# Help with RC circuits

1. Mar 4, 2008

### abk80

[SOLVED] Help with RC circuits

Can someone explain how to find the intantaneous value of voltage in a capacitor at any specific instant in time. Im taking a course in electronics and the text book isn't really clear on this. I have the equation:
-t/T
Vc=E(1-e )
t=RC
Not sure why Im subracting from one. And why the negative symbols. Im sure this question is nonsense to an engineer or tech but Im stuck. Thanks

2. Mar 4, 2008

### Staff: Mentor

The fundamental equation to use when calculating the voltages and currents for a capacitor is the following:

$$i(t) = C\frac{dv(t)}{dt}$$

If you know the v(t) for the capacitor, you differentiate to get the i(t). If you know the i(t) for the capacitor, you integrate to get the v(t).

If you have a step change in current, you can solve the differential equation assuming a solution of the form:

$$v(t) = Ve^{\frac{-t}{\tau}}$$ subject to initial conditions, and where tau is related to the R and C values in the circuit.

So when you solve this differential equation for a series RC circuit where there is a step change in voltage across the whole RC, you end up with a solution for the voltage across the capacitor that looks something like:

$$v(t) = V_i * (1-e^{\frac{-t}{RC}})$$

You get the "1-" term, because the capacitor voltage exponentially approaches the full input voltage. If instead you were discharging the capacitor through a resistor, then you don't get the "1-" term.

This page at wikipedia.org may be of help to you too: http://en.wikipedia.org/wiki/RC_circuit

Welcome to the PF!

Last edited: Mar 6, 2008
3. Mar 5, 2008

### abk80

thank you that really helped.