Now we'll exchange the AC voltage source for a 1V DC voltage source.
Since the frequency is 0Hz, X_{C} is infinite, so
there will be no current flow. That's true, but not for the first period
of time after connecting the voltage source as we already saw in the
introduction of this chapter.

Assume that capacitor C is completely discharged:
V_{C}=0 => V_{R}=1V. So the
current flow in resistor R will be 1mA. Having nowhere else to go to, this
current will flow 'in' the capacitor, charging it. While the capacitor is
charging, the voltage across it raises, leaving less voltage for resistor
R. This means that the current flow decreases. Suppose that after T
seconds, the capacitor is half full: V_{C}=0.5V. In
that case V_{R}=0.5V => I_{R} =
I_{C} = 0.5mA. So after 2T seconds, the capacitor will
not be completely charged since the current flow isn't 1mA anymore. To
calculate the voltage at any given time, use the following
equation.

V_{B} is the voltage of the DC voltage source. t
is the time in seconds since the capacitor was connected to the voltage
source. e is Euler's constant (2.7182818).

When t=RC, -t/(RC) will be -1 and V_{C} = 0.63V,
so the capacitor will be 63% full. This time is referred to as the 'RC
time'.

RC circuits are often used in timers, for example in a simple burglar alarm:

When you enter your own house, you don't want the alarm to go off immediately; you want to have some time to switch it off. In the circuit above you have R∙C = 100k∙100u = 10 seconds to do that. After 10 seconds the voltage across the capacitor will raise above 0.63V, and a switch will close causing the flash light to give alarm.