31. Alternating Current

(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-μF capacitor?

What capacitance, in μF, has its potential difference increasing at 1.0×10⁶ V/s when the displacement current in the capacitor is 1.0 A?

For an RC circuit, find an expression for the angular frequency at which V_R = ½ ε₀. What is V_C at this frequency?

A capacitor has a peak current of 330 μA when the peak voltage at 250 kHz is 2.2 V. What is the capacitance?

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

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 the maximum conduction current I. Neglect fringing.

A capacitor is connected to a 15 kHz oscillator. The peak current is 65 mA when the rms voltage is 6.0 V. What is the value of the capacitance C?

The peak current to and from a capacitor is 10 mA. What is the peak current if the emf frequency is doubled?

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?

What are V_R and V_C if the emf frequency in FIGURE EX32.19 is 25 kHz?

You have a resistor and a capacitor of unknown values. First, you charge the capacitor and discharge it through the resistor. By monitoring the capacitor voltage on an oscilloscope, you see that the voltage decays to half its initial value in 2.5 ms. You then use the resistor and capacitor to make a low-pass filter. What is the crossover frequency f_c?