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Question: A series LCR-circuit with\(R = 20\Omega\) L = 1.5 H and \(C = 35\mu F\) is connected to a variable f...

A series LCR-circuit withR=20ΩR = 20\Omega L = 1.5 H and C=35μFC = 35\mu F is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the supply equals the natural frequency of the circuit. The average power transferred to the circuit in one complete cycle is

A

200 W

B

2000 W

C

100 W

D

4000 W

Answer

2000 W

Explanation

Solution

: If the frequency of the ac source equals the natural frequency of the circuit, the impedance

Z = R = 20 Ω\Omega

The average power dissipated per cycle,

Pav(vkSlr)=V2rmsZ=V2rmsR=(200)220P_{av(vkSlr)} = \frac{{V^{2}}_{rms}}{Z} = \frac{{V^{2}}_{rms}}{R} = \frac{(200)^{2}}{20}

=2000W= 2000W