Dielectric materials used in the manufacture of capacitors are characterized by

Question

Dielectric materials used in the manufacture
of capacitors are characterized by conductivities that are small but not zero. Therefore,
a charged capacitor slowly loses its charge by
“leaking” across the dielectric.
If a certain 1.83 µF capacitor leaks charge
such that the potential di?erence decreases
to half its initial value in 3.6 s, what is the
equivalent resistance of the dielectric?
Answer in units of ?

Explanation / Answer

I think in the previous post there was a typo. The equation is q(t) = Qe^(-t / tao) or q(t) = Qe^(-t / RC) So in your case it would be 1/2 = 1 * e^(-t / RC) --> ln(1/2) = -t / RC --> -ln(1/2) = t / RC --> -Cln(1/2) = t / R --> R = t / -Cln(1/2) or R = t / Cln(2) R = 2.8*10^6 ohms

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