Quantitative Treatment
We could use the graph above to find the charge on the capacitor after a time, t. We could also use it to find the time it takes for the charge to fall to a value of Q.
This requires the graph to be drawn very accurately and values need to be taken from it very carefully.
Instead of doing this we can use the following equation to calculate the charge, Q after a time, t.
t is the time that has elapsed since discharge began
Q is the remaining charge
Q0 is the initial (or starting) charge
RC is the time constant, also equal to the resistance multiplied by the capacitance.
Time is measured in seconds, s
When the time elapsed is equal to the time constant the charge should have fallen to 37% of the initial value.
(but e-1 = 0.37)
When the time elapsed is equal to twice the time constant the charge should have fallen to 37% of 37% of the initial value.
(but e-2 = 0.37 x 0.37)
Similar equations can be established for the current flowing through and the potential difference across the capacitor after time, t: