Electromagnetic Induction

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

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

$\varepsilon = Bvl \qquad \text{(Motional EMF, } v \perp B \perp l\text{)} \qquad [\text{M L}^2\text{ T}^{-3}\text{ A}^{-1}]$

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

$\varepsilon = -L\frac{dI}{dt} \qquad L = \frac{\mu_0 N^2 A}{l} = \mu_0 n^2 Al \qquad [\text{M L}^2\text{ T}^{-2}\text{ A}^{-2}] \qquad \text{(Henry, H)}$

$\varepsilon_2 = -M\frac{dI_1}{dt} \qquad M = \mu_0 n_1 n_2 Al \qquad [\text{M L}^2\text{ T}^{-2}\text{ A}^{-2}]$

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

AC Fundamentals

$V_\text{rms} = \frac{V_0}{\sqrt{2}} = 0.707\,V_0 \qquad V_\text{mean} = \frac{2V_0}{\pi} = 0.637\,V_0$

$X_L = \omega L = 2\pi f L \qquad X_C = \frac{1}{\omega C} = \frac{1}{2\pi f C} \qquad [\Omega]$

$Z = \sqrt{R^2 + (X_L - X_C)^2} \qquad \tan\phi = \frac{X_L - X_C}{R} \qquad [\text{M L}^2\text{ T}^{-3}\text{ A}^{-2}]$

$f_0 = \frac{1}{2\pi\sqrt{LC}} \qquad \text{(Resonant frequency, Hz)}$

$P = V_\text{rms}\,I_\text{rms}\cos\phi \qquad \cos\phi = \frac{R}{Z} \qquad \text{(Power factor)}$

Transformer

$\frac{V_s}{V_p} = \frac{N_s}{N_p} = \frac{I_p}{I_s} \qquad \eta = \frac{P_\text{output}}{P_\text{input}} = \frac{V_s I_s}{V_p I_p}$