated by that load?\ifkey\endnote{Example 10.1 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:SFE57-D2@4/101-Electromotive-Force\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1895273}}}\fi
\begin{choices}
\choice 1.503E+02\,W
\choice 1.653E+02\,W
\choice 1.818E+02\,W
\CorrectChoice 2.000E+02\,W
\choice 2.200E+02\,W
\end{choices}

\question A battery with a terminal voltage of 9\,V is connected to a circuit consisting of 4 20\,\textOmega\  resistors and one 10\,\textOmega\  resistor. What is the voltage drop across the 10\,\textOmega\  resistor?\ifkey\endnote{Example 10.\# from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:Aghicpfd@2/102-Resistors-in-Series-and-Pa\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1895273}}}\fi
\begin{choices}
\choice 7.513E-01\,V
\choice 8.264E-01\,V
\choice 9.091E-01\,V
\CorrectChoice 1.000E+00\,V
\choice 1.100E+00\,V
\end{choices}

\question Three resistors, R\textsubscript{1}\,=\,1\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,2\,\textOmega\ , are connected in parallel to a 3\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.) \ifkey\endnote{Example 10.3 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:Aghicpfd@2/102-Resistors-in-Series-and-Pa\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1895273}}}\fi
\begin{choices}
\choice 6.762E+00\,W
\choice 7.438E+00\,W
\choice 8.182E+00\,W
\CorrectChoice 9.000E+00\,W
\choice 9.900E+00\,W
\end{choices}

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=12\,V, R\textsubscript{1}=1\,\textOmega\ , R\textsubscript{2}=6\,\textOmega\ , and R\textsubscript{3}=13\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?\ifkey\endnote{Example 10.4 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:Aghicpfd@2/102-Resistors-in-Series-and-Pa\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1895273}}}\fi
\begin{choices}
\CorrectChoice 1.552E+01\,W
\choice 1.707E+01\,W
\choice 1.878E+01\,W
\choice 2.066E+01\,W
\choice 2.272E+01\,W
\end{choices}

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2\,\textOmega\ , R\textsubscript{2}= 1\,\textOmega\ , and R\textsubscript{2}= 3\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.5\,V and 2.3\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.6\,V. What is the absolute value of the current through R\textsubscript{1}?\ifkey\endnote{Example 10.6 from OpenStax University Physics 2: https://cnx.org/contents/eg-XcBxE@9.8:7DqkHtKM@2/103-Kirchhoffs-Rules\#CNX\_UPhysics\_27\_02\_Specified\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1895273}}}\fi
\begin{choices}
\choice 1.653E-01\,A
\choice 1.818E-01\,A
\CorrectChoice 2.000E-01\,A
\choice 2.200E-01\,A
\choice 2.420E-01\,A
\end{choices}

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=22.5\,V, and  \textepsilon\textsubscript{2}=10\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2\,k\textOmega\  and  R\textsubscript{2}=1\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=5.0\,mA and I\textsubscript{4}=1.25\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?\ifkey\endnote{Kirchhoff rules [[user:Guy vandegrift]] Public Domain\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1895273}}}\fi
\begin{choices}
\choice 3.099E+00\,mA
\choice 3.409E+00\,mA
\CorrectChoice 3.750E+00\,mA
\choice 4.125E+00\,mA
\choice 4.538E+00\,mA
\end{choices}

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=22.5\,V, and  \textepsilon\textsubscript{2}=10\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2\,k\textOmega\  and  R\textsubscript{2}=1\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=5.0\,mA and I\textsubscript{4}=1.25\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?\ifkey\endnote{Kirchhoff rules [[user:Guy vandegrift]] Public Domain\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1895273}}}\fi
\begin{choices}
\CorrectChoice 5.000E+00\,V
\choice 5.500E+00\,V
\choice 6.050E+00\,V
\choice 6.655E+00\,V
\choice 7.321E+00\,V
\end{choices}

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=22.5\,V, and  \textepsilon\textsubscript{2}=10\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2\,k\textOmega\  and  R\textsubscript{2}=1\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=5.0\,mA and I\textsubscript{4}=1.25\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?\ifkey\endnote{Kirchhoff rules [[user:Guy vandegrift]] Public Domain\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1895273}}}\fi
\begin{choices}
\choice 6.198E+00\,V
\choice 6.818E+00\,V
\CorrectChoice 7.500E+00\,V
\choice 8.250E+00\,V
\choice 9.075E+00\,V
\end{choices}

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  100\,V.  If the combined external and internal resistance is 101\,\textOmega\ and the capacitance is  50\,mF, how long will it take for the capacitor's voltage to reach 80\,V?\ifkey\endnote{Example 10.8 from OpenStax University Physics2: https://cnx.org/contents/eg-XcBxE@9.8:h2kCjzVL@3/105-RC-Circuits\_1 placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1895273}}}\fi
\begin{choices}
\CorrectChoice 8.128E+00\,s
\choice 8.940E+00\,s
\choice 9.834E+00\,s
\choice 1.082E+01\,s
\choice 1.190E+01\,s
\end{choices}

\end{questions}
\newpage
\section{Renditions}  %%% Renditions %%%%

\subsection{}%%%% subsection 1

\begin{questions} %%%%%%% begin questions

\question A given battery has a 12\,V emf and an internal resistance of 0.193\,\textOmega\ . If it is connected to a  0.89\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  8.210E+01\,W
\choice  9.030E+01\,W
\choice  9.934E+01\,W
\CorrectChoice 1.093E+02\,W
\choice  1.202E+02\,W
\end{choices} %%% end choices

\question A given battery has a 14\,V emf and an internal resistance of 0.0842\,\textOmega\ . If it is connected to a  0.835\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.455E+02\,W
\choice  1.601E+02\,W
\choice  1.761E+02\,W
\CorrectChoice 1.937E+02\,W
\choice  2.131E+02\,W
\end{choices} %%% end choices

\question A given battery has a 13\,V emf and an internal resistance of 0.159\,\textOmega\ . If it is connected to a  0.617\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.301E+02\,W
\choice  1.431E+02\,W
\choice  1.574E+02\,W
\CorrectChoice 1.732E+02\,W
\choice  1.905E+02\,W
\end{choices} %%% end choices

\question A given battery has a 12\,V emf and an internal resistance of 0.107\,\textOmega\ . If it is connected to a  0.814\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.382E+02\,W
\choice  1.520E+02\,W
\choice  1.672E+02\,W
\choice  1.839E+02\,W
\choice  2.023E+02\,W
\end{choices} %%% end choices

\question A given battery has a 14\,V emf and an internal resistance of 0.198\,\textOmega\ . If it is connected to a  0.534\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.776E+02\,W
\CorrectChoice 1.953E+02\,W
\choice  2.149E+02\,W
\choice  2.364E+02\,W
\choice  2.600E+02\,W
\end{choices} %%% end choices

\question A given battery has a 13\,V emf and an internal resistance of 0.106\,\textOmega\ . If it is connected to a  0.752\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.569E+02\,W
\CorrectChoice 1.726E+02\,W
\choice  1.899E+02\,W
\choice  2.089E+02\,W
\choice  2.298E+02\,W
\end{choices} %%% end choices

\question A given battery has a 15\,V emf and an internal resistance of 0.162\,\textOmega\ . If it is connected to a  0.561\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.814E+02\,W
\choice  1.996E+02\,W
\choice  2.195E+02\,W
\CorrectChoice 2.415E+02\,W
\choice  2.656E+02\,W
\end{choices} %%% end choices

\question A given battery has a 11\,V emf and an internal resistance of 0.0998\,\textOmega\ . If it is connected to a  0.417\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.419E+02\,W
\choice  1.561E+02\,W
\choice  1.717E+02\,W
\CorrectChoice 1.889E+02\,W
\choice  2.078E+02\,W
\end{choices} %%% end choices

\question A given battery has a 15\,V emf and an internal resistance of 0.113\,\textOmega\ . If it is connected to a  0.645\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.898E+02\,W
\choice  2.087E+02\,W
\choice  2.296E+02\,W
\CorrectChoice 2.526E+02\,W
\choice  2.778E+02\,W
\end{choices} %%% end choices

\question A given battery has a 14\,V emf and an internal resistance of 0.132\,\textOmega\ . If it is connected to a  0.689\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.656E+02\,W
\choice  1.821E+02\,W
\CorrectChoice 2.003E+02\,W
\choice  2.204E+02\,W
\choice  2.424E+02\,W
\end{choices} %%% end choices

