A $L-C-R$ series circuit is connected to a source of alternating current. At resonance, the applied voltage and the current flowing through the circuit will have a phase difference of

• A

  $\pi$
• B

  $\frac{\pi}{2}$
• C

  $\frac{\pi}{4}$
• Correct answer
  D

  $0^{\circ}$

Solution

In $L-C-R$ series circuit, phase difference $\phi$ between current and voltage is related as,
At resonance condition, $X_L=X_C$ $\therefore Z=\sqrt{R^2+\left(X_L-X_C\right)^2}=\sqrt{R^2+0}=R$ $\therefore$ from Eqs. (i), $\cos \phi=\frac{R}{R}=1$ $\Rightarrow \quad \cos \phi=\cos 0^{\circ} \Rightarrow \phi=0^{\circ}$

Hence, the correct answer is option: 'D'.