An RC circuit is one that contains a resistor and capacitor.
Consider the RC circuit shown in the figure. Suppose that the
switch is closed at time *t* = 0 s and
that the capacitor has no initial stored charge on it. Once the
switch closes, a current will begin flowing in the circuit.
This current will deposit charge on the capacitor, leading to a
voltage *vC*(*t*) across
the capacitor.

The current *i*(*t*) is given by the formula:

(equation 1)

for
where *i* is the current (in amperes),
*E* is the battery voltage (in volts),
*R* is the resistance (in Ohms,
Ω), *C* is the capacitance (in
Farads, F) and *t* is time (in seconds,
s).

- Find a formula for the capacitor voltage
*vC*(*t*). - Given that
*E, R*and*C*have the values shown in the diagram, find the capacitor voltage 2 seconds after the switch is closed. - How long after the switch is closed will the capacitor voltage be equal to 70% of its final value?

From Kirchhoff's voltage law we know that:

(equation 2)

Then from Ohm's law we have:

Thus the capacitor voltage reaches 70% of maximum after 1.20s.

Written by Jim Waterman, October 6, 1997