# Discharging capacitors

1. Jul 12, 2011

### 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.

2. Jul 12, 2011

### sophiecentaur

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)

3. Jul 12, 2011

### 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.

4. Jul 12, 2011

### sophiecentaur

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

5. Jul 12, 2011

### uart

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.

Last edited: Jul 12, 2011
6. Jul 12, 2011

### Rupturez

Ahh 5 time constants that rings a bell. thanks uart