OpenStax University Physics/E&M/Current and Resistance

Chapter 9

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

▭ $I = J A \to \int \vec{J} \cdot d \vec{A}$ , $A$ is the perpendicular area, and $J$ is current density. $\vec{E} = ρ \vec{J}$ is electric field, where $ρ$ is resistivity.
▭ Resistivity varies with temperature as $ρ = ρ_{0} [1 + α (T - T_{0})]$ . Similarily, $R = R_{0} [1 + α Δ T]$ where $R = ρ \frac{L}{A}$ is resistance (Ω)
▭ Ohm's law $V = I R$ ▭ Power $= P = I V = I^{2} R = V^{2} / R$

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

Current= $I = d Q / d t = n q v_{d} A$ , where

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

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

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

$ρ = ρ_{0} [1 + α (T - T_{0})]$ , and $R = R_{0} [1 + α Δ T]$ ,

where $R = ρ \frac{L}{A}$ is resistance

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