First slide

AC Circuits

Question

In an LCR circuit R=100 ohm. When capacitance C is removed, the current lags behind the voltage by $π / 3$ . When inductance L is removed, the current leads the voltage by $π / 3$ . The impedance of the circuit is

Moderate

A

50 ohm
B

100 ohm
C

200 ohm
D

400 ohm

Solution

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

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