A series RLC circuit has resistance $R=50,\Omega$, inductance $L=0.2,\text{H}$, and capacitance $C=100,\mu \text{F}$. It is connected to a $200,{\text{V}}_{\text{rms}}$ sinusoidal source at $60,\text{Hz}$. Calculate (i) the magnitude of the impedance $|Z|$, and (ii) the phase angle $\phi$ (in degrees) between the source voltage and current.

Step-by-step solution

1. Calculate inductive reactance: $X_L=2pifL=2pi(60)(0.2)approx75.4,Omega$.
2. Calculate capacitive reactance: $X_C=\frac{1}{2pifC}=\frac{1}{2pi(60)(100\times 10^{-6})}\approx 26.5,Omega$.
3. Net reactance: $X=X_L-X_C\approx 75.4-26.5=48.9,Omega$ (inductive).
4. Magnitude of impedance: $|Z|=\sqrt{R^2+X^2}=\sqrt{50^2+48.9^2}\approx 69.9\approx 70,Omega$.
5. Phase angle: $\phi ={\tan }^{-1}\left(\frac{X}{R}\right)={\tan }^{-1}\left(\frac{48.9}{50}\right)\approx 44.3^{\circ }\approx 44^{\circ }$.
6. Thus $|Z|\approx 70,Omega$ and $\phi \approx 44^{\circ }$.

Concept tested: Series RLC impedance

Published 17 September 2026 · How this solution was prepared and checked