Question

An $AC$ voltage $V=V_0\sin 100t$ is applied to the circuit, the phase difference between current and voltage is found to be $\pi /4$, then:

• A. $R=100\Omega ;C=1\mu F$
• B. $R=1k\Omega ;C=10\mu F$
• C. $R=10k\Omega ;L=1H$
• D. $R=1k\Omega ;L=10H$

Answer 1

The correct option is B $R=1k\Omega ;C=10\mu F$

$V$ function is $\sin$ function.

$I$ function is ahead of $V$ function.

Hence, the circuit should be capacitive in nature.
Further, $\varphi ={45}^o$
$\therefore X_C=R$
or $\omega C=R$
or $C=\frac{R}{\omega }=\frac{R}{100}=0.01R$
In option $\left(b\right)$, this condition is satisfied.