Electric current: 1 Amp (A) = 1 Coulomb (C) per second (s)
Current= I = d Q / d t = n q v d A {\displaystyle I=dQ/dt=nqv_{d}A} , where
( n , q , v d , A ) {\displaystyle (n,q,v_{d},A)} = (density, charge, speed, Area)
I = ∫ J → ⋅ d A → {\displaystyle I=\int {\vec {J}}\cdot d{\vec {A}}} where J → = n q v → d {\displaystyle {\vec {J}}=nq{\vec {v}}_{d}} =current density.
E → = ρ J → {\displaystyle {\vec {E}}=\rho {\vec {J}}} = electric field where ρ {\displaystyle \rho } = resistivity
ρ = ρ 0 [ 1 + α ( T − T 0 ) ] {\displaystyle \rho =\rho _{0}\left[1+\alpha (T-T_{0})\right]} , and R = R 0 [ 1 + α Δ T ] {\displaystyle R=R_{0}\left[1+\alpha \Delta T\right]} ,
where R = ρ L A {\displaystyle R=\rho {\tfrac {L}{A}}} is resistance
V = I R {\displaystyle V=IR} and Power= P = I V = I 2 R = V 2 / R {\displaystyle P=IV=I^{2}R=V^{2}/R}
V t e r m i n a l = ε − I r e q {\displaystyle V_{terminal}=\varepsilon -Ir_{eq}} where r e q {\displaystyle r_{eq}} =internal resistance and ε {\displaystyle \varepsilon } =emf.
R s e r i e s = ∑ i = 1 N R i {\displaystyle R_{series}=\sum _{i=1}^{N}R_{i}} and R p a r a l l e l − 1 = ∑ i = 1 N R i − 1 {\displaystyle R_{parallel}^{-1}=\sum _{i=1}^{N}R_{i}^{-1}}
Kirchhoff Junction: ∑ I i n = ∑ I o u t {\displaystyle \sum I_{in}=\sum I_{out}} and Loop: ∑ V = 0 {\displaystyle \sum V=0}
Charging an RC (resistor-capacitor) circuit: q ( t ) = Q ( 1 − e t / τ ) {\displaystyle q(t)=Q\left(1-e^{t/\tau }\right)} and I = I 0 e − t / τ {\displaystyle I=I_{0}e^{-t/\tau }} where τ = R C {\displaystyle \tau =RC} is RC time, Q = ε C {\displaystyle Q=\varepsilon C} and I 0 = ε / R {\displaystyle I_{0}=\varepsilon /R} .
Discharging an RC circuit: q ( t ) = Q e − t / τ {\displaystyle q(t)=Qe^{-t/\tau }} and I ( t ) = − Q R C e − t / τ {\displaystyle I(t)=-{\tfrac {Q}{RC}}e^{-t/\tau }}