Transient response of a simple RC circuit

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? :-) )
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
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.