31. Alternating Current

For an RC circuit, find an expression for the angular frequency at which V_R = ½ ε₀.

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 series RC circuit is built with a 12 kΩ resistor and a parallel-plate capacitor with 15-cm-diameter electrodes. A 12 V, 36 kHz source drives a peak current of 0.65 mA through the circuit. What is the spacing between the capacitor plates?

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?

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?

A 10-cm-diameter parallel-plate capacitor has a 1.0 mm spacing. The electric field between the plates is increasing at the rate 1.0×10⁶ V/m s. What is the magnetic field strength on the axis?

Show that the quantity ϵ₀(dΦ_e/dt) has units of current.

A wire with conductivity σ carries current I. The current is increasing at the rate dI/dt. Evaluate the displacement current for a copper wire in which the current is increasing at 1.0×10⁶ A/s.

A simple series circuit consists of a 150 Ω resistor, a 25 V battery, a switch, and a 2.5 pF parallel-plate capacitor (initially uncharged) with plates 5.0 mm apart. The switch is closed at t = 0 s. Find the electric flux and the displacement current at t = 0.50 ns.

A 1.0 μF capacitor is discharged, starting at t = 0 s.The displacement current between the plates is $I_{\text{disp}}=\left(10\text{ A}\right)\exp (-\frac{t}{2.0}\mu \text{s})$. What was the capacitor’s initial voltage (ΔV_C)₀?