A sinusoidal voltage of peak value 283 V and frequency 50 Hz is . . .

Question :  A sinusoidal voltage of peak value 283 V and frequency 50 Hz is applied to a series LCR circuit in which R=3Ω, L=25.48 mH and C=796 µF, then the power dissipated at the resonant condition will be 

a) 39.70 kW
b) 26.70 kW
c) 13.35 kW
d) Zero.

Doubt by Tushar

Solution :

Vrms = 283 V
f = 50 Hz
R=3Ω,
L=25.48 mH 
C=796 µF

Power dissipated in AC circuit
Pav = εrmsIrms cosΦ

At resonance, Φ=0
so cosΦ = 1

P_av = ε_rmsI_rms
P_av = ε_rms(ε_rms/Z)
At resonance, Z = R
P_av = ε_rms(ε_rms/R) 
P_av = ε²_rms/R
P_av = (283)²/3
P_av = 80089/3
P_av = 26696.33 W
P_av =26696.33/1000 kW
P_av = 26.69633 kW
P_av = 26.70 kW

Hence, b) would be the correct option.