\question A given battery has a 14\,V emf and an internal resistance of 0.192\,\textOmega\ . If it is connected to a  0.766\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.229E+02\,W
\choice  1.352E+02\,W
\choice  1.487E+02\,W
\CorrectChoice 1.636E+02\,W
\choice  1.799E+02\,W
\end{choices} %%% end choices

\question A given battery has a 13\,V emf and an internal resistance of 0.161\,\textOmega\ . If it is connected to a  0.814\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.087E+02\,W
\choice  1.196E+02\,W
\choice  1.316E+02\,W
\CorrectChoice 1.447E+02\,W
\choice  1.592E+02\,W
\end{choices} %%% end choices

\question A given battery has a 12\,V emf and an internal resistance of 0.0984\,\textOmega\ . If it is connected to a  0.485\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.052E+02\,W
\choice  2.257E+02\,W
\choice  2.483E+02\,W
\choice  2.731E+02\,W
\choice  3.004E+02\,W
\end{choices} %%% end choices

\question A given battery has a 15\,V emf and an internal resistance of 0.177\,\textOmega\ . If it is connected to a  0.824\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.682E+02\,W
\CorrectChoice 1.850E+02\,W
\choice  2.035E+02\,W
\choice  2.239E+02\,W
\choice  2.463E+02\,W
\end{choices} %%% end choices

\question A given battery has a 15\,V emf and an internal resistance of 0.0536\,\textOmega\ . If it is connected to a  0.64\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  2.721E+02\,W
\CorrectChoice 2.993E+02\,W
\choice  3.293E+02\,W
\choice  3.622E+02\,W
\choice  3.984E+02\,W
\end{choices} %%% end choices

\question A given battery has a 9\,V emf and an internal resistance of 0.141\,\textOmega\ . If it is connected to a  0.663\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  5.674E+01\,W
\choice  6.242E+01\,W
\choice  6.866E+01\,W
\choice  7.553E+01\,W
\CorrectChoice 8.308E+01\,W
\end{choices} %%% end choices

\question A given battery has a 9\,V emf and an internal resistance of 0.16\,\textOmega\ . If it is connected to a  0.45\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  6.691E+01\,W
\choice  7.360E+01\,W
\choice  8.096E+01\,W
\choice  8.905E+01\,W
\CorrectChoice 9.796E+01\,W
\end{choices} %%% end choices

\question A given battery has a 10\,V emf and an internal resistance of 0.119\,\textOmega\ . If it is connected to a  0.445\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.272E+02\,W
\CorrectChoice 1.399E+02\,W
\choice  1.539E+02\,W
\choice  1.693E+02\,W
\choice  1.862E+02\,W
\end{choices} %%% end choices

\question A given battery has a 13\,V emf and an internal resistance of 0.113\,\textOmega\ . If it is connected to a  0.686\,\textOmega\  resistor what is the power dissipated by that load?
\begin{choices} %%%%%%% begin choices
\choice  1.501E+02\,W
\choice  1.651E+02\,W
\CorrectChoice 1.816E+02\,W
\choice  1.998E+02\,W
\choice  2.197E+02\,W
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 2

\begin{questions} %%%%%%% begin questions

\question A battery with a terminal voltage of 14.9\,V is connected to a circuit consisting of 2 23.3\,\textOmega\  resistors and one 13.6\,\textOmega\  resistor. What is the voltage drop across the 13.6\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 3.366E+00\,V
\choice  3.703E+00\,V
\choice  4.073E+00\,V
\choice  4.480E+00\,V
\choice  4.928E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 8.14\,V is connected to a circuit consisting of 2 21.5\,\textOmega\  resistors and one 13.1\,\textOmega\  resistor. What is the voltage drop across the 13.1\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.298E+00\,V
\choice  1.428E+00\,V
\choice  1.571E+00\,V
\choice  1.728E+00\,V
\CorrectChoice 1.901E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 14.1\,V is connected to a circuit consisting of 3 15.7\,\textOmega\  resistors and one 10.2\,\textOmega\  resistor. What is the voltage drop across the 10.2\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  2.074E+00\,V
\choice  2.282E+00\,V
\CorrectChoice 2.510E+00\,V
\choice  2.761E+00\,V
\choice  3.037E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 8.72\,V is connected to a circuit consisting of 2 15.8\,\textOmega\  resistors and one 9.58\,\textOmega\  resistor. What is the voltage drop across the 9.58\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.677E+00\,V
\choice  1.844E+00\,V
\CorrectChoice 2.029E+00\,V
\choice  2.231E+00\,V
\choice  2.455E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 8.41\,V is connected to a circuit consisting of 3 16.1\,\textOmega\  resistors and one 10.9\,\textOmega\  resistor. What is the voltage drop across the 10.9\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.058E+00\,V
\choice  1.163E+00\,V
\choice  1.280E+00\,V
\choice  1.408E+00\,V
\CorrectChoice 1.548E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 6.49\,V is connected to a circuit consisting of 3 18.0\,\textOmega\  resistors and one 10.3\,\textOmega\  resistor. What is the voltage drop across the 10.3\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  7.101E-01\,V
\choice  7.811E-01\,V
\choice  8.592E-01\,V
\choice  9.451E-01\,V
\CorrectChoice 1.040E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 9.88\,V is connected to a circuit consisting of 3 15.9\,\textOmega\  resistors and one 10.8\,\textOmega\  resistor. What is the voltage drop across the 10.8\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.370E+00\,V
\choice  1.507E+00\,V
\choice  1.658E+00\,V
\CorrectChoice 1.824E+00\,V
\choice  2.006E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 8.01\,V is connected to a circuit consisting of 3 22.1\,\textOmega\  resistors and one 14.5\,\textOmega\  resistor. What is the voltage drop across the 14.5\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  9.818E-01\,V
\choice  1.080E+00\,V
\choice  1.188E+00\,V
\choice  1.307E+00\,V
\CorrectChoice 1.437E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 14.1\,V is connected to a circuit consisting of 2 20.3\,\textOmega\  resistors and one 13.1\,\textOmega\  resistor. What is the voltage drop across the 13.1\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  2.843E+00\,V
\choice  3.127E+00\,V
\CorrectChoice 3.440E+00\,V
\choice  3.784E+00\,V
\choice  4.162E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 13.2\,V is connected to a circuit consisting of 3 15.7\,\textOmega\  resistors and one 10.3\,\textOmega\  resistor. What is the voltage drop across the 10.3\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.958E+00\,V
\choice  2.153E+00\,V
\CorrectChoice 2.369E+00\,V
\choice  2.606E+00\,V
\choice  2.866E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 7.82\,V is connected to a circuit consisting of 2 19.3\,\textOmega\  resistors and one 12.2\,\textOmega\  resistor. What is the voltage drop across the 12.2\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.552E+00\,V
\choice  1.707E+00\,V
\CorrectChoice 1.878E+00\,V
\choice  2.066E+00\,V
\choice  2.272E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 10.6\,V is connected to a circuit consisting of 2 21.1\,\textOmega\  resistors and one 12.8\,\textOmega\  resistor. What is the voltage drop across the 12.8\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.467E+00\,V
\choice  2.714E+00\,V
\choice  2.985E+00\,V
\choice  3.283E+00\,V
\choice  3.612E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 8.66\,V is connected to a circuit consisting of 3 19.6\,\textOmega\  resistors and one 10.6\,\textOmega\  resistor. What is the voltage drop across the 10.6\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.202E+00\,V
\CorrectChoice 1.323E+00\,V
\choice  1.455E+00\,V
\choice  1.600E+00\,V
\choice  1.761E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 10.7\,V is connected to a circuit consisting of 2 24.5\,\textOmega\  resistors and one 15.2\,\textOmega\  resistor. What is the voltage drop across the 15.2\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.730E+00\,V
\choice  1.903E+00\,V
\choice  2.094E+00\,V
\choice  2.303E+00\,V
\CorrectChoice 2.533E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 14.6\,V is connected to a circuit consisting of 2 21.7\,\textOmega\  resistors and one 14.4\,\textOmega\  resistor. What is the voltage drop across the 14.4\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 3.637E+00\,V
\choice  4.001E+00\,V
\choice  4.401E+00\,V
\choice  4.841E+00\,V
\choice  5.325E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 7.63\,V is connected to a circuit consisting of 3 20.9\,\textOmega\  resistors and one 12.1\,\textOmega\  resistor. What is the voltage drop across the 12.1\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.234E+00\,V
\choice  1.358E+00\,V
\choice  1.493E+00\,V
\choice  1.643E+00\,V
\choice  1.807E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 14.9\,V is connected to a circuit consisting of 2 16.3\,\textOmega\  resistors and one 9.8\,\textOmega\  resistor. What is the voltage drop across the 9.8\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  2.352E+00\,V
\choice  2.587E+00\,V
\choice  2.846E+00\,V
\choice  3.131E+00\,V
\CorrectChoice 3.444E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 7.63\,V is connected to a circuit consisting of 2 15.9\,\textOmega\  resistors and one 10.4\,\textOmega\  resistor. What is the voltage drop across the 10.4\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.709E+00\,V
\CorrectChoice 1.880E+00\,V
\choice  2.068E+00\,V
\choice  2.275E+00\,V
\choice  2.503E+00\,V
\end{choices} %%% end choices

