Calculating leakage of a capacitor?

Question

Help!

I have a leaky capacitor. I know the relative permittivity is 12 and the resistivity is 10^14 OhmM, capacitance of 100pF.

How can i calculate the leakage resistance with only this information?

At first i done:

(E0 x Er x A)/C = (A x R)/resistivity

So the areas on each side cancel out and hence you dont need to know the area.

Then from this i worked out R to be 1.062 x10^14 Ohms!

What am i doing wrong?

From this i also need to work out the time for the cap to completely discharge if it holds a charge of 10nC.

Any help would be brilliant. There are a few questions on here already but they havnt been much help....

Answer 1

Leakage in a cap usually can't be calculated, only measured, as it is the result of indirect causes, like moisture and contamination.

But you do have a resistivity measure, which is usually not available for the same reason. But you need to know the area of the plates and the separation of the plates to calculate the resistance from the resistivity.

Your method of calculating the R is interesting, and may be OK. I need to think about that.

"R to be 1.062 x10^14 Ohms" That is a possible value. A ceramic cap is very low leakage.

Time to discharge a cap fully is infinity, as it never completely discharges, it approaches it's final voltage exponentially.  For practical purposes, 5 time constants is usually taken as a full discharge, as it gets you to 99% of the final value. That is t = 5RC.

Using your numbers, t = 5(10e-10)(10e14) = 50000 seconds, a high but possible number.

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