Subject: capacitor discharge rate
Bill Phillips
Senior High level

I'm need my math checked! I need to be solve for t in the following rate problem for an electrical capacitor. Vr = E(e^-t/RC), e=nat. log 2.718 raised to the -t/RC power. Every time I do this it comes out different. Thanks for your time.

Bill Phillips teacher of Science

Hi Bill,

With Vr = E e-t/RC I would first divide both sides by E and then take the natural log. Thus

Vr = E e-t/RC
Vr /E = e-t/RC
ln(Vr /E) = -t/RC
t = -RC ln(Vr /E)

There are different ways you can write this which is maybe why you got different answers.

t = -RC ln(Vr /E)
t = -RC (lnVr - ln E)
t = RC (ln E - lnVr)
t = RC (ln E /Vr)
I hope this helps,

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