Solve RC Circuits: Instantaneous Voltage in Capacitors

[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. I am taking a course in electronics and the textbook isn't really clear on this. I have the equation:
-t/T
Vc=E(1-e )
t=RC
Not sure why I am subracting from one. And why the negative symbols. I am sure this question is nonsense to an engineer or tech but I am stuck. Thanks

 

[berkeman]

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!

 

[abk80]

thank you that really helped.