Question

When an $A C$ source of voltage $V=V_{0} \sin 100 t$ 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 $R C$ or $R L$ or $L C$ in series, find possible values of two elements.

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

Answer 1

Answer: (A)

Figure given in the question shows that current $I$ leads the voltage $V$ by a phase angle $\pi / 4$.
Therefore, the circuit can be $R C$ circuit alone.
$\tan \phi=\frac{X_{C}}{R}=\frac{1}{\omega C R}$
$\left(\because X_{C}=\frac{1}{\omega C}\right)$
$\tan \frac{\pi}{4}=\frac{1}{\omega C R} ; 1=\frac{1}{\omega C R}$ ...(i)
From $V=V_{0} \sin 100\, t$,
we get, $\omega=100\, rad s^{-1}$
$\therefore C R=\frac{1}{\omega}=\frac{1}{100}$ (using (i))
When $R=1\, k\, \Omega=10^{3} \Omega,$
$C=\frac{1}{10^{5}}=10^{-5} F=10\, \mu F$