A capacitor has two parallel plates with area A separated by a distance d. The s

Question

A capacitor has two parallel plates with area A separated by a distance d. The space between plates is filled with a material having dielectric constant K. The material is not a perfect insulator but has resistivity . The capacitor is initially charged with charge of magnitude Qo on each plate that gradually discharges by conduction through the dielectric.

a) Calculate the conduction current density jC(t) in the dielectric.

b) Show that at any instant the displacement current density in the dielectric is equal in magnitude to the conduction current density but opposite in direction, so the total current density is zero at every instant.

Explanation / Answer

a) jC(t) = I(t)/A

I(t) = I0(e-t/RC)

Q = Q0(1-e-t/RC)

jC(t) = I(t)/A = I0(e-t/RC) / A

b) Calculate the electric field in the capacitor as a function of Q and t. Hence it can be proved with the help of relation between dispalcement current and electric field.

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