Question

In an LCR circuit $R=100\Omega$ when capacitance C is removed, the current lags behind the voltage by $\pi /3$. when inductance L is removed, the current leads the voltage by $\pi /3$. the imoedance of the circuit is

• A. 50 ohm
• B. 100 ohm
• C. 200 ohm
• D. 400 ohm

Answer 1

The correct option is B 100 ohm

When $C$ is removed circuit becomes $RL$ circuit hence
$tan\frac{\pi }{3}=\frac{X_L}{R}$ ....(i)
When $L$ is removed circuit becomes $RC$ circuit hence
$tan\frac{\pi }{3}=\frac{X_C}{R}$ ......(ii)
From equation (i) and (ii) we obtain $X_L=X_C$. This is the condition of resonance and in resonance $Z=R=100\Omega$