To increase the rate of discharge, the resistance of the circuit should be reduced. This would be represented by a steeper gradient on the decay curve. The time constant of a discharging capacitor is the time taken for the current, charge or potential difference to decrease to 37 \% of the original amount.
The time constant of a discharging capacitor is the time taken for the current, charge or potential difference to decrease to 37 \% of the original amount. It can also be calculated for a charging capacitor to reach 63 \% of its maximum charge or potential difference.
To do this experiment, you will need the following: Large-value capacitors are required for this experiment to produce time constants slow enough to track with a voltmeter and stopwatch. CAUTION: Be warned that most large capacitors are of the electrolytic type, and they are polarity sensitive!
This process will be continued until the potential difference across the capacitor is equal to the potential difference across the battery. Because the current changes throughout charging, the rate of flow of charge will not be linear. At the start, the current will be at its highest but will gradually decrease to zero.
For the equation of capacitor discharge, we put in the time constant, and then substitute x for Q, V or I: Where: is charge/pd/current at time t is charge/pd/current at start is capacitance and is the resistance When the time, t, is equal to the time constant the equation for charge becomes:
It can also be calculated for a charging capacitor to reach 63 \% of its maximum charge or potential difference. The time constant \left (\tau\right) is proportional to the resistance and the capacitance of the capacitor. This can be represented in the equation: