# Discharging capacitors

#### Rupturez

Hi there,
okay my Question is on discharging capacitors.
the equation for instantanious voltage of a capacitor whilst dischargeing is : v=Vi*e^-t/R*C

However im not sure how to find the time for a capacitor to completely discharge to zero volts.

When I transpose for t
t=-(R*C)*ln(v/Vi)

and input v as zero (cap has completly discharge) we get an undefined answear.
I havnt studied calculus and am not familiar with the concept of limits.

how would I go about finding the precise time for a capacitor to discharge without using a normalised universal time constant curve to estimate the answear.

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#### sophiecentaur

Gold Member
Of course you get a dippy answer. With exponential processes, you Never get to zero. Each interval of RC seconds, the volts decrease by 1/e. You can't get to zero without an infinite value for the time.
Of course, 'as near zero as dammit' would take a very finite time! (Engineer speaking)

#### Rupturez

I understand the voltage will never actually reach absolute zero, however Im after the "practicle" time for the capacitor to reach "practicle" zero voltage.

#### sophiecentaur

Gold Member
First decide on what is an acceptably low voltage for your purpose and then put it in your formula.

#### uart

I understand the voltage will never actually reach absolute zero, however Im after the "practicle" time for the capacitor to reach "practicle" zero voltage.
Hi Ruptures. As sophiecentaur has pointed out, it is the nature of the (negative) exponential function that it never reaches precisely zero in any finite time. A "practical" time depends upon just how close to zero you consider "practically zero", but two common choices are

- 5%, which takes almost exactly 3 time constants, and

- 1%, which takes approximately 5 times constants.

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#### Rupturez

Ahh 5 time constants that rings a bell. thanks uart

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