# Realistic Capacitor with leaking dielectric

1. Oct 6, 2015

### yango_17

1. The problem statement, all variables and given/known data
A realistic capacitor is almost always filled with dielectric, but invariably this dielectric will conduct just a little, and the charge stored on the capacitor's plates will "leak." Over time, quite a bit of current can leak away. A good capacitor has a small leakage current.
Consider a parallel-plate capacitor with the plates of area A and distance between them d, filled with a dielectric with the dielectric constant κ. At t=0, some charge is put on the capacitor so that it's voltage is $V_{0}$. At some later time $\tau =t$, the voltage on the capacitor is $V(\tau )=\frac{V_{0}}{e}$ (where e is Euler's constant). What is the conductivity σ of the dielectric?

2. Relevant equations
$C=\kappa C_{0}$
$\sigma=\frac{1}{\rho }$
$R=\frac{V}{I}$
3. The attempt at a solution
I would like to know how to begin to set up the problem. I'm not sure how to go about finding a relation between the voltage of the capacitor and the conductivity of the dielectric, especially when one has to take into account the "leaking" of the dielectric. Any help getting started on this problem would be appreciated. Thanks!

2. Oct 6, 2015

### ehild

You can handle the leakage as if a resistor was connected parallel to the capacitor.

3. Oct 6, 2015

### yango_17

Ah, that's a great hint. Alright, I'll see how far I can take it from here