31. Alternating Current

An AC source operates at a maximum voltage of 120 V and a frequency of 60 Hz. If it is connected to a 175 µF capacitor, what is the maximum charge stored on the capacitor?

A 300 µF capacitor is connected to an AC source operating at an RMS voltage of 120 V. If the maximum current in the circuit is 1.5 A, what is the oscillation frequency of the AC source?

537

The peak current to and from a capacitor is i when the emf source has a peak voltage V and frequency f. What is the peak current to and from the capacitor if the frequency and peak voltage are doubled to 2f and

2 V

An AC circuit consists of a capacitor and an emf source with frequency

0.25 Hz

. If the source is turned on at

t = 0 s

, and the first time the voltage across the capacitor reaches a maximum value is at

t = 1.4 s

, when is the first time the current in the capacitor is at a maximum?

372

An AC circuit consists of a

20 μ F

capacitor and an emf source with a peak voltage of 40 V. What is the frequency of the source if the peak current is

430 mA

224

A low-pass RC filter has a

10 k Ω

resistor in series with a

450 μ F

Capacitor. What is the crossover angular frequency?

249

A 0.30 μF capacitor is connected across an AC generator that produces a peak voltage of 10 V. What is the peak current to and from the capacitor if the emf frequency is (a) 100 Hz?

186

What is the peak current supplied by the emf in FIGURE P32.42?

105

The small transformers that power many consumer products produce a 12.0 V rms, 60 Hz emf. Design a circuit using resistors and capacitors that uses the transformer voltage as an input and produces a 6.0 V rms output that leads the input voltage by 45°.

A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. (a) What is the phase angle Φ for the source voltage relative to the current? Does the source voltage lag or lead the current?

325

A capacitance C and an inductance L are operated at the same angular frequency. (a) At what angular frequency will they have the same reactance? (b) If L = 5 00 mH and C = 3.50 μF, what is the numerical value of the angular frequency in part (a), and what is the reactance of each element?

387

A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. (b) What is the capacitance C of the capacitor if the current amplitude is 5.30 A?

782

(a) Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600 Hz. (b) Compute the reactance of a 2.50-μF capacitor at the same frequencies. (c) At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50-μFcapacitor?

267

(II) At a given instant, a 2.4-A current flows in the wires connected to a parallel-plate capacitor. What is the rate at which the electric field is changing between the plates if the square plates are 1.60 cm on a side?

(II) Suppose an air-gap capacitor has circular plates of radius r = 2.5 cm and separation d = 1.6 mm. A 68.0-Hz emf, ε = ε₀ cos ωt, is applied to the capacitor. The maximum displacement current is 35 μA. Determine (a) the maximum conduction current I. Neglect fringing.

(II) Suppose an air-gap capacitor has circular plates of radius r = 2.5 cm and separation d = 1.6 mm. A 68.0-Hz emf, ε = ε₀ cos ωt, is applied to the capacitor. The maximum displacement current is 35 μA. Determine (c) the maximum value of dΦE/dt between the plates. Neglect fringing.