A parallel plate capacitor has plate area A and separation d between the plates. The space between the plates is filled with a dielectric of dielectric constant K and resistivity ρ . The capacitor is initially charged to Q 0 using a battery. After removing battery at t = 0 , current density…

Question

A parallel plate capacitor has plate area A and separation d between the plates. The space between the plates is filled with a dielectric of dielectric constant K and resistivity &#961; . The capacitor is initially charged to Q 0 using a battery. After removing battery at t = 0 , current density in the dielectric at any time t is

Aicharya · Accepted Answer

Current through a discharging capacitor in

R - C

circuit is given by

i = \frac{Q_{0}}{RC} e^{- \frac{t}{RC}}

, where resistance and capacitance are given by

R = ρ \frac{d}{A}

and

C = \frac{ε_{0} KA}{d}

The time constant of the

R - C

circuit is given by

τ = CR= \frac{ε_{0} K A}{d} × ρ \frac{d}{A} = ε_{0} K ρ

Thus, the current density is given by

J = \frac{i}{A} = \frac{Q_{0}}{ρ K ε_{0} A} e^{- (\frac{t}{ε_{0} K ρ})}

A parallel plate capacitor has plate area A and separation d between the plates. The space between the…

Solution