Discharging a capacitor — common mistakes

Pay close attention to units, especially for capacitance (Farads) and resistance (Ohms) when calculating the time constant. Milliseconds, microseconds, kilohms, and megaohms are common, so convert them to base units (seconds, Farads, Ohms) before calculations. When asked to determine a value from a graph, always show your working by drawing a large triangle on the graph and stating the coordinates you used to calculate the gradient.

Exponential decay means that the charge, voltage, and current decrease by a constant fraction over equal time intervals, rather than by a constant amount. This results in a curve that drops quickly at first and then levels off.

As the capacitor discharges, the amount of charge stored on its plates decreases. This directly reduces the potential difference (voltage) across the capacitor. According to Ohm's Law (I = V/R), a lower voltage across the resistor leads to a smaller current.

The time constant dictates how fast a capacitor charges or discharges. In timing circuits (like traffic lights or blinking LEDs), engineers choose specific R and C values to achieve desired delays. For filtering or smoothing circuits, a larger time constant might be chosen to maintain a stable output voltage longer.

You can plot a graph of the natural logarithm of the voltage (ln V) against time (t). This produces a straight line. The time constant τ is the negative reciprocal of the gradient (τ = -1/gradient).