Alternating Currents — Formula Sheet

V = V_m \cos \omega t

I = I_m \cos \omega t

V_{rms} = \frac{V_m}{\sqrt{2}}, I_{rms} = \frac{I_m}{\sqrt{2}}

X_C = \frac{1}{\omega C} = \frac{1}{2\pi \nu C}

X_L = \omega L = 2\pi \nu L

I_{rms} = \frac{V_{rms}}{X_C}

I_{rms} = \frac{V_{rms}}{X_L}

Z = \sqrt{R^2 + (X_L - X_C)^2}

I_{rms} = \frac{V_{rms}}{Z}

\tan \phi = \frac{X_L - X_C}{R}

\nu_r = \frac{1}{2\pi \sqrt{LC}}

P_{av} = V_{rms} I_{rms} \cos \phi

\omega_0 = \frac{1}{\sqrt{LC}}

In a pure resistor, voltage and current are in phase (phase difference = 0).

In pure resistor, power factor = 1; in pure L or C, power factor = 0.

Ohm’s law applies

$ I_m = V_m / R $.

Capacitive reactance $ X_C = 1/(\omega C) $ and inductive reactance $ X_L = \omega L $ oppose AC flow like resistance but depend on frequency.