A series RLC circuit has R=20\,$\Omega$, L=0.6\,$\text{H}$, C=80\,$\mu \text{F}$ and is driven at f=100\,$\text{Hz}$ by a 200\,$\text{V rms}$ source. Calculate the magnitude |Z| of the impedance and the phase angle $\phi$ (in degrees) between the source voltage and current.

Step-by-step solution

1. Compute the inductive reactance X_L=2$\pi$ f L.\nX_L=2$\pi \times 100\times 0$.6=376.99\,$\Omega$.
2. Compute the capacitive reactance X_C=1/(2$\pi$ f C).\nX_C=1/(2$\pi \times 100\times 80\times 10^{-6}$)$\approx 19$.90\,$\Omega$.
3. Find the net reactance X=X_L-X_C=376.99-19.90=357.09\,$\Omega$.
4. Calculate the impedance magnitude |Z|=$\sqrt{R^2+X^2}$.\n|Z|=$\sqrt{20^2+357.09^2}\approx 357$.5\,$\Omega$.
5. Determine the phase angle $\phi =\arctan \frac{X}{R}$.$\text{n}\phi =\arctan \frac{357.09}{20}\approx 86$.8$°$.
6. State that the positive angle means voltage leads current.

Concept tested: Impedance of RLC series circuit

Published 12 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked