Question

When an alternating voltage $V=V_0\sin \left(100t\right)$ is applied across a circuit, then the phase difference between voltage $V$ and current $I$ in the circuit is observed to be $\frac{\pi }{4}$ as shown in the figure. If circuit is possibly a series RC, LC or RL circuit, then the relationship between two elements is:

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

Answer 1

The correct option is A $R=1k\Omega ,C=10\mu F$

Here voltage lags by $\frac{\pi }{4}$

i.e. circuit is capacitive

$\therefore \cos \theta =\frac{R}{\sqrt{R^2+X_c^2}}=\frac{1}{\sqrt{2}}$

$\omega =100$

$2R^2=R^2+\frac{1}{{100}^2{C}^2}$

${100}^2{R}^2=\frac{1}{c^2}$

$100RC=1$

if $R=1000\Omega$

$C=10\mu F$