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7.9 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?

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    Answered by

    Payal Gupta | Contributor-Level 10

    4 months ago

    7.9 Given values:

    Resistance R = 20 Ω

    Inductance, L = 1.5 H

    Capacitance, C = 35 μF = 35 ×10-6 F

    AC power supply, V = 200 V

    Impedance of the circuit is given by the relation,

    Z = R2+(XL-XC)2 where XL = Inductive reactance and XC = Capacitive reactance

    At resonance XL = XC

    Hence Z = R = 20 Ω

    Current in the circuit, I = VZ = 20020 = 10 A

    Hence, the average power transferred to the circuit in one complete cycle = VI = 200 ×10 = 2000 W

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