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

## Chapter 9

#### Current and Resistance

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

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

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

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

Current=$I=dQ/dt=nqv_{d}A$ , where

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

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

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

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

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

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