# Transient response of a simple RC circuit

The switch is closed at time=0. After the switch is closed, the voltage on the capacitor changes from its initial value to a value that aproaches Vb in an exponential manner.

The following equations describe the voltage change with regard to time.

Vc(t) = Vb + (Vc(0) - Vb)e^(-t/T) T = RC

Where:

C Is the value of the capacitor in farads. e is 2.718 (you knew that, right? :-) )(The base of the natural logrithm) R Is the value of the resistor in ohms. t Is the time in seconds after the switch is closed. T Is actually Tau, but that's not in ASCII (Which was all we could count on when this was posted) It is the time constant, the product of R and C Vb Is the voltage supplied by the voltage source. In this case, the battery symbol represents an ideal voltage source. Vc(t) Is the voltage across the capacitor at the specified time.