For a series RC circuit with R=1 kΩ and C=1 μF charging from 0 V to 12 V, calculate τ and Vc after t=3τ.

For a series RC circuit with R=1 kΩ and C=1 μF charging from 0 V to 12 V, calculate τ and Vc after t=3τ.

• A. τ = 0.5 ms; Vc(3τ) ≈ 11.0 V
• B. τ = 1 ms; Vc(3τ) ≈ 11.40 V
• C. τ = 2 ms; Vc(3τ) ≈ 12.0 V
• D. τ = 1 ms; Vc(3τ) ≈ 8.0 V

Answer: (B)

The key idea is how a series RC charges over time. The time constant τ equals RC, and the capacitor voltage follows Vc(t) = Vs(1 − e^{−t/τ}) as it charges toward the supply Vs. Compute τ: R = 1 kΩ = 1000 Ω, C = 1 μF = 1×10^−6