Question

When an $A C$ source of emf $e=E_{0}$ sin (100t) is connected across a circuit, the phase difference between the emf e and the current $i$ in the circuit is observed to be $\frac{\pi}{4}$ ahead, as shown in the diagram. If the circuit consists possibly only of $R-C$ or $R-L$ or $L-C$ in series, find the relationship between the two elements.

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

Answer 1

Answer: (A)

Here, the current is ahead of potential. Thus the circuit is R-C circuit. Since the phase difference is $\phi=\pi / 4$,
$ \tan \phi=1=\frac{1}{R \omega C} $
$ \Longrightarrow R =\frac{1}{\omega C } $