OpenStax University Physics/E&M/Current and Resistance

${\mathcal {E}}\&{\mathcal {M}}$ (Vol. 2): 5:Electric Charges and Fields 6:Gauss's Law 7:Electric Potential 8:Capacitance 9:Current and Resistance 10:Direct-Current Circuits 11:Magnetic Forces and Fields 12:Sources of Magnetic Fields 13:Electromagnetic Induction 14:Inductance 15:Alternating-Current Circuits 16:Electromagnetic Waves

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

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