\question A battery with a terminal voltage of 12.4\,V is connected to a circuit consisting of 3 21.6\,\textOmega\  resistors and one 12.1\,\textOmega\  resistor. What is the voltage drop across the 12.1\,\textOmega\  resistor?
\begin{choices} %%%%%%% begin choices
\choice  1.333E+00\,V
\choice  1.466E+00\,V
\choice  1.612E+00\,V
\choice  1.774E+00\,V
\CorrectChoice 1.951E+00\,V
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 3

\begin{questions} %%%%%%% begin questions

\question Three resistors, R\textsubscript{1}\,=\,1.7\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,3.75\,\textOmega\ , are connected in parallel to a 9.74\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  4.193E+01\,W
\choice  4.612E+01\,W
\choice  5.073E+01\,W
\CorrectChoice 5.580E+01\,W
\choice  6.138E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,0.672\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,1.52\,\textOmega\ , are connected in parallel to a 5.34\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  2.898E+01\,W
\choice  3.188E+01\,W
\choice  3.507E+01\,W
\choice  3.858E+01\,W
\CorrectChoice 4.243E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.82\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,4.14\,\textOmega\ , are connected in parallel to a 5.65\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.754E+01\,W
\choice  1.929E+01\,W
\choice  2.122E+01\,W
\choice  2.335E+01\,W
\choice  2.568E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,0.61\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,1.35\,\textOmega\ , are connected in parallel to a 7.04\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  7.386E+01\,W
\CorrectChoice 8.125E+01\,W
\choice  8.937E+01\,W
\choice  9.831E+01\,W
\choice  1.081E+02\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,0.624\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,1.37\,\textOmega\ , are connected in parallel to a 7.46\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  7.371E+01\,W
\choice  8.108E+01\,W
\CorrectChoice 8.919E+01\,W
\choice  9.810E+01\,W
\choice  1.079E+02\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,0.87\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,2.0\,\textOmega\ , are connected in parallel to a 8.57\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  6.977E+01\,W
\choice  7.674E+01\,W
\CorrectChoice 8.442E+01\,W
\choice  9.286E+01\,W
\choice  1.021E+02\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.41\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,3.17\,\textOmega\ , are connected in parallel to a 5.89\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  1.681E+01\,W
\choice  1.849E+01\,W
\choice  2.033E+01\,W
\choice  2.237E+01\,W
\CorrectChoice 2.460E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.74\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,3.92\,\textOmega\ , are connected in parallel to a 8.5\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  2.836E+01\,W
\choice  3.120E+01\,W
\choice  3.432E+01\,W
\choice  3.775E+01\,W
\CorrectChoice 4.152E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,0.906\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,2.02\,\textOmega\ , are connected in parallel to a 5.98\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  3.262E+01\,W
\choice  3.588E+01\,W
\CorrectChoice 3.947E+01\,W
\choice  4.342E+01\,W
\choice  4.776E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.43\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,3.25\,\textOmega\ , are connected in parallel to a 9.03\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  5.184E+01\,W
\CorrectChoice 5.702E+01\,W
\choice  6.272E+01\,W
\choice  6.900E+01\,W
\choice  7.590E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.23\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,2.73\,\textOmega\ , are connected in parallel to a 5.41\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  1.788E+01\,W
\choice  1.967E+01\,W
\choice  2.163E+01\,W
\CorrectChoice 2.380E+01\,W
\choice  2.617E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.39\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,3.06\,\textOmega\ , are connected in parallel to a 6.21\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  2.293E+01\,W
\choice  2.522E+01\,W
\CorrectChoice 2.774E+01\,W
\choice  3.052E+01\,W
\choice  3.357E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.2\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,2.75\,\textOmega\ , are connected in parallel to a 6.42\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  2.581E+01\,W
\choice  2.839E+01\,W
\choice  3.122E+01\,W
\CorrectChoice 3.435E+01\,W
\choice  3.778E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.31\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,2.91\,\textOmega\ , are connected in parallel to a 6.03\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  2.294E+01\,W
\choice  2.523E+01\,W
\CorrectChoice 2.776E+01\,W
\choice  3.053E+01\,W
\choice  3.359E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.52\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,3.38\,\textOmega\ , are connected in parallel to a 5.82\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  1.842E+01\,W
\choice  2.026E+01\,W
\CorrectChoice 2.228E+01\,W
\choice  2.451E+01\,W
\choice  2.696E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,0.686\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,1.58\,\textOmega\ , are connected in parallel to a 8.97\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.173E+02\,W
\choice  1.290E+02\,W
\choice  1.419E+02\,W
\choice  1.561E+02\,W
\choice  1.717E+02\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,0.855\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,1.91\,\textOmega\ , are connected in parallel to a 6.97\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.682E+01\,W
\choice  6.250E+01\,W
\choice  6.875E+01\,W
\choice  7.563E+01\,W
\choice  8.319E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,1.25\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,2.82\,\textOmega\ , are connected in parallel to a 8.6\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  4.890E+01\,W
\choice  5.379E+01\,W
\CorrectChoice 5.917E+01\,W
\choice  6.508E+01\,W
\choice  7.159E+01\,W
\end{choices} %%% end choices

\question Three resistors, R\textsubscript{1}\,=\,0.548\,\textOmega\ , and  R\textsubscript{2}\,=\,R\textsubscript{2}\,=\,1.24\,\textOmega\ , are connected in parallel to a 7.16\,V voltage source. Calculate the power dissipated by the smaller resistor (R\textsubscript{1}.)
\begin{choices} %%%%%%% begin choices
\choice  7.029E+01\,W
\choice  7.731E+01\,W
\choice  8.505E+01\,W
\CorrectChoice 9.355E+01\,W
\choice  1.029E+02\,W
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 4

