# in series LCR circuit L=10 mH, C = 10 F, R= 20  is connected to AC Source of V =200 sint.find power at half power frequencies?

Suppose two angular frequencies for which the power transferred to the circuit is half the power at the resonant frequency

We need to calculate the resonant frequency

Using formula of resonant frequency

Put the value into the formula

We need to calculate the peak voltage

Using formula of peak voltage

We need to calculate the current

Using formula of current

Put the value into the formula

We need to calculate the resonant frequency

Using formula of angular frequency

Where,

Put the value into the formula

We need to calculate the angular frequency at which power transferred is half at the resonant frequency

Using formula of angular frequency

Put the value into the formula

Hence, The frequencies which the power transferred to the circuit is half the power at the resonant frequency are 2162.27 rad/s and 4162.27 rad/s.

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