Question

A capacitance of $\left(\frac{{10}^{-3}}{2\pi }\right)F$ and an inductance of $\left[\frac{100}{\pi }\right]mH$ and a resistance of $10\Omega$ are connected in series with an AC voltage source of $220V$, $50Hz$. The phase angle of the circuit is

• A. ${60}^o$
• B. ${30}^o$
• C. ${45}^o$
• D. ${90}^o$

Answer 1

The correct option is C ${45}^o$

Given : $C=\frac{{10}^{-3}}{2\pi }F$ $L=\frac{100}{\pi }\times {10}^{-3}H$ $V_{rms}=220V$ $f=50Hz$ $R=10\Omega$
Capacitive reactance $X_C=\frac{1}{2\pi fC}=\frac{2\pi }{2\pi \times 50\times {10}^{-3}}=20\Omega$
Inductive reactance $X_L=2\pi fL=2\pi \times 50\times \frac{100}{\pi }\times {10}^{-3}=10\Omega$
Using $\tan \varphi =\frac{X_L-X_C}{R}$
$\tan \varphi =\frac{20-10}{10}=1$
$⟹\varphi ={45}^o$