A series RLC circuit has $R=35$ Ω, $L=0.45$ H, $C=60,mu$F and is driven by a 250 V rms source at 80 Hz. Find the magnitude of the impedance $|Z|$ and the phase angle $varphi$ (in degrees) between the source voltage and current.

Step-by-step solution

1. Compute angular frequency: $\omega =2\pi f=2\pi \times 80=502.7$ rad/s.
2. Inductive reactance: $X_L=\omega L=502.7\times 0.45=226.2$ Ω.
3. Capacitive reactance: $X_C=1/(\omega C)=1/(502.7\times 60\times 10^{-6})=33.2$ Ω.
4. Net reactance: $X=X_L-X_C=226.2-33.2=193.0$ Ω (inductive).
5. Impedance magnitude: $|Z|=\sqrt{R^2+X^2}=\sqrt{35^2+193^2}=196$ Ω.
6. Phase angle: $\phi ={\tan }^{-1}!\left(\frac{X}{R}\right)={\tan }^{-1}!\left(\frac{193}{35}\right)\approx 79.4^{\circ }$.

Concept tested: Series RLC impedance

Published 15 September 2026 · How this solution was prepared and checked