Question

A series LCR circuit with R = 20 Ω, 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 equals the 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,

At resonance,

Current in the circuit can be calculated as:

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

= 200 × 10 = 2000 W.