A series `LCR` circuit with `R = 20 Omega, L = 1.5 H` 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 in `kW` transferred to the circuit in one complete cycle?

Explanation

At resonance, the frequency of the supply power equals the natural frequency of the given LCR circuit.
Resistance, `R=20Omega`
Inductance, L=1.5H
Capacitance, `C=35muF=30xx10^(-6)F`
AC supply voltage to the LCR circuit, V=200V
Impedance of the circuit is given by the relation.
`Z=sqrt(R^(2)=(omegaL-(1)/(omegaC))^(2)) `
At resonance, ` omegaL(1)/( omegaC)`
`thereforeZ=R20Omega`
Current in the circuit can be calculated as:
`I=(v)/(Z)`
`=(200)/(20)=10A`
Hence, the average power tranferred to the circuit in one complete cycle =VI
`=200xx10=2000W`.