Question

In a series $LCR$ circuit the voltage across an inductor, capacitor and resistor are $20\,V$, $20\,V$ and $40\,V$ respectively. The phase difference between the applied voltage and the current in the circuit is

• A. $30^°$
• B. $45^°$
• C. $60^°$
• D. $0^°$

Answer 1

Answer: (D)

Let $(\phi)$ be the phase difference between the applied voltage and current. Then
$tan\,\phi=\frac{X_{L}-X_{C}}{R}$
$=\frac{I_{V}\left(X_{L}-X_{C}\right)}{I_{V}R}$
$=\frac{V_{L}-V_{C}}{V_{R}}$
$=\frac{20\,V-20\,V}{40\,V}$
$=0$
$\therefore \phi =tan^{-1}\left(0\right)=0^{\circ}$