The RC time constant
A capacitor charges through a resistor from a battery. After one time constant (τ = RC), the capacitor's voltage has reached about what fraction of the battery voltage?
Answer C: explanation for every choice
A
37% (e⁻¹) is what remains during discharge, or the fraction still to be gained during charging.
B
50% is reached at about 0.69 RC.
C
Correct. V(t) = V₀(1 − e−t/RC). At t = RC, that's 1 − e⁻¹ ≈ 0.63.
D
Charging approaches 100% only gradually, after about 5 time constants.
TakeawayAfter one τ: charging reaches ~63%, discharging falls to ~37%.
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Reviewed 2026-11-05 by a medical student. Spot an error? Report it with question ID cp123.