Halliday, Resnick & Walker — Electromagnetic Oscillations and Alternating Current: Problem 7

7 An RLC circuit such as that of Fig. 31-7 has \(R = 5.00\ \Omega\), \(C = 20.0\ \mu\text{F}\), \(L = 2.00\ \text{H}\), and \(\mathcal{E}_m = 30.0\ \text{V}\). (a) At what angular frequency \(\omega_d\) will the current amplitude have its maximum value, as in the resonance curves of Fig. 31-16? (b) What is this maximum value? At what (c) lower angular frequency \(\omega_{d1}\) and (d) higher angular frequency \(\omega_{d2}\) will the current amplitude be half this maximum value? (e) For the resonance curve for this circuit, what is the fractional half-width \((\omega_{d2} - \omega_{d1})/\omega\)?