\begin{questions} %%%%%%% begin questions

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=19.9\,V, R\textsubscript{1}=1.69\,\textOmega\ , R\textsubscript{2}=7.02\,\textOmega\ , and R\textsubscript{3}=12.8\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.993E+01\,W
\choice  3.293E+01\,W
\choice  3.622E+01\,W
\choice  3.984E+01\,W
\choice  4.383E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=11.9\,V, R\textsubscript{1}=2.75\,\textOmega\ , R\textsubscript{2}=7.19\,\textOmega\ , and R\textsubscript{3}=14.6\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 7.982E+00\,W
\choice  8.780E+00\,W
\choice  9.658E+00\,W
\choice  1.062E+01\,W
\choice  1.169E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=18.4\,V, R\textsubscript{1}=1.64\,\textOmega\ , R\textsubscript{2}=6.56\,\textOmega\ , and R\textsubscript{3}=12.8\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  2.470E+01\,W
\CorrectChoice 2.717E+01\,W
\choice  2.989E+01\,W
\choice  3.288E+01\,W
\choice  3.617E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=16.1\,V, R\textsubscript{1}=1.18\,\textOmega\ , R\textsubscript{2}=5.28\,\textOmega\ , and R\textsubscript{3}=14.8\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  2.172E+01\,W
\choice  2.389E+01\,W
\choice  2.628E+01\,W
\CorrectChoice 2.891E+01\,W
\choice  3.180E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=17.8\,V, R\textsubscript{1}=2.27\,\textOmega\ , R\textsubscript{2}=6.79\,\textOmega\ , and R\textsubscript{3}=15.1\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.446E+01\,W
\choice  1.591E+01\,W
\choice  1.750E+01\,W
\choice  1.925E+01\,W
\CorrectChoice 2.117E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=15.4\,V, R\textsubscript{1}=2.55\,\textOmega\ , R\textsubscript{2}=5.12\,\textOmega\ , and R\textsubscript{3}=12.7\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.096E+01\,W
\choice  1.206E+01\,W
\choice  1.326E+01\,W
\choice  1.459E+01\,W
\CorrectChoice 1.605E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=15.2\,V, R\textsubscript{1}=1.6\,\textOmega\ , R\textsubscript{2}=7.89\,\textOmega\ , and R\textsubscript{3}=15.3\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.713E+01\,W
\choice  1.885E+01\,W
\choice  2.073E+01\,W
\choice  2.280E+01\,W
\choice  2.508E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=15.8\,V, R\textsubscript{1}=1.86\,\textOmega\ , R\textsubscript{2}=7.66\,\textOmega\ , and R\textsubscript{3}=12.9\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.157E+01\,W
\choice  1.273E+01\,W
\choice  1.400E+01\,W
\choice  1.540E+01\,W
\CorrectChoice 1.694E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=19.6\,V, R\textsubscript{1}=1.45\,\textOmega\ , R\textsubscript{2}=7.85\,\textOmega\ , and R\textsubscript{3}=15.8\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  2.730E+01\,W
\CorrectChoice 3.003E+01\,W
\choice  3.304E+01\,W
\choice  3.634E+01\,W
\choice  3.998E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=16.2\,V, R\textsubscript{1}=2.84\,\textOmega\ , R\textsubscript{2}=7.06\,\textOmega\ , and R\textsubscript{3}=13.1\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.418E+01\,W
\choice  1.560E+01\,W
\choice  1.716E+01\,W
\choice  1.887E+01\,W
\choice  2.076E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=18.8\,V, R\textsubscript{1}=2.59\,\textOmega\ , R\textsubscript{2}=5.47\,\textOmega\ , and R\textsubscript{3}=15.8\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  2.191E+01\,W
\CorrectChoice 2.410E+01\,W
\choice  2.651E+01\,W
\choice  2.916E+01\,W
\choice  3.208E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=11.8\,V, R\textsubscript{1}=2.38\,\textOmega\ , R\textsubscript{2}=5.11\,\textOmega\ , and R\textsubscript{3}=14.6\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  8.489E+00\,W
\choice  9.338E+00\,W
\CorrectChoice 1.027E+01\,W
\choice  1.130E+01\,W
\choice  1.243E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=17.5\,V, R\textsubscript{1}=2.34\,\textOmega\ , R\textsubscript{2}=7.1\,\textOmega\ , and R\textsubscript{3}=15.3\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.784E+01\,W
\CorrectChoice 1.963E+01\,W
\choice  2.159E+01\,W
\choice  2.375E+01\,W
\choice  2.612E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=10.8\,V, R\textsubscript{1}=1.26\,\textOmega\ , R\textsubscript{2}=5.65\,\textOmega\ , and R\textsubscript{3}=14.8\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  8.240E+00\,W
\choice  9.064E+00\,W
\choice  9.970E+00\,W
\choice  1.097E+01\,W
\CorrectChoice 1.206E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=17.9\,V, R\textsubscript{1}=1.3\,\textOmega\ , R\textsubscript{2}=5.1\,\textOmega\ , and R\textsubscript{3}=12.1\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  2.543E+01\,W
\choice  2.798E+01\,W
\choice  3.077E+01\,W
\CorrectChoice 3.385E+01\,W
\choice  3.724E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=17.9\,V, R\textsubscript{1}=1.68\,\textOmega\ , R\textsubscript{2}=7.84\,\textOmega\ , and R\textsubscript{3}=12.3\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.240E+01\,W
\choice  2.464E+01\,W
\choice  2.710E+01\,W
\choice  2.981E+01\,W
\choice  3.279E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=13.5\,V, R\textsubscript{1}=2.66\,\textOmega\ , R\textsubscript{2}=7.29\,\textOmega\ , and R\textsubscript{3}=14.5\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  7.123E+00\,W
\choice  7.835E+00\,W
\choice  8.618E+00\,W
\choice  9.480E+00\,W
\CorrectChoice 1.043E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=10.9\,V, R\textsubscript{1}=1.68\,\textOmega\ , R\textsubscript{2}=7.52\,\textOmega\ , and R\textsubscript{3}=12.8\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  7.827E+00\,W
\CorrectChoice 8.610E+00\,W
\choice  9.470E+00\,W
\choice  1.042E+01\,W
\choice  1.146E+01\,W
\end{choices} %%% end choices

\question \includegraphics[width=0.19\textwidth]{DC-circuit-3-resistors-1-voltage-source.png}In the circuit shown V=15.4\,V, R\textsubscript{1}=2.77\,\textOmega\ , R\textsubscript{2}=6.07\,\textOmega\ , and R\textsubscript{3}=14.5\,\textOmega\ . What is the power dissipated by R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.190E+01\,W
\choice  1.309E+01\,W
\CorrectChoice 1.440E+01\,W
\choice  1.584E+01\,W
\choice  1.742E+01\,W
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 5

