For the circuit of Problem 69, what is the average rate at which energy is delivered by the source when the circuit is operated at the resonant frequency? When it is operated at \(1.00 \mathrm{kHz}\) ? What is the power factor in each case?

Data from Problem 69

An RLC series circuit contains an AC source of emf for which \(\mathscr{E}_{\max }=30.0 \mathrm{~V}\), a \(5.00-\Omega\) resistor, a \(4.00-\mathrm{mH}\) inductor, and an \(8.00-\mu \mathrm{F}\) capacitor. What are \((a)\) the resonant angular frequency and \((b)\) the current amplitude if it is driven at the resonant angular frequency? (c) If a \(1.00-\mathrm{kHz}, 30. 0-\mathrm{V}\) source is used, what is the current amplitude?