# Capacitance equation

1. ### dan greig

41
how would i rearrange this equation to find the capacitance, c?

V=Vo exp(-t/RC)

2. ### daveb

923
Do you know what the inverse of the exponential function is?

3. ### dan greig

41
would it go to,

V = Vo ln + (-t/RC)

then to,

V = ln Vo - t x 1/RC

Last edited: Apr 26, 2006
4. ### daveb

923
You're right that you use the natural log function, but your form is incorrect. What would happen if you take the natural log of the exponential function, or ln(e^x) = ?

5. ### dan greig

41
ln(e) + x ?????

not really sure you've lost me a bit sorry

### Staff: Mentor

Let's do it first with the more familiar base 10.

log( 10^2 ) = 2 (right?)

log( 10^x ) = ?

ln( e^x ) is analogous to log( 10^x )...

7. ### dan greig

41
log(10^x) = x ?

analogous?? The same as??

but log e = 1

does that mean log e^x = 1^x ?

therefore log e^x = x ?

Last edited: Apr 26, 2006

### Staff: Mentor

No, you need to keep your log() and ln() straight. log() is used with base 10 math, and ln() is used with base e math.

log( 10^x ) = x

ln( e^x ) = ?

Try a few numbers on your calculator to help you keep it straight. There's a reason that most calculators overload the log() key with 10^x and overload the ln() key with e^x.....

9. ### Reshma

777
How come you did not take the natural log on the left hand side? :surprised
If this is your original equation, then:
$$\ln V = \ln V_0 - {t\over RC}$$

Furthur evaluation is simple.