Question Detail
Question
A 2µF capacitor is charged to 50V and then discharged through a 1 MΩ resistor. Find the time for the capacitor voltage to drop to 25V.
Correct Answer
Option D is the correct answer.
Detailed Explanation
Time constant τ = RC = (1×10⁶)(2×10⁻⁶) = 2 s. V(t) = V₀ e^{-t/τ}. 25 = 50 e^{-t/2} → 0.5 = e^{-t/2} → ln(0.5) = -t/2 → -0.693 = -t/2 → t = 1.386 s ≈ 1.39 s.
Hint
Use V = V₀ e^{-t/RC}.