Final answer:
The time constant for a charging capacitor is the time it takes to reach about 63.2% of its maximum charge, so the closest answer would be option (e), which is about 66% of its maximum charge after one time constant.
Step-by-step explanation:
The time constant for a charging capacitor is defined as the time it takes the capacitor to reach approximately 63.2% of its maximum charge. When discussing the charging and discharging of capacitors in electronic circuits, the time constant is a critical concept and is represented as T = RC, where R represents the resistance and C the capacitance.
In the given options, none explicitly mention this percentage, but since one time constant correlates to the capacitor reaching 1 - (1/e), or approximately 63.2% of its full charge, the closest given answer would be option (e), the time it takes a capacitor to reach 66 % of its maximum charge. It is important to note that the charging curve of a capacitor is exponential, meaning that it never truly reaches 100% but asymptotically approaches its maximum charge.
Option (c) refers to the fraction of the charge after one RC time constant, which is approximately 63.2%, not 33%. Thus, option (e) would be the best selection if the choices are to be interpreted with some leniency towards typical round-off approximations in educational contexts.