A series LCR circuit has $R=10$ Ω, $L=0.5$ H, $C=100$ µF and is driven at $f=50$ Hz by a 100 V rms source. Calculate the magnitude $|Z|$ of the impedance and the phase angle $varphi$ between the source voltage and current.

Step-by-step solution

1. Calculate angular frequency: $\omega =2\pi f=2\pi \times 50=314.16$ rad s⁻¹.
2. Compute inductive reactance: $X_L=\omega L=314.16\times 0.5=157.08$ Ω.
3. Compute capacitive reactance: $X_C=\frac{1}{\omega C}=\frac{1}{314.16\times 100\times 10^{-6}}=31.83$ Ω.
4. Find net reactance: $X=X_L-X_C=157.08-31.83=125.25$ Ω.
5. Compute impedance magnitude: $|Z|=\sqrt{R^2+X^2}=\sqrt{10^2+125.25^2}=125.6$ Ω.
6. Find phase angle: $\phi =\arctan \frac{X}{R}=\arctan \frac{125.25}{10}=85.4^{\circ }$.

Concept tested: Series LCR impedance

Published 5 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked