Question

A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 µ F is connected to a variable-frequency 200 V AC supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

Answer 1

L = 1.5 H
C = 35 µF = 35 x 10^-6 F
R = 20q
E_v = 200V
When the frequency of the supply equals the natural frequency of the circuit, the impedance of the circuit is equal to the resistance of the circuit. Therefore, rms value of the current in the circuit
\(I_V=\frac{E_v}{R}=\frac{200}{20}= 10A\)
Therefore, average power transferred to the circuit in one complete cycle,
P = EI = 200 × 10 = 2000 W.