Q. 93.9( 21 Votes )

A series LCR circuit with R = 20Ω, L = 1.5 H and C = 35 μF is connected to a variable-frequency 200 V A.C. 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 :

Given:

R = 20


L = 1.5 H


C = 35 μF = 35 × 10-6F


Voltage supplied V = 200 V


The diagram given is:



Impedance of the circuit can be calculated as follows:



At resonance condition i.e. when ωL = 1/ωC


Z = R = 20 Ω


Current is given by the relation


I = V/R


I = 200V /20Ω


I = 10A


Therefore, the average power transferred to the circuit in one complete cycle can be calculated as follows:


Power = VI


Power = 200V × 10A


Power = 2000 W.


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