Q: In a series LCR circuit, R = 200 Ω , the voltage and the frequency of the main supply is 220 V and 50 Hz respectively . On taking out the capacitance from the circuit, the current lags behind the voltage by 30°. The power dissipated in the LCR circuit is

Sol: Here, R = 200 Ω , E_{V} = 220 V

In L-R circuit, tan30° = X_{L}/R

In C-R circuit, tan30° = X_{C}/R

∴ X_{L}/R = X_{C}/R or X_{L} = X_{C}

In L – C – R circuit, if φ is the phase difference between voltage and current, then

$\large tan\phi = \frac{X_L -X_C}{R}$

$\large tan\phi = \frac{0}{R} = 0 $

tan φ = 0°

i.e., current and voltage are in the same phase.

∴ Average power $\large = E_v I_v cos\phi = \frac{E_v^2}{R} $

(∵ φ = 0)

$\large = \frac{220^2}{200} $

= 242 W