Question

An inductance of $\frac{200}{\pi }mH$, a capacitance of $\frac{{10}^{-3}}{\pi }F$ and a resistance of $10\Omega$ are connected in series with an a.c. source 220 V, 50 Hz. The phase angle of the circuit for the current and voltage source is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{6}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is D

$\frac{\pi }{4}$

Here $X_L=2\pi fL=2\pi \times 50\times \frac{200}{\pi }\times {10}^{-3}=20\Omega$ and $X_c=\frac{1}{2\pi fC}=\frac{1}{2\pi \times 50\times \frac{{10}^{-3}}{\pi }}=10\Omega$ $tan\varphi =\frac{X_L-X_C}{R}=\frac{20-10}{10}=1\therefore \varphi ={45}^{\circ }=\frac{\pi }{4}rd$