• 30.27. A 18-µF capacitor is fully charged by a 12-V battery and is then disconnected from the battery and allowed to discharge through a 0.9-H inductor. Find the first three times when (the magnitude of) the charge on the capacitor is 78-µC, taking t = 0 as the instant when the capacitor is connected to the inductor.

• 30.31. A 2.10-µF capacitor was fully charged by being connected to a 12.0-V battery. The fully charged capacitor is then connected in series with a resistor and an inductor: R = 53 Ω and L = 0.240 H. Calculate the damped frequency of the resulting circuit.

• 30.34. A capacitor with capacitance C = 6. 10^-6 F is connected to an AC power source having a peak value of 13 V and f = 120 Hz. Find the reactance of the capacitor and the maximum current in the circuit. (When entering units, use ohm for Ω.)

• 30.44. Design an RC high-pass filter that passes a signal with frequency 9 kHz, has a ratio Vout/Vin = 0.5, and has an impedance of 4.9 kΩ at very high frequencies. (When entering units, use ohm for Ω.) (a) What components will you use? (b) What is the phase of Vout relative to Vin at the frequency of 9 kHz?

• 30.50. A circuit contains a 100-Ω resistor, a 0.0510-H inductor, a 0.450-µF capacitor, and a source of time-varying emf connected in series. The time-varying emf is 55.0 V at a frequency of 2000 Hz. (a) Determine the current in the circuit. (b) Determine the voltage drop across each component of the circuit. (c) How much power is drawn from the source of emf?

• 30.54. A transformer has 820 turns in the primary coil and 34 turns in the secondary coil. (a) What happens if an AC voltage of 100 V is across the primary coil? (What is the voltage across the secondary coil?) (b) If the initial AC current is 2 A, what is the output current? (c) What happens if a DC current at 100 V flows into the primary coil? (What is the voltage across the secondary coil?) (d) If the initial DC current is 2 A, what is the output current?