\begin{questions} %%%%%%% begin questions

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 1.35\,\textOmega\ , R\textsubscript{2}= 1.52\,\textOmega\ , and R\textsubscript{2}= 2.45\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.419\,V and 2.37\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.511\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  8.841E-02\,A
\CorrectChoice 9.725E-02\,A
\choice  1.070E-01\,A
\choice  1.177E-01\,A
\choice  1.294E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.41\,\textOmega\ , R\textsubscript{2}= 1.74\,\textOmega\ , and R\textsubscript{2}= 3.35\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.508\,V and 1.36\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.595\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.203E-01\,A
\choice  1.324E-01\,A
\CorrectChoice 1.456E-01\,A
\choice  1.602E-01\,A
\choice  1.762E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.04\,\textOmega\ , R\textsubscript{2}= 1.19\,\textOmega\ , and R\textsubscript{2}= 2.5\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.507\,V and 3.07\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.602\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.401E-01\,A
\choice  1.542E-01\,A
\choice  1.696E-01\,A
\choice  1.865E-01\,A
\choice  2.052E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.38\,\textOmega\ , R\textsubscript{2}= 1.87\,\textOmega\ , and R\textsubscript{2}= 2.32\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.605\,V and 3.8\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.67\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  8.147E-02\,A
\choice  8.962E-02\,A
\choice  9.858E-02\,A
\CorrectChoice 1.084E-01\,A
\choice  1.193E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 1.1\,\textOmega\ , R\textsubscript{2}= 1.55\,\textOmega\ , and R\textsubscript{2}= 2.11\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.545\,V and 3.22\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.744\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.886E-01\,A
\CorrectChoice 2.075E-01\,A
\choice  2.282E-01\,A
\choice  2.510E-01\,A
\choice  2.761E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 1.54\,\textOmega\ , R\textsubscript{2}= 0.927\,\textOmega\ , and R\textsubscript{2}= 2.46\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.632\,V and 2.12\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.586\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.770E-01\,A
\choice  1.947E-01\,A
\CorrectChoice 2.141E-01\,A
\choice  2.355E-01\,A
\choice  2.591E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 1.18\,\textOmega\ , R\textsubscript{2}= 0.878\,\textOmega\ , and R\textsubscript{2}= 2.11\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.637\,V and 3.51\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.547\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.701E-01\,A
\CorrectChoice 1.871E-01\,A
\choice  2.058E-01\,A
\choice  2.264E-01\,A
\choice  2.490E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 1.6\,\textOmega\ , R\textsubscript{2}= 1.3\,\textOmega\ , and R\textsubscript{2}= 2.22\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.55\,V and 3.18\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.743\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.721E-01\,A
\choice  1.893E-01\,A
\choice  2.082E-01\,A
\choice  2.291E-01\,A
\choice  2.520E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.42\,\textOmega\ , R\textsubscript{2}= 1.09\,\textOmega\ , and R\textsubscript{2}= 3.89\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.677\,V and 1.86\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.745\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  2.089E-01\,A
\choice  2.298E-01\,A
\CorrectChoice 2.528E-01\,A
\choice  2.781E-01\,A
\choice  3.059E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 1.81\,\textOmega\ , R\textsubscript{2}= 1.18\,\textOmega\ , and R\textsubscript{2}= 2.62\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.628\,V and 2.54\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.748\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.552E-01\,A
\choice  1.707E-01\,A
\choice  1.878E-01\,A
\choice  2.065E-01\,A
\CorrectChoice 2.272E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.34\,\textOmega\ , R\textsubscript{2}= 1.34\,\textOmega\ , and R\textsubscript{2}= 2.94\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.609\,V and 1.68\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.541\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.464E-01\,A
\CorrectChoice 1.610E-01\,A
\choice  1.772E-01\,A
\choice  1.949E-01\,A
\choice  2.144E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.49\,\textOmega\ , R\textsubscript{2}= 1.72\,\textOmega\ , and R\textsubscript{2}= 3.58\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.417\,V and 1.83\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.53\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  8.220E-02\,A
\choice  9.042E-02\,A
\choice  9.946E-02\,A
\CorrectChoice 1.094E-01\,A
\choice  1.203E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.67\,\textOmega\ , R\textsubscript{2}= 1.78\,\textOmega\ , and R\textsubscript{2}= 3.63\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.448\,V and 2.29\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.656\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  9.287E-02\,A
\choice  1.022E-01\,A
\choice  1.124E-01\,A
\CorrectChoice 1.236E-01\,A
\choice  1.360E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.73\,\textOmega\ , R\textsubscript{2}= 1.4\,\textOmega\ , and R\textsubscript{2}= 2.35\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.549\,V and 1.27\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.584\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.213E-01\,A
\choice  1.334E-01\,A
\choice  1.468E-01\,A
\CorrectChoice 1.614E-01\,A
\choice  1.776E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 1.57\,\textOmega\ , R\textsubscript{2}= 1.25\,\textOmega\ , and R\textsubscript{2}= 3.38\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.585\,V and 2.91\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.55\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.427E-01\,A
\choice  1.569E-01\,A
\CorrectChoice 1.726E-01\,A
\choice  1.899E-01\,A
\choice  2.089E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 1.33\,\textOmega\ , R\textsubscript{2}= 1.72\,\textOmega\ , and R\textsubscript{2}= 3.69\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.606\,V and 3.31\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.608\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.137E-01\,A
\choice  1.251E-01\,A
\choice  1.376E-01\,A
\CorrectChoice 1.514E-01\,A
\choice  1.665E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.74\,\textOmega\ , R\textsubscript{2}= 1.63\,\textOmega\ , and R\textsubscript{2}= 2.75\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.485\,V and 2.01\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.555\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.114E-01\,A
\CorrectChoice 1.225E-01\,A
\choice  1.348E-01\,A
\choice  1.483E-01\,A
\choice  1.631E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.54\,\textOmega\ , R\textsubscript{2}= 1.15\,\textOmega\ , and R\textsubscript{2}= 2.9\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.446\,V and 3.39\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.744\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.285E-01\,A
\choice  1.414E-01\,A
\choice  1.555E-01\,A
\choice  1.711E-01\,A
\choice  1.882E-01\,A
\end{choices} %%% end choices

\question \includegraphics[width=0.2\textwidth]{KirchhoffLaws-simple.png}The resistances in the figure shown are R\textsubscript{1}= 2.24\,\textOmega\ , R\textsubscript{2}= 1.03\,\textOmega\ , and R\textsubscript{2}= 2.39\,\textOmega\ . V\textsubscript{1} and V\textsubscript{3} are text 0.595\,V and 2.58\,V, respectively. But V\textsubscript{2} is opposite to that shown in the figure, or, equivalently, V\textsubscript{2}=$$-$$0.707\,V. What is the absolute value of the current through R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.834E-01\,A
\CorrectChoice 2.018E-01\,A
\choice  2.220E-01\,A
\choice  2.441E-01\,A
\choice  2.686E-01\,A
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 6

\begin{questions} %%%%%%% begin questions

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=52.2\,V, and  \textepsilon\textsubscript{2}=15.4\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.89\,k\textOmega\  and  R\textsubscript{2}=2.76\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.99\,mA and I\textsubscript{4}=0.693\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  1.726E+00\,mA
\choice  1.898E+00\,mA
\choice  2.088E+00\,mA
\CorrectChoice 2.297E+00\,mA
\choice  2.527E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=40.3\,V, and  \textepsilon\textsubscript{2}=16.8\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.57\,k\textOmega\  and  R\textsubscript{2}=2.25\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.96\,mA and I\textsubscript{4}=0.752\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  1.825E+00\,mA
\choice  2.007E+00\,mA
\CorrectChoice 2.208E+00\,mA
\choice  2.429E+00\,mA
\choice  2.672E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=44.4\,V, and  \textepsilon\textsubscript{2}=16.8\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.58\,k\textOmega\  and  R\textsubscript{2}=1.2\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=8.43\,mA and I\textsubscript{4}=1.46\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 6.970E+00\,mA
\choice  7.667E+00\,mA
\choice  8.434E+00\,mA
\choice  9.277E+00\,mA
\choice  1.020E+01\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=24.9\,V, and  \textepsilon\textsubscript{2}=10.1\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.32\,k\textOmega\  and  R\textsubscript{2}=2.31\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.74\,mA and I\textsubscript{4}=0.444\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  1.725E+00\,mA
\choice  1.898E+00\,mA
\choice  2.087E+00\,mA
\CorrectChoice 2.296E+00\,mA
\choice  2.526E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=43.7\,V, and  \textepsilon\textsubscript{2}=13.1\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.21\,k\textOmega\  and  R\textsubscript{2}=1.72\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.86\,mA and I\textsubscript{4}=0.9\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  2.691E+00\,mA
\CorrectChoice 2.960E+00\,mA
\choice  3.256E+00\,mA
\choice  3.582E+00\,mA
\choice  3.940E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=31.0\,V, and  \textepsilon\textsubscript{2}=10.0\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.22\,k\textOmega\  and  R\textsubscript{2}=1.37\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.32\,mA and I\textsubscript{4}=1.03\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.290E+00\,mA
\choice  2.519E+00\,mA
\choice  2.771E+00\,mA
\choice  3.048E+00\,mA
\choice  3.353E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=20.6\,V, and  \textepsilon\textsubscript{2}=9.53\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.46\,k\textOmega\  and  R\textsubscript{2}=2.55\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=1.5\,mA and I\textsubscript{4}=0.415\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.085E+00\,mA
\choice  1.194E+00\,mA
\choice  1.313E+00\,mA
\choice  1.444E+00\,mA
\choice  1.589E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=29.5\,V, and  \textepsilon\textsubscript{2}=11.0\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.45\,k\textOmega\  and  R\textsubscript{2}=1.96\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.03\,mA and I\textsubscript{4}=0.783\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.247E+00\,mA
\choice  2.472E+00\,mA
\choice  2.719E+00\,mA
\choice  2.991E+00\,mA
\choice  3.290E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=38.9\,V, and  \textepsilon\textsubscript{2}=15.7\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.24\,k\textOmega\  and  R\textsubscript{2}=2.23\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.01\,mA and I\textsubscript{4}=0.86\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  1.955E+00\,mA
\CorrectChoice 2.150E+00\,mA
\choice  2.365E+00\,mA
\choice  2.601E+00\,mA
\choice  2.862E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=36.3\,V, and  \textepsilon\textsubscript{2}=12.9\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.28\,k\textOmega\  and  R\textsubscript{2}=1.58\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.16\,mA and I\textsubscript{4}=1.2\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  2.224E+00\,mA
\choice  2.446E+00\,mA
\choice  2.691E+00\,mA
\CorrectChoice 2.960E+00\,mA
\choice  3.256E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=30.5\,V, and  \textepsilon\textsubscript{2}=12.0\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.79\,k\textOmega\  and  R\textsubscript{2}=1.86\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.07\,mA and I\textsubscript{4}=0.73\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  2.281E+00\,mA
\choice  2.509E+00\,mA
\choice  2.760E+00\,mA
\choice  3.036E+00\,mA
\CorrectChoice 3.340E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=40.6\,V, and  \textepsilon\textsubscript{2}=13.5\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.35\,k\textOmega\  and  R\textsubscript{2}=2.44\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.73\,mA and I\textsubscript{4}=0.78\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  1.332E+00\,mA
\choice  1.465E+00\,mA
\choice  1.612E+00\,mA
\choice  1.773E+00\,mA
\CorrectChoice 1.950E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=13.6\,V, and  \textepsilon\textsubscript{2}=6.53\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.89\,k\textOmega\  and  R\textsubscript{2}=2.12\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=1.11\,mA and I\textsubscript{4}=0.311\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  7.264E-01\,mA
\CorrectChoice 7.990E-01\,mA
\choice  8.789E-01\,mA
\choice  9.668E-01\,mA
\choice  1.063E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=18.2\,V, and  \textepsilon\textsubscript{2}=6.59\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.47\,k\textOmega\  and  R\textsubscript{2}=2.81\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=1.64\,mA and I\textsubscript{4}=0.341\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.299E+00\,mA
\choice  1.429E+00\,mA
\choice  1.572E+00\,mA
\choice  1.729E+00\,mA
\choice  1.902E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=29.3\,V, and  \textepsilon\textsubscript{2}=11.0\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.65\,k\textOmega\  and  R\textsubscript{2}=2.68\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.81\,mA and I\textsubscript{4}=0.525\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  1.717E+00\,mA
\choice  1.888E+00\,mA
\choice  2.077E+00\,mA
\CorrectChoice 2.285E+00\,mA
\choice  2.514E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=49.6\,V, and  \textepsilon\textsubscript{2}=19.3\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.87\,k\textOmega\  and  R\textsubscript{2}=2.81\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.37\,mA and I\textsubscript{4}=1.01\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  3.055E+00\,mA
\CorrectChoice 3.360E+00\,mA
\choice  3.696E+00\,mA
\choice  4.066E+00\,mA
\choice  4.472E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=43.0\,V, and  \textepsilon\textsubscript{2}=13.8\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.97\,k\textOmega\  and  R\textsubscript{2}=1.12\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=6.25\,mA and I\textsubscript{4}=1.82\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  3.661E+00\,mA
\choice  4.027E+00\,mA
\CorrectChoice 4.430E+00\,mA
\choice  4.873E+00\,mA
\choice  5.360E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=24.8\,V, and  \textepsilon\textsubscript{2}=10.3\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.19\,k\textOmega\  and  R\textsubscript{2}=1.6\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.49\,mA and I\textsubscript{4}=0.83\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.660E+00\,mA
\choice  1.826E+00\,mA
\choice  2.009E+00\,mA
\choice  2.209E+00\,mA
\choice  2.430E+00\,mA
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=39.0\,V, and  \textepsilon\textsubscript{2}=15.9\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.4\,k\textOmega\  and  R\textsubscript{2}=2.12\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.58\,mA and I\textsubscript{4}=0.978\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of I\textsubscript{5}?
\begin{choices} %%%%%%% begin choices
\choice  2.150E+00\,mA
\choice  2.365E+00\,mA
\CorrectChoice 2.602E+00\,mA
\choice  2.862E+00\,mA
\choice  3.148E+00\,mA
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 7

