Question

When an ac source of voltage $V = V_{0}\sin 100t$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 circuit consists possibly only of RC or RL or LC in series, find possible value of two elements.

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

Answer 1

Answer: (A)

$R = 1k\Omega,C = 10\mu F$

Answer 2

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

$\tan\varphi = \frac{XC}{R} = \frac{1}{\omega CR}$ $\left( \because X_{C} = \frac{1}{\omega C} \right)$

$\tan\frac{\pi}{4} = \frac{1}{\omega CR}$

$1 = \frac{1}{\omega CR}$ …(i)

From $V = V_{0}\sin 100t,$ we get

$\omega = 100rads^{- 1}$

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

When , $R = 1k\Omega = 10^{3}\Omega$

$C = \frac{1}{10^{5}} = 10^{- 5}F = 10\mu F$