Displacement Current

Figure shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A.

1. Calculate the capacitance and the rate of charge of the potential difference between the plates.
2. Obtain the displacement current across the plates.
3. Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

The charge on a parallel plate capacitor varies as q = q₀ cos 2πνt. The plates are very large and close together (area = A, separation = d). Neglecting the edge effects, find the displacement current through the capacitor?

Sea water at frequency ν = 4 × 10⁸ Hz has permittivity ε ≈ 80 εo, permeability µ ≈ µo and resistivity ρ = 0.25 Ω–m. Imagine a parallel plate capacitor immersed in seawater and driven by an alternating voltage source V(t) = V_o sin (2πνt). What fraction of the conduction current density is the displacement current density?

A capacitor has been charged by a dc source. What are the magnitude of conduction and displacement current, when it is fully charged?

A variable frequency a.c source is connected to a capacitor. How will the displacement current change with decrease in frequency?

When an ideal capacitor is charged by a dc battery, no current flows. However, when an ac source is used, the current flows continuously. How does one explain this, based on the concept of displacement current?

A parallel plate capacitor (Figure) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s⁻¹.

1. What is the rms value of the conduction current?
2. Is the conduction current equal to the displacement current?
3. Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

A parallel-plate capacitor of plate-area A and plate separation d is joined to a battery of emf ε and internal resistance R at t = 0. Consider a plane surface of area A/2, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time.