\begin{questions} %%%%%%% begin questions

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=57.8\,V, and  \textepsilon\textsubscript{2}=18.5\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.53\,k\textOmega\  and  R\textsubscript{2}=1.8\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=7.15\,mA and I\textsubscript{4}=1.27\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.276E+01\,V
\choice  1.404E+01\,V
\CorrectChoice 1.544E+01\,V
\choice  1.699E+01\,V
\choice  1.869E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=38.9\,V, and  \textepsilon\textsubscript{2}=16.9\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.3\,k\textOmega\  and  R\textsubscript{2}=2.51\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.34\,mA and I\textsubscript{4}=0.955\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  7.031E+00\,V
\CorrectChoice 7.734E+00\,V
\choice  8.507E+00\,V
\choice  9.358E+00\,V
\choice  1.029E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=26.2\,V, and  \textepsilon\textsubscript{2}=11.5\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.13\,k\textOmega\  and  R\textsubscript{2}=1.72\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.11\,mA and I\textsubscript{4}=0.746\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  4.275E+00\,V
\choice  4.703E+00\,V
\CorrectChoice 5.173E+00\,V
\choice  5.691E+00\,V
\choice  6.260E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=28.6\,V, and  \textepsilon\textsubscript{2}=11.1\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.73\,k\textOmega\  and  R\textsubscript{2}=1.95\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.27\,mA and I\textsubscript{4}=0.774\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  6.641E+00\,V
\CorrectChoice 7.305E+00\,V
\choice  8.035E+00\,V
\choice  8.839E+00\,V
\choice  9.723E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=52.7\,V, and  \textepsilon\textsubscript{2}=17.5\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.86\,k\textOmega\  and  R\textsubscript{2}=2.08\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.48\,mA and I\textsubscript{4}=0.988\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 2.064E+01\,V
\choice  2.270E+01\,V
\choice  2.497E+01\,V
\choice  2.747E+01\,V
\choice  3.021E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=16.8\,V, and  \textepsilon\textsubscript{2}=7.15\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.12\,k\textOmega\  and  R\textsubscript{2}=1.51\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=1.95\,mA and I\textsubscript{4}=0.603\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  4.108E+00\,V
\CorrectChoice 4.519E+00\,V
\choice  4.970E+00\,V
\choice  5.468E+00\,V
\choice  6.014E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=26.2\,V, and  \textepsilon\textsubscript{2}=8.29\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.43\,k\textOmega\  and  R\textsubscript{2}=1.16\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.09\,mA and I\textsubscript{4}=1.06\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  6.720E+00\,V
\choice  7.392E+00\,V
\choice  8.131E+00\,V
\choice  8.944E+00\,V
\CorrectChoice 9.838E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=35.5\,V, and  \textepsilon\textsubscript{2}=12.3\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.49\,k\textOmega\  and  R\textsubscript{2}=1.53\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.63\,mA and I\textsubscript{4}=0.972\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.093E+01\,V
\CorrectChoice 1.202E+01\,V
\choice  1.322E+01\,V
\choice  1.454E+01\,V
\choice  1.600E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=49.8\,V, and  \textepsilon\textsubscript{2}=18.1\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.78\,k\textOmega\  and  R\textsubscript{2}=2.63\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.51\,mA and I\textsubscript{4}=0.969\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  7.886E+00\,V
\choice  8.675E+00\,V
\choice  9.542E+00\,V
\choice  1.050E+01\,V
\CorrectChoice 1.155E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=38.8\,V, and  \textepsilon\textsubscript{2}=14.9\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.83\,k\textOmega\  and  R\textsubscript{2}=1.77\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.57\,mA and I\textsubscript{4}=1.19\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.013E+01\,V
\choice  1.115E+01\,V
\choice  1.226E+01\,V
\CorrectChoice 1.349E+01\,V
\choice  1.484E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=30.6\,V, and  \textepsilon\textsubscript{2}=12.0\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.46\,k\textOmega\  and  R\textsubscript{2}=2.77\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=1.97\,mA and I\textsubscript{4}=0.643\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  4.986E+00\,V
\choice  5.484E+00\,V
\choice  6.033E+00\,V
\choice  6.636E+00\,V
\CorrectChoice 7.299E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=39.2\,V, and  \textepsilon\textsubscript{2}=12.6\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.86\,k\textOmega\  and  R\textsubscript{2}=1.89\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.05\,mA and I\textsubscript{4}=0.701\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  8.687E+00\,V
\choice  9.555E+00\,V
\choice  1.051E+01\,V
\choice  1.156E+01\,V
\CorrectChoice 1.272E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=57.0\,V, and  \textepsilon\textsubscript{2}=18.1\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.95\,k\textOmega\  and  R\textsubscript{2}=2.09\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.23\,mA and I\textsubscript{4}=1.04\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  1.921E+01\,V
\CorrectChoice 2.114E+01\,V
\choice  2.325E+01\,V
\choice  2.557E+01\,V
\choice  2.813E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=38.9\,V, and  \textepsilon\textsubscript{2}=14.4\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.33\,k\textOmega\  and  R\textsubscript{2}=1.65\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=5.59\,mA and I\textsubscript{4}=1.07\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  9.142E+00\,V
\choice  1.006E+01\,V
\CorrectChoice 1.106E+01\,V
\choice  1.217E+01\,V
\choice  1.338E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=30.3\,V, and  \textepsilon\textsubscript{2}=8.6\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.81\,k\textOmega\  and  R\textsubscript{2}=2.39\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.38\,mA and I\textsubscript{4}=0.416\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  8.945E+00\,V
\CorrectChoice 9.840E+00\,V
\choice  1.082E+01\,V
\choice  1.191E+01\,V
\choice  1.310E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=21.0\,V, and  \textepsilon\textsubscript{2}=8.72\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.12\,k\textOmega\  and  R\textsubscript{2}=1.15\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.41\,mA and I\textsubscript{4}=0.816\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 5.267E+00\,V
\choice  5.794E+00\,V
\choice  6.373E+00\,V
\choice  7.011E+00\,V
\choice  7.712E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=27.1\,V, and  \textepsilon\textsubscript{2}=8.04\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.94\,k\textOmega\  and  R\textsubscript{2}=1.61\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.87\,mA and I\textsubscript{4}=0.57\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  8.482E+00\,V
\CorrectChoice 9.330E+00\,V
\choice  1.026E+01\,V
\choice  1.129E+01\,V
\choice  1.242E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=16.8\,V, and  \textepsilon\textsubscript{2}=6.85\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.43\,k\textOmega\  and  R\textsubscript{2}=1.24\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.68\,mA and I\textsubscript{4}=0.758\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  3.890E+00\,V
\choice  4.279E+00\,V
\choice  4.707E+00\,V
\CorrectChoice 5.178E+00\,V
\choice  5.695E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=26.8\,V, and  \textepsilon\textsubscript{2}=10.1\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.2\,k\textOmega\  and  R\textsubscript{2}=2.55\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.29\,mA and I\textsubscript{4}=0.464\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{1}?
\begin{choices} %%%%%%% begin choices
\choice  3.436E+00\,V
\choice  3.779E+00\,V
\choice  4.157E+00\,V
\choice  4.573E+00\,V
\CorrectChoice 5.030E+00\,V
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 8

