Electromagnetic Induction

$\Phi = BA\cos\theta \quad [M\,L^2\,T^{-2}\,A^{-1}] \quad \text{Weber (Wb)}$

$\text{EMF} = -\frac{d\Phi}{dt} = -N\frac{d\Phi}{dt} \quad [M\,L^2\,T^{-3}\,A^{-1}] \quad \text{Volt (V)}$

$\varepsilon = Bvl \quad \text{(Motional EMF, mutually perpendicular } v,B,l\text{)}$

$\varepsilon = NBA\omega\sin(\omega t), \quad \varepsilon_0 = NBA\omega \quad \text{(Rotating coil)}$

$\varepsilon = -L\frac{dI}{dt} \quad [M\,L^2\,T^{-2}\,A^{-2}] \quad \text{Henry (H)}$

$L = \mu_0 n^2 Al = \frac{\mu_0 N^2 A}{l} \quad \text{(Solenoid self-inductance)}$

$\varepsilon_2 = -M\frac{dI_1}{dt}, \quad M = \mu_0 n_1 n_2 Al \quad \text{(Mutual inductance)}$

$U = \frac{1}{2}LI^2 \quad [M\,L^2\,T^{-2}] \quad \text{Joule (J)}$

$q = \frac{N\Delta\Phi}{R} \quad \text{(Induced charge — independent of rate)}$

Alternating Current

$V_\text{rms} = \frac{V_0}{\sqrt{2}},\quad V_\text{mean} = \frac{2V_0}{\pi}$

$X_L = \omega L = 2\pi fL \quad [\Omega] \quad \text{(Inductive reactance)}$

$X_C = \frac{1}{\omega C} = \frac{1}{2\pi fC} \quad [\Omega] \quad \text{(Capacitive reactance)}$

$Z = \sqrt{R^2 + (X_L - X_C)^2} \quad [\Omega] \quad \tan\phi = \frac{X_L - X_C}{R}$

$f_0 = \frac{1}{2\pi\sqrt{LC}}, \quad Z_\text{res} = R, \quad I_\text{max} = \frac{V_\text{rms}}{R}$

$P = V_\text{rms}\,I_\text{rms}\cos\phi = I_\text{rms}^2 R, \quad \cos\phi = \frac{R}{Z}$

$Q\text{-factor} = \frac{\omega_0 L}{R} = \frac{1}{R}\sqrt{\frac{L}{C}}$

Transformer

$\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s} \quad \eta = \frac{P_\text{out}}{P_\text{in}} = \frac{V_s I_s}{V_p I_p}$