Question

A series LCR circuit with R = 20 W, L = 1.5 H and C = 35 μF 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

At resonance, the frequency of the supply power equalsthe natural frequency of the given LCR circuit.

Resistance, R = 20 Ω Inductance, L = 1.5 H Capacitance, C = 35 µF = 30 × 10−6 F

AC supply voltage to the LCR circuit, V = 200 V

Impedance of the circuit is given by the relation,

$Z=√(R^2+(X_L-X_C))^2 At resonance, X_L=X_C$

Z=R=20Ω

Current in the circuit can be calculated as:

$I=\frac{V}{Z}=\frac{200}{20}=10 A$

Hence, the average power transferred to the circuit in one complete cycle:

VI = 200 × 10 = 2000 W.