Question

When an ac source of voltage $V=V_{0}sin100t$ is connected across a circuit, the phase difference between the voltage V and current I in the circuit is observed to be $\pi$/4, as shown in figure. If the circuit consists possibly only of RC or RL or LC in series, find possible values of two elements.

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

Answer 1

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

Figure given in the question shows that current I leads to voltage V by a phase angle $\pi /4$. Therefore, the circuit can be RC circuit alone.

$tan\varphi =\frac{X_C}{R}=\frac{1}{\omega CR}$ $[\because X_C=\frac{1}{\omega C}]$

$tan\frac{\pi }{4}=\frac{1}{\omega CR};1=\frac{1}{\omega CR}$ .....(i)

From $V=V_{0}sin100t,weget,\omega =100rad{s}^{-}1$

$\therefore CR=\frac{1}{\omega }=\frac{1}{100}$ (Using (i))

$WhenR=1k\Omega ={10}^3\Omega ,C=\frac{1}{{10}^5}={10}^{-5}F=10\mu F$