# What is the Charging Capacitor formula?????

Joined Jul 28, 2007
4
In my textbook,.. the formula is given by VC(t) = VS(1-e-t/ t)

Where does the (e) come from????

and if any of u got any alternate formula.,, feel free to write it down...

THANKS

#### BrianH

Joined Mar 21, 2007
43
Hello there.

e is a very special number which occurs in nature. It represents an exponential growth and is approximately equal to 2.135675x10-3.

Whether e is a problem for you depends on what you're looking to get out of that equation. If you want the answer to VC or VS and you know all of the other parameters then you're fine. Just work out -t/rc, save the answer and then press the ex button on your calculator and recall the answer to -t/rc. This will give you the answer to the e-t/rc bit and the rest should be easy.

If your unknown is in the -t/rc part of the equation then it's a little more complicated because you'll need to get rid of the e before you can get an answer. In this case you would need to transpose the equation so you get e-t/rc= .... and then take natural logs of both sides. Then the e will dissapear and you'll end up with -t/rc = ......

Hope this helps!

Brian

#### BrianH

Joined Mar 21, 2007
43
If you need any further help, write down what your question is and I'll give you the solution with explanatory comments for each stage.

Brian

#### Papabravo

Joined Feb 24, 2006
16,776
Hello there.
....
e is a very special number which occurs in nature. It represents an exponential growth and is approximately equal to 2.135675x10-3.
...
Isn't the value of e about 2.718281828... give or take a bit? Where did you get your number?

The answer to the OP's question is that it comes from the solution to the differential equation for an RC circuit. Exponential functions to the base e have a very unique property, in that the function can be its own derivative.

#### BrianH

Joined Mar 21, 2007
43
Yes you're right papabravo! Where did I get my number from? <shrug!>

Brian

#### Papabravo

Joined Feb 24, 2006
16,776
's alright. I sometimes refer to the phenomena, by analogy to a heart attack, as a "myocranial infarction"

#### thingmaker3

Joined May 16, 2005
5,084
http://en.wikipedia.org/wiki/E_(mathematical_constant)

I was taught "e" meant "Euler's number." I always assumed it was because [SIZE=-1]Leonhard [/SIZE]Euler came up with the value. Turns out I was mistaken - the number is simply named in Euler's honor.

Like rho, and pi, Euler's number turns up a lot when studying How Things Work.