Passive sign convention

Introduction

This is the first of eight lessons in Electric Circuit Analysis. This course is a pre-requisite course to most Level 2 courses in this school. As such it is imperative that a student gains insight into the methods and theory introduced and explained in this course.

There are plenty of worked examples and an exercises at the end of the lesson. Work through the exercise on your own, and only then you can compare your results with the solutions given on a linked Sub-page.

Lesson Preview

This Lesson is about Passive sign convention. This Lesson introduces a student to Circuit Components which will be encountered in Electric Circuit Analysis.The student/User is expected to understand the following at the end of the lesson

• Active Components
• Passive Components
• Passive Sign Convention
• Guidelines for Passive sign Convention

Remember that Open Learning is all about you. You can set your own pace in this course and you will be helped to evaluate your self along the way.

Part 1: Electric Circuit

An electric circuit is a connection of components (Voltage/Current sources; Resistors; Inductors & Capacitors ) such that there is some power supplied and dissipated.This means that if you connect a resistor to a battery using conductor wires, then you have created an electrical circuit.

Figure 1.1: Active components

Active Components:

All components that Supply electric power are called Active components. the following picture shows circuit symbols used to depict a Voltage Source and a Current Source. Notice that the components show a general orientation of where the direction of conventional current.

Figure 1.2 and 1.3: Passive components

Passive Components:

All components that Absorb or Dissipate electric power are called Passive components. the following picture shows circuit symbols used to depict a Resistor. Figure 1.2 is generally the preferred symbol of a resistor and will be used throughout this course.
Please note that capacitors and inductors are beyond the scope of this course as they introduce complex resistance where real and reactive power complexities come in.

Part 2: Passive Sign Convention

The concept of passive sign convention comes directly from the definition of voltage.

Voltage is a difference of charge between two places in space. Not an absolute quality. You could think of it in terms of depth and height.

Something has an elevation or height only with respect to something else such as sea level. Likewise depth, something is only deep compared to some level, again such as sea level.

There is one difference between depth and height. We consider height to be positive and depth to be negative. One of the reasons why we do this is because we usually deal more with height then depth, and we wish to minimize the amount of subtraction that we perform.

The passive sign convention is the same concept. It is an algorithm to decide what is adding potential energy to the system and what is taking it away.

Here are some basic ground rules:

• All resistors are either positive or negative uniformly. Which means that if you consider one resistor to be positive (which is the common case) then all the resistors are positive.

• At least one source is the opposite sign of the resistors. If only one is present then that is the one.

• Always start by making your loop.

Why do we use this Passive sign convention?

One of the most important ideas of an electric circuit is that there is a source of power and a dissapator of power. As circuit connections become more intricate this basic idea becomes more blurred. In some cases there are more than one power supply at different circuit locations, such that simple addition of their power magnitudes is not possible. We need to know which direction power supply and consumption is. The next examples will illustrate this.

Part 3

Figure 1.4: Passive Sign Convention scenario 1

Here is what we can deduce from figure 1.4. Points A & B are physical end points of Resistor R. A is more positive than B thus electrical charge at point A is higher than the electrical charge at point B. This creates electric potential.

Explanation of Part 3

This simply means that an electrical charge Q at point A will easily move to point B if a path is set up (i.e Points A and B connected by a conductor.) Thus the resistor loses electric potential and the electric charge is evenly spread. If electric charge is forced to point A from point B, then point A gains electric potential.

Thus for -V ; -I and +V ; +I cases The Electrical charge will lose electric potential by effectively moving from high electric potential to low electric potential.The resistor has effectively absorbed power from the electric charge to enable it to move to a low potential point. Hence, the resistor, a passive component, absorbs power in this case.

Thus for -V ; +I and -V ; +I cases the electrical charge will gain electric potential by effectively moving from low electric potential to high electric potential. The resistor has effectively powered the electric charge to a high potential point. Hence, the resistor, a passive component, supplies power in this case.

It is therefore important to understand the flow and direction of conventional current in order to correctly apply passive sign convention. This becomes important later on in the course when we treat Mesh and Nodal Analysis.

The following examples are related to the lesson. The answers to the exercise questions are given as a link to a sub page. Attempt the problems before viewing the answers.

Example 1.1

Figure 1.5: Example 1.1

Figure 1.5 shows a simple resistor with the following parameters.
V_R = 9Volts , I_R = 3A
Find P_Total and Determine if this resistor is supplying power or dissipating it.

Solution:

.

Since power is positive this resistor is absorbing power.

Example 1.2

Figure 1.6: Example 1.2

Figure 1.6 shows a simple resistor with the following parameters:
V_R = − 6Volts , I_R = 3A
Find P_Total and Determine if this resistor is supplying power or dissipating it.

Solution:

.

Since power is negative this resistor is supplying power.

Example 1.3

Figure 1.7: Example 1.3

Figure 1.7 shows a simple resistor with the following parameters.
V_R = − 6Volts , I_R = − 3A
Find P_Total and Determine if this Resistor is Supplying power or Dissipating it.

Solution:

.

Since Power is Positive thus this Resistor is Dissipating power. Suprised?

Well let's look at figure 1.7 again. If Voltage is Given as -6V it means that despite the given sign convention of the resistor, Point A is More Positive Compared to point B.

The Current is shown entering Point A but by the fact that current is -3A it means that the current is infact leaving at point A. Thus The resistor is effectively Dissipating power. Refer to part 3 & 4 of this lesson.

Try the exercises.

Exercises

1. From Figure 1.5 given current is 4 Amps and the Voltage across the resistor is 4 Volts how much power is being produced or consumed?
2. From Figure 1.5 given current is 1.5 milli-Amps and the Voltage across the resistor is -1.5 Volts how much power is being produced or consumed?
3. From Figure 1.7 given current is 15 Amps and the Voltage across the resistor is 15 Volts how much power is being produced or consumed?
4. From Figure 1.5 given current is -20 milli-Amps and the Voltage across the resistor is -1.5 Volts how much power is being produced or consumed?

• Answers to Exercise 1

Completion list

Once you finish your Exercises you can post your score here! To post your score just e-mail your course co-ordinator your name and score *Click Here.

• 1. Ozzimotosan -- 75% & Corrected
  2. Doldham -- 75% & Corrected
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