# Where's the RC timing formula?

Discussion in 'Math' started by StephenDJ, Oct 27, 2008.

1. ### StephenDJ Thread Starter Active Member

May 31, 2008
58
0
There used to be a formula I knew of for RC circuits where you could plug in the starting voltage or current, the ending voltage or current, and the amount of time in between, and project exactly what the voltage or current will be after exactly x amount time has passed. I know it rises/drops to 63% within the first time constant. But where's the formula for the other times? Also would like to have the vise versa: i.e. plug in the voltage or current and find the time.

2. ### mik3 Senior Member

Feb 4, 2008
4,846
63
For an RC network with initial voltage on the capacitor Vo its voltage with respect to time is given by:

Vc(t)=V(1-exp(-t/RC)+Vo*exp(-t/RC)

where

V=the steady state voltage across the capacitor when fully charged
Vo=initial voltage (if exists)

3. ### StephenDJ Thread Starter Active Member

May 31, 2008
58
0
Mik3,Thanks so much. I have been needing a formula like this for so long!

Ratch,I believe the plain V (steady state) in mik3's formula is what the voltage is only AFTER the time has passed and it is then resting comfortably at its new level of satisfaction, or "charged" state.

Through it all, I've failed to mention one very important point:I'm assuming that this formula of course implies that the RC's supply voltage changed completely and suddenly (like a square wave) at the BEGINNING of the time, and stayed that way during the time the capacitor was catching up. If the supply voltage were to go wiggleing all up and down during this time only to wait untill the very end to reach its final steady state, V, then it's very difficult to establish any kind of formula as this would affect the way in which the capacitor charges. But I believe this formula implies steady state of the supply while capacitor is catching up. That is what I'm looking for.

4. ### StephenDJ Thread Starter Active Member

May 31, 2008
58
0
There was a message from Ratch in here a while ago... looks like he may have came back and deleted it.

5. ### Wendy Moderator

Mar 24, 2008
20,772
2,540
Naw, it got moved to here by a moderator.

6. ### Ron H AAC Fanatic!

Apr 14, 2005
7,050
657
One formula covers both charging and discharging:

V=Vf+(Vi-Vf)*e^(-t/(R*C))
Where
V=instantaneous voltage
Vi=initial voltage
Vf=final voltage

Which is another way of expressing mik3's equation.
(I posted this before thoroughly reading his post.)

Last edited: Nov 4, 2008
7. ### mik3 Senior Member

Feb 4, 2008
4,846
63
The formula posted is valid for both charging and discharging.

8. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,047
295

The natural logarithm.....shows up EVERYWHERE in nature. Learn to love it.

eric

9. ### mik3 Senior Member

Feb 4, 2008
4,846
63
The exponential function is the solution to many differential equations and because many natural effects are described by differential equations is logic to see the exponential function a lot.