How to Calculate the Time Constant (τ) of a Capacitor

To calculate the Time Constant (τ) of a Capacitor, the formula to do this is:

Time Constant (τ)=RC

The unit for the time constant is seconds (s). R stands for the resistance value of the resistor and C is the capacitance of the capacitor.

The time constant is the amount of time it takes for a capacitor to charge to 63% of the voltage that is charging. Therefore, if a 10-volt DC source charges a capacitor, after one time constant, the capacitor will charge to 6.3V.

Example

Below we have a circuit of a 9-volt battery charging a 1000µF capacitor through a 3KΩ resistor:

One time constant, τ=RC=(3KΩ)(1000µF)=3 seconds. So after 3 seconds, the capacitor is charged to 63% of the 9 volts that the battery is supplying it, which would be approximately 5.67 volts.

More Examples

If R=1KΩ and C=1000µF, the time constant of the circuit is τ=RC=(1KΩ)(1000µF)=1 second.

If R=330KΩ and C=0.05µF, the time constant of the circuit is τ=RC=(330KΩ)(0.05µF)=16.5ms.