Mastering Alternating Current: Formulas, Traps & Exam Strategy | ExamiFly

Over a complete cycle, energy stored in the electric field (capacitor) or magnetic field (inductor) during one half-cycle is returned entirely back to the source in the next half-cycle. Mathematically, the phase angle between voltage and current is $\phi = \frac{\pi}{2}$, rendering the power factor $\cos\phi = 0$, so $P_{\text{avg}} = V_{\text{rms}} I_{\text{rms}} \cos\left(\frac{\pi}{2}\right) = 0$.

Wattless current is the component of AC current $I_{\text{rms}} \sin \phi$ that is $\frac{\pi}{2}$ out of phase with the voltage. Because its phase difference relative to voltage is $90^\circ$, its average power dissipation over a cycle is $P = V_{\text{rms}} (I_{\text{rms}} \sin \phi) \cos(90^\circ) = 0$. It occurs in purely inductive, purely capacitive, or ideal zero-resistance $LC$ circuits.

First, calculate individual reactances $X_L = \omega L$ and $X_C = \frac{1}{\omega C}$. Draw a phasor diagram with current on the reference axis. Calculate net impedance $Z = \sqrt{R^2 + (X_L - X_C)^2}$ and phase angle $\tan \phi = \frac{X_L - X_C}{R}$. Always use $V_{\text{rms}}$ values for circuit calculations unless peak values $V_0$ are explicitly requested.