The percentage of the final value reached after one time constant.

• A. 63.2%
• B. 36.8%
• C. 50%
• D. 75%

Answer: (A)

When a first‑order system responds toward a final value, the approach is governed by the time constant. In an charging RC circuit, the capacitor voltage follows Vc(t) = Vfinal[1 − e^(−t/τ)]. At one time constant (t = τ), this becomes Vc = Vfinal[1 − e^(−1)] ≈ 0.632 Vfinal, so about 63.2% of the final value is reached. The remaining portion to reach the final value is e^(−1) ≈ 36.8%. That explains why 63.2% is the correct choice: it’s the actual fraction attained after one time constant. The other numbers don’t match the exponential progression: 36.8% is the portion left to reach the final value, 50% is the midpoint in a linear sense, and 75% would occur after more than one time constant.