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An L-R-C series circuit consists of a 2.50μF2.50-\mu F capacitor, a 5.00-mH inductor, and a 75.0Ω75.0-\Omega resistor connected across an ac source of voltage amplitude 15.0 V having variable frequency. (a) Under what circumstances is the average power delivered to the circuit equal to 12VrmsIrms\frac{1}{2} V_{\mathrm{rms}} I_{\mathrm{rms}} (b) Under the conditions of part (a), what is the average power delivered to each circuit element and what is the maximum current through the capacitor?

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The average power PavgP_{avg} is given by the following equation:

Pav=VIcosϕ\begin{equation} P_{\mathrm{av}}=V I \cos \phi \end{equation}

Where cosϕ\cos \phi is the power factor of the phase angle of voltage with respect to current.

We are given the average power in the problem by

Pav=12(VrmsIrms)\begin{equation} P_{\mathrm{av}}=\dfrac{1}{2}\left(V_{\mathrm{rms}} I_{\mathrm{rms}}\right) \end{equation}

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