Halliday, Resnick & Walker — Electromagnetic Oscillations and Alternating Current: Problem 23

23 Figure 31-23 shows an ac generator connected to a “black box” through a pair of terminals. The box contains an RLC circuit, possibly even a multiloop circuit, whose elements and connections we do not know. Measurements outside the box reveal that \(\mathcal{E}(t) = (61.4 \text{ V}) \sin \omega_d t\) and \(i(t) = (0.930 \text{ A}) \sin(\omega_d t + 42.0^\circ)\). (a) What is the power factor? (b) Does the current lead or lag the emf? (c) Is the circuit in the box largely inductive or largely capacitive? (d) Is the circuit in the box in resonance? (e) Must there be a capacitor in the box? (f) An inductor? (g) A resistor? (h) At what average rate is energy delivered to the box by the generator? (i) Why don’t you need to know \(\omega_d\) to answer all these questions?