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Which of the following quantities is equal to the time constant for a charging capacitor? Select one:

a. the time it takes a capacitor to reach 50 % of its maximum charge
b. the time it takes a capacitor to reach 75 % of its maximum charge
c. the time it takes a capacitor to reach 33 % of its maximum charge
d. the time it takes a capacitor to reach its maximum charge
e. the time it takes a capacitor to reach 66 % of its maximum charge

1 Answer

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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.

User Justin Dominic
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