Chapter 16, Problem 35P

A potential difference V(t) = V₀sin $\omega t$is maintained across a parallel-plate capacitor with capacitance C consisting of two circular parallel plates. A thin wire with resistance R connects the centers of the two plates, allowing charge to leak between plates while they are charging.

(a) Obtain expressions for the leakage current I_res(t) in the thin wire. Use these results to obtain an expression for the current I_real(t) in the wires connected to the capacitor.

(b) Find the displacement current in the space between the plates from the changing electric field between the plates.

(c) Compare I_real(t) with the sum of the displacement current $I_d\left(t\right)$and resistor current $I_{\text{res}}\left(t\right)$ between the plates, and explain why the relationship you observe would be expected.