\begin{questions} %%%%%%% begin questions

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=60.7\,V, and  \textepsilon\textsubscript{2}=16.7\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.72\,k\textOmega\  and  R\textsubscript{2}=2.33\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.65\,mA and I\textsubscript{4}=0.946\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.981E+01\,V
\CorrectChoice 2.180E+01\,V
\choice  2.398E+01\,V
\choice  2.637E+01\,V
\choice  2.901E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=36.7\,V, and  \textepsilon\textsubscript{2}=12.1\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.52\,k\textOmega\  and  R\textsubscript{2}=1.22\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.14\,mA and I\textsubscript{4}=1.19\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  7.805E+00\,V
\choice  8.586E+00\,V
\choice  9.444E+00\,V
\choice  1.039E+01\,V
\CorrectChoice 1.143E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=21.6\,V, and  \textepsilon\textsubscript{2}=8.59\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.97\,k\textOmega\  and  R\textsubscript{2}=1.69\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.2\,mA and I\textsubscript{4}=0.749\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  6.064E+00\,V
\choice  6.670E+00\,V
\CorrectChoice 7.337E+00\,V
\choice  8.071E+00\,V
\choice  8.878E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=14.3\,V, and  \textepsilon\textsubscript{2}=5.6\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.31\,k\textOmega\  and  R\textsubscript{2}=2.39\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=1.12\,mA and I\textsubscript{4}=0.284\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  3.416E+00\,V
\choice  3.757E+00\,V
\choice  4.133E+00\,V
\CorrectChoice 4.546E+00\,V
\choice  5.001E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=58.5\,V, and  \textepsilon\textsubscript{2}=17.3\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.06\,k\textOmega\  and  R\textsubscript{2}=1.88\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=5.25\,mA and I\textsubscript{4}=1.25\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.981E+01\,V
\CorrectChoice 2.179E+01\,V
\choice  2.397E+01\,V
\choice  2.637E+01\,V
\choice  2.901E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=18.6\,V, and  \textepsilon\textsubscript{2}=5.63\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.9\,k\textOmega\  and  R\textsubscript{2}=1.1\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.41\,mA and I\textsubscript{4}=0.614\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  4.342E+00\,V
\choice  4.776E+00\,V
\choice  5.254E+00\,V
\CorrectChoice 5.779E+00\,V
\choice  6.357E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=42.2\,V, and  \textepsilon\textsubscript{2}=17.8\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=4.2\,k\textOmega\  and  R\textsubscript{2}=2.83\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.5\,mA and I\textsubscript{4}=0.749\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.056E+01\,V
\choice  1.161E+01\,V
\choice  1.277E+01\,V
\CorrectChoice 1.405E+01\,V
\choice  1.545E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=40.9\,V, and  \textepsilon\textsubscript{2}=16.1\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.55\,k\textOmega\  and  R\textsubscript{2}=1.55\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=6.11\,mA and I\textsubscript{4}=1.06\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  8.754E+00\,V
\choice  9.630E+00\,V
\choice  1.059E+01\,V
\choice  1.165E+01\,V
\CorrectChoice 1.282E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=27.9\,V, and  \textepsilon\textsubscript{2}=11.1\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.82\,k\textOmega\  and  R\textsubscript{2}=2.25\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.1\,mA and I\textsubscript{4}=0.676\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  8.334E+00\,V
\choice  9.167E+00\,V
\CorrectChoice 1.008E+01\,V
\choice  1.109E+01\,V
\choice  1.220E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=39.4\,V, and  \textepsilon\textsubscript{2}=12.2\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.84\,k\textOmega\  and  R\textsubscript{2}=2.01\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.71\,mA and I\textsubscript{4}=0.669\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  8.825E+00\,V
\choice  9.708E+00\,V
\choice  1.068E+01\,V
\choice  1.175E+01\,V
\CorrectChoice 1.292E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=46.1\,V, and  \textepsilon\textsubscript{2}=16.2\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.17\,k\textOmega\  and  R\textsubscript{2}=2.06\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=4.97\,mA and I\textsubscript{4}=1.07\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.309E+01\,V
\choice  1.440E+01\,V
\CorrectChoice 1.584E+01\,V
\choice  1.742E+01\,V
\choice  1.917E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=45.3\,V, and  \textepsilon\textsubscript{2}=13.3\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.82\,k\textOmega\  and  R\textsubscript{2}=1.5\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=6.17\,mA and I\textsubscript{4}=1.11\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.177E+01\,V
\choice  1.295E+01\,V
\choice  1.424E+01\,V
\CorrectChoice 1.567E+01\,V
\choice  1.723E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=36.7\,V, and  \textepsilon\textsubscript{2}=13.6\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.86\,k\textOmega\  and  R\textsubscript{2}=2.2\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.02\,mA and I\textsubscript{4}=0.854\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.380E+01\,V
\choice  1.518E+01\,V
\choice  1.670E+01\,V
\choice  1.837E+01\,V
\choice  2.020E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=67.2\,V, and  \textepsilon\textsubscript{2}=18.7\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.45\,k\textOmega\  and  R\textsubscript{2}=1.2\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=9.49\,mA and I\textsubscript{4}=1.81\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  1.906E+01\,V
\CorrectChoice 2.097E+01\,V
\choice  2.306E+01\,V
\choice  2.537E+01\,V
\choice  2.790E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=34.7\,V, and  \textepsilon\textsubscript{2}=13.9\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.68\,k\textOmega\  and  R\textsubscript{2}=1.55\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=5.68\,mA and I\textsubscript{4}=0.933\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  9.286E+00\,V
\choice  1.021E+01\,V
\choice  1.124E+01\,V
\CorrectChoice 1.236E+01\,V
\choice  1.360E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=40.7\,V, and  \textepsilon\textsubscript{2}=12.3\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.5\,k\textOmega\  and  R\textsubscript{2}=1.94\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=3.42\,mA and I\textsubscript{4}=0.932\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.440E+01\,V
\choice  1.584E+01\,V
\choice  1.742E+01\,V
\choice  1.916E+01\,V
\choice  2.108E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=54.9\,V, and  \textepsilon\textsubscript{2}=19.8\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=3.93\,k\textOmega\  and  R\textsubscript{2}=1.31\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=9.18\,mA and I\textsubscript{4}=1.83\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.779E+01\,V
\choice  1.957E+01\,V
\choice  2.153E+01\,V
\choice  2.368E+01\,V
\choice  2.605E+01\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=17.3\,V, and  \textepsilon\textsubscript{2}=6.46\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=2.54\,k\textOmega\  and  R\textsubscript{2}=2.79\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=1.1\,mA and I\textsubscript{4}=0.281\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  6.488E+00\,V
\CorrectChoice 7.137E+00\,V
\choice  7.850E+00\,V
\choice  8.635E+00\,V
\choice  9.499E+00\,V
\end{choices} %%% end choices

