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A series LCR circuit with R =20 omega ,L = 1. 5 H and C = 35 omega F is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit.

Q7.9  A series LCR circuit with R=20\OmegaL=1.5H  and c=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 circuit, what is the average power transferred to the circuit in one complete cycle?

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Given,

Resistance R=20\Omega

Inductance L=1.5H

Capacitance C=35\mu F=35*10^{-6}F

Voltage supply V = 200V

At resonance, supply frequency is equal to the natural frequency, and at the natural frequency, the total impedance of the circuit is equal to the resistance of the circuit 

as inductive and capacitive reactance cancels each other. in other words,

Z = \sqrt{\left ( \omega L-\frac{1}{\omega C} \right )^2+R^2}=\sqrt{0^2+R^2}=R=20\Omega

As 

 \omega L=\frac{1}{\omega C}

Now,

Current in the circuit

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

Average Power transferred in the circuit :

P=VI=200*10=2000W

Hence average power transferred is 2000W.

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