Average Power in an L-R-C Circuit
An circuit consists of a resistor (resistance ), inductor (inductance ), and capacitor (capacitance ) connected in series with an AC source supplying sinusoidal voltage .Assume that all circuit elements are ideal, so that the only resistancein the circuit is due to the resistor. Also assume that is the resonant frequency of the circuit.

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What is the average power supplied by the voltage source?
What is the instantaneous power dissipated in the circuit? Note: You will need to use the fact that thecircuit is being driven at its resonant frequency to remove from your answer.
The power dissipated in the circuit is equal to the voltage supplied by the AC source times the current in the circuit: .

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The L-R-C circuit described in the problem introduction obeys the differential equation ,

where is the charge on one of the capacitor plates. After solving tsdrta.nets equation for as a function of time, you can take the derivative to find the current in the circuit: . The result is , where , and .
The problem introduction states that the circuit is being driven at its resonant frequency . What is the value the in terms of other given quantities?