\question \includegraphics[width=0.18\textwidth]{Kirchhoff-loop-w-external-current.png} Two sources of emf \textepsilon\textsubscript{1}=24.4\,V, and  \textepsilon\textsubscript{2}=6.73\,V are oriented as shown in the circuit. The resistances are R\textsubscript{1}=5.7\,k\textOmega\  and  R\textsubscript{2}=1.95\,k\textOmega\ .  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I\textsubscript{3}=2.36\,mA and I\textsubscript{4}=0.418\,mA enter and leave near R\textsubscript{2}, while the current I\textsubscript{5} exits near R\textsubscript{1}.What is the magnitude (absolute value) of voltage drop across R\textsubscript{2}?
\begin{choices} %%%%%%% begin choices
\choice  5.418E+00\,V
\choice  5.960E+00\,V
\choice  6.556E+00\,V
\choice  7.212E+00\,V
\CorrectChoice 7.933E+00\,V
\end{choices} %%% end choices
%\pagebreak
%\end{choices}%??????????????
\end{questions}%%%%%%%% end questions

\subsection{}%%%% subsection 9

\begin{questions} %%%%%%% begin questions

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  379\,V.  If the combined external and internal resistance is 158\,\textOmega\ and the capacitance is  95\,mF, how long will it take for the capacitor's voltage to reach 234.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  1.084E+01\,s
\choice  1.192E+01\,s
\choice  1.311E+01\,s
\CorrectChoice 1.442E+01\,s
\choice  1.586E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  319\,V.  If the combined external and internal resistance is 231\,\textOmega\ and the capacitance is  64\,mF, how long will it take for the capacitor's voltage to reach 175.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  9.718E+00\,s
\choice  1.069E+01\,s
\CorrectChoice 1.176E+01\,s
\choice  1.293E+01\,s
\choice  1.423E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  558\,V.  If the combined external and internal resistance is 198\,\textOmega\ and the capacitance is  80\,mF, how long will it take for the capacitor's voltage to reach 345.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  1.146E+01\,s
\choice  1.261E+01\,s
\choice  1.387E+01\,s
\CorrectChoice 1.525E+01\,s
\choice  1.678E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  213\,V.  If the combined external and internal resistance is 118\,\textOmega\ and the capacitance is  61\,mF, how long will it take for the capacitor's voltage to reach 142.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  5.401E+00\,s
\choice  5.941E+00\,s
\choice  6.535E+00\,s
\choice  7.189E+00\,s
\CorrectChoice 7.908E+00\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  543\,V.  If the combined external and internal resistance is 201\,\textOmega\ and the capacitance is  82\,mF, how long will it take for the capacitor's voltage to reach 281.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  9.024E+00\,s
\choice  9.927E+00\,s
\choice  1.092E+01\,s
\CorrectChoice 1.201E+01\,s
\choice  1.321E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  554\,V.  If the combined external and internal resistance is 228\,\textOmega\ and the capacitance is  93\,mF, how long will it take for the capacitor's voltage to reach 450.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  3.224E+01\,s
\CorrectChoice 3.547E+01\,s
\choice  3.902E+01\,s
\choice  4.292E+01\,s
\choice  4.721E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  569\,V.  If the combined external and internal resistance is 137\,\textOmega\ and the capacitance is  76\,mF, how long will it take for the capacitor's voltage to reach 419.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  1.043E+01\,s
\choice  1.147E+01\,s
\choice  1.262E+01\,s
\CorrectChoice 1.388E+01\,s
\choice  1.527E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  505\,V.  If the combined external and internal resistance is 189\,\textOmega\ and the capacitance is  74\,mF, how long will it take for the capacitor's voltage to reach 374.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  1.560E+01\,s
\choice  1.716E+01\,s
\CorrectChoice 1.887E+01\,s
\choice  2.076E+01\,s
\choice  2.284E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  130\,V.  If the combined external and internal resistance is 109\,\textOmega\ and the capacitance is  59\,mF, how long will it take for the capacitor's voltage to reach 69.9\,V?
\begin{choices} %%%%%%% begin choices
\choice  3.728E+00\,s
\choice  4.101E+00\,s
\choice  4.511E+00\,s
\CorrectChoice 4.962E+00\,s
\choice  5.458E+00\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  190\,V.  If the combined external and internal resistance is 255\,\textOmega\ and the capacitance is  54\,mF, how long will it take for the capacitor's voltage to reach 101.0\,V?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.044E+01\,s
\choice  1.149E+01\,s
\choice  1.264E+01\,s
\choice  1.390E+01\,s
\choice  1.529E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  466\,V.  If the combined external and internal resistance is 123\,\textOmega\ and the capacitance is  76\,mF, how long will it take for the capacitor's voltage to reach 331.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  9.571E+00\,s
\choice  1.053E+01\,s
\CorrectChoice 1.158E+01\,s
\choice  1.274E+01\,s
\choice  1.401E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  598\,V.  If the combined external and internal resistance is 170\,\textOmega\ and the capacitance is  73\,mF, how long will it take for the capacitor's voltage to reach 436.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  1.218E+01\,s
\choice  1.339E+01\,s
\choice  1.473E+01\,s
\CorrectChoice 1.621E+01\,s
\choice  1.783E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  301\,V.  If the combined external and internal resistance is 245\,\textOmega\ and the capacitance is  63\,mF, how long will it take for the capacitor's voltage to reach 192.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  1.296E+01\,s
\choice  1.425E+01\,s
\CorrectChoice 1.568E+01\,s
\choice  1.725E+01\,s
\choice  1.897E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  327\,V.  If the combined external and internal resistance is 204\,\textOmega\ and the capacitance is  68\,mF, how long will it take for the capacitor's voltage to reach 218.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  1.385E+01\,s
\CorrectChoice 1.524E+01\,s
\choice  1.676E+01\,s
\choice  1.844E+01\,s
\choice  2.028E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  129\,V.  If the combined external and internal resistance is 169\,\textOmega\ and the capacitance is  76\,mF, how long will it take for the capacitor's voltage to reach 109.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  2.177E+01\,s
\CorrectChoice 2.394E+01\,s
\choice  2.634E+01\,s
\choice  2.897E+01\,s
\choice  3.187E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  467\,V.  If the combined external and internal resistance is 172\,\textOmega\ and the capacitance is  74\,mF, how long will it take for the capacitor's voltage to reach 258.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  7.688E+00\,s
\choice  8.457E+00\,s
\choice  9.303E+00\,s
\CorrectChoice 1.023E+01\,s
\choice  1.126E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  433\,V.  If the combined external and internal resistance is 275\,\textOmega\ and the capacitance is  61\,mF, how long will it take for the capacitor's voltage to reach 223.0\,V?
\begin{choices} %%%%%%% begin choices
\choice  1.104E+01\,s
\CorrectChoice 1.214E+01\,s
\choice  1.335E+01\,s
\choice  1.469E+01\,s
\choice  1.616E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  351\,V.  If the combined external and internal resistance is 148\,\textOmega\ and the capacitance is  60\,mF, how long will it take for the capacitor's voltage to reach 227.0\,V?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 9.240E+00\,s
\choice  1.016E+01\,s
\choice  1.118E+01\,s
\choice  1.230E+01\,s
\choice  1.353E+01\,s
\end{choices} %%% end choices

\question \includegraphics[width=0.16\textwidth]{RC-switch.png}In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of  439\,V.  If the combined external and internal resistance is 221\,\textOmega\ and the capacitance is  54\,mF, how long will it take for the capacitor's voltage to reach 350.0\,V?
\begin{choices} %%%%%%% begin choices
\CorrectChoice 1.905E+01\,s
\choice  2.095E+01\,s
\choice  2.304E+01\,s
\choice  2.535E+01\,s
\choice  2.788E+01\,s
\end{choices} %%% end choices
\end{questions}
\pagebreak