When a 470 micro farad capacitor is discharged through a fixed resistor R, the pd across it decreases by 80% in 45 s. Calculate the time constant of the circuit

Using the equation V=V₀e^-t/RC where RC is the time constant to be calculated: We know that the pd decreases by 80%, therefore the pd remaining, V is 0.2*V₀. Putting this into the equation above: 0.2=e^-t/RC, rearranging for RC gives RC=-t/ln(0.2), and substituing t=45s, we have: RC=28 s. The answer reflects the time it takes for the potential difference across the resistor to decrease to 37% of its original value when the capacitor is discharged through it.