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A series LCR circuit with R = 20 Omega, ...

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?

Text Solution

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Given, resistance , R = 20 `Omega` Inductance, L = 1.5 H
capacitance , C = 35 `mu F = 35 xx 10^(-6) `F
rms value of voltage , `E_(rms) ` = 200 V
when frequency of supply equal the natural frequency of the circuit, we get resonance condition.
In this case, impedance of the circuit is
Z = R = 20 `Omega`
the rms value of current is
` I_(rms) = (E_(rms))/(Z ) = (220)/(20) = 10 A. `
phase angle , `phi` = 0
Average power transferred to the circuit in one complete cycle is
`P = E_(rms ) I_(rms) cos phi`
= ` 200 xx 10 xx 1 `
`rArr " " ` p = 2,000 W
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