# OpenStax University Physics/E&M/Current and Resistance

## Chapter 9

#### Current and Resistance

Current (1A=1C/s) ${\displaystyle I=dQ/dt=nqv_{d}A}$ where ${\displaystyle (n,q,v_{d})=}$ (density, charge, drift velocity) of the carriers.

▭ ${\displaystyle I=JA\rightarrow \int {\vec {J}}\cdot d{\vec {A}}}$ , ${\displaystyle A}$ is the perpendicular area, and ${\displaystyle J}$ is current density. ${\displaystyle {\vec {E}}=\rho {\vec {J}}}$ is electric field, where ${\displaystyle \rho }$ is resistivity.
▭ Resistivity varies with temperature as ${\displaystyle \rho =\rho _{0}\left[1+\alpha (T-T_{0})\right]}$. Similarily, ${\displaystyle R=R_{0}\left[1+\alpha \Delta T\right]}$ where ${\displaystyle R=\rho {\tfrac {L}{A}}}$ is resistance (Ω)
▭ Ohm's law ${\displaystyle V=IR}$ ▭  Power ${\displaystyle =P=IV=I^{2}R=V^{2}/R}$

#### For quiz at QB/d_cp2.9

Electric current: 1 Amp (A) = 1 Coulomb (C) per second (s)

Current=${\displaystyle I=dQ/dt=nqv_{d}A}$, where

${\displaystyle (n,q,v_{d},A)}$ = (density, charge, speed, Area)

${\displaystyle I=\int {\vec {J}}\cdot d{\vec {A}}}$ where ${\displaystyle {\vec {J}}=nq{\vec {v}}_{d}}$ =current density.

${\displaystyle {\vec {E}}=\rho {\vec {J}}}$ = electric field where ${\displaystyle \rho }$ = resistivity

${\displaystyle \rho =\rho _{0}\left[1+\alpha (T-T_{0})\right]}$, and ${\displaystyle R=R_{0}\left[1+\alpha \Delta T\right]}$,

where ${\displaystyle R=\rho {\tfrac {L}{A}}}$ is resistance

${\displaystyle V=IR}$ and Power=${\displaystyle P=IV=I^{2}R=V^{2}/R}$