Question

In an LCR circuit ohm. When capacitance C is removed, the current lags behind the voltage by $\frac{\pi }{3}$ . When inductance L is removed, the current leads the voltage by $\pi$. The impedance 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 $tan\frac{\pi }{3}=\frac{X_L}{R}......\left(i\right)$
When L is removed circuit becomes RC circuit hence $tan\frac{\pi }{3}=\frac{X_c}{R}....\left(ii\right)$

From equation (i) and (ii) we obtain $X_L=X_c.$ This is the condition of resonance and in resonance Z=R=100$\Omega$