The Time Constant (AQA A Level Physics): Revision Note

The time constant

• The time constant of a capacitor discharging through a resistor is a measure of how long it takes for the capacitor to discharge

• The definition of the time constant is:

The time taken for the charge, current or voltage of a discharging capacitor to decrease to 37% of its original value

• Alternatively, for a charging capacitor:

The time taken for the charge or voltage of a charging capacitor to rise to 63% of its maximum value

• The value 37% is 0.37 or $\frac{1}{e}$ (where $e$ is the exponential function) multiplied by the original value ($Q_0$, $I_0$ or $V_0$)

• This is represented by the Greek letter tau, $\tau$, and measured in units of seconds (s)

  • It is a useful way of comparing the rate of change of similar quantities e.g. charge, current or p.d

• It is defined by the equation:

$\tau =RC$

• Where:

  • $\tau$ = time constant (s)

  • $R$ = resistance of the resistor (Ω)

  • $C$ = capacitance of the capacitor (F)

• For example, to find the time constant from a voltage-time graph, calculate $0.37V_0$ and determine the corresponding time for that value

• The time to halve, $t_{1/2}$ (half-life) for a discharging capacitor is:

The time taken for the charge, current or voltage of a discharging capacitor to reach half of its initial value

• This can also be written in terms of the time constant:

$t_{1/2}=0.69\tau =0.69RC$