An uncharged capacitor is charged through a resistor from a battery. What fraction of its final voltage does it reach after one time constant?

1. Charging follows an exponential approach to the battery emf rather than a straight line. 2. One time constant closes 0.632 of the gap to the final value. 3. In the next time constant it closes 0.632 of what remains, and so on without ever arriving. 4. The complementary figure 0.368 is what is left of the gap, and it is also the discharging fraction. 5. The value 1.000 would mean the capacitor arrives exactly at the emf, which an exponential never does. _Source: OpenStax College Physics (CC BY 4.0), Ch 21 "Circuits and DC Instruments", section 21.6 DC Circuits Containing Resistors and Capacitors_