A 2.0-μF capacitor is charged to 12 V and then discharged through a 4.0 × 10⁶ Ω resistor. How long will it take for the voltage across the capacitor to drop to 3.0 V? A)4.5 s B)8.0 s C)11 s D)22 s E)24 s

Question

Quizplus · Accepted Answer

The time constant τ for an RC circuit is given by τ = R × C. Here, τ = 4.0 × 10^6 Ω × 2.0 × 10^-6 F = 8 s. The voltage across a discharging capacitor is given by V(t) = V0 * e^(-t/τ). Solving 3 = 12 * e^(-t/8) gives t ≈ 11 s.

A 20-μF Capacitor Is Charged to 12 V and Then Discharged