Capacitors discharge exponentially. That means that their charge falls away in a similar way to radioactive material decay. In radioactivity you have a half-life, in capacitance you have a 'time constant'.
The rate of removal of charge is proportional to the amount of charge remaining.
As time steps forward in equal intervals, T (called the time constant), the charge drops by the same proportion each time. It turns out that each for interval, T, the charge or current drops to about 0.37 (37%) of its initial value. (Note: For the mathematicians amongst you, this number can be calculated using 1/e, where e is the exponential constant with a value of 2.718.)
We can calculate the time constant, T using the equation:
T = RC
T = time constant
R = resistance in the circuit (Ω)
C = capacitance of the circuit (F)
So the factor that governs how quickly the charge drops is a combination of the capacitance of the capacitor and the resistance it is discharging through.
In practice it takes 0.69 x RC (ln2 x RC) for the charge to be half its original value. In this time the discharge current also drops to half its original value too.
To calculate the charge left, Q, on a capacitor after time, t, you need to use the equation:
Q0 = initial charge on the capacitor
Q = charge on the capacitor at any time
t = time
RC = time constant
Likewise the current or voltage at any time can be found using:
As all of these relationships are exponential, natural log graphs can be drawn to obtain values for the time constant. For instance:
(Remeber for y = mx + c
m gives the gradient of the graph
c is the intercept on the y axis when x = 0)
The potential difference across the plates of a capacitor is directly proportional to the charge stored on the plates. This gives a straight line through the origin on a voltage-charge graph. The area under this graph gives the energy stored in a capacitor.
As the area under the graph is a triangle,
area = ½ base x height.
Note: the energy used by the cell to charge the capacitor, W = QV, but the energy stored on the capacitor = 1/2 QV. So half the energy is lost in the circuit as heat energy as the capacitor is changed.
As capacitors are able to store energy, they can be used in back-up systems in electrical devices, such as computers.