How much charge will have accumulated on the plates of a charging capacitor after a length of time equal to one time constant?

63% of the final charge

Explanation:

When a capacitor is connected to a battery/power supply, the capacitor charges following the exponential law:

where

is the final charge of the capacitor, which is

where C is the capacitance and the potential difference of the battery

t is the time

is the time constant of the circuit

Re-writing the equation,

After a time equal to one time constant,

Therefore the charge on the capacitor will be

Which means 63% of the final charge.

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