One time constant in an RC circuit corresponds to which percentage of the final value for the capacitor voltage?

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Multiple Choice

One time constant in an RC circuit corresponds to which percentage of the final value for the capacitor voltage?

In an RC charging circuit, the capacitor voltage rises toward a final value following an exponential curve: Vc(t) = Vfinal [1 − e^(−t/RC)]. The time constant RC sets the time scale. At one time constant, t = RC, so e^(−1) ≈ 0.3679. That gives Vc(RC) ≈ Vfinal [1 − 0.3679] ≈ 0.6321 Vfinal, i.e., about 63.2% of the final value. The remaining 36.8% is what’s left to reach the final value (since e^(−1) ≈ 0.3679). A full 100% would require infinite time, and 86.5% isn’t the result produced by one time constant.

In an RC charging circuit, the capacitor voltage rises toward a final value following an exponential curve: Vc(t) = Vfinal [1 − e^(−t/RC)]. The time constant RC sets the time scale. At one time constant, t = RC, so e^(−1) ≈ 0.3679. That gives Vc(RC) ≈ Vfinal [1 − 0.3679] ≈ 0.6321 Vfinal, i.e., about 63.2% of the final value. The remaining 36.8% is what’s left to reach the final value (since e^(−1) ≈ 0.3679). A full 100% would require infinite time, and 86.5% isn’t the result produced by one time constant.

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