A charged capacitor discharges through a resistor. What fraction of its starting voltage is left after one time constant?
A0.368 of it
B0.632 of it
C0.500 of it
D0.050 of it
Answer & Solution
Correct answer: A. 0.368 of it
1. Discharge is an exponential decay towards zero, set by the same time constant as charging.
2. After one time constant the voltage has fallen to 0.368 of the value it started from.
3. In each further time constant it falls to 0.368 of whatever it had at the start of that interval.
4. So after three time constants only about 5 percent of the starting voltage is left.
5. The figure 0.632 belongs to charging, where it is the fraction of the gap already closed.
_Source: OpenStax College Physics (CC BY 4.0), Ch 21 "Circuits and DC Instruments", section 21.6 DC Circuits Containing Resistors and Capacitors_
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