Halliday, Resnick & Walker — Electromagnetic Oscillations and Alternating Current: Problem 17

17 An ac generator has emf \(\mathcal{E} = \mathcal{E}_m \sin(\omega_d t - \pi/4)\), where \(\mathcal{E}_m = 25.0 \text{ V}\) and \(\omega_d = 270 \text{ rad/s}\). The current produced in a connected circuit is \(i(t) = I \sin(\omega_d t - 3\pi/4)\), where \(I = 620 \text{ mA}\). At what time after \(t = 0\) does (a) the generator emf first reach a maximum and (b) the current first reach a maximum? (c) The circuit contains a single element other than the generator. Is it a capacitor, an inductor, or a resistor? Justify your answer. (d) What is the value of the capacitance, inductance, or resistance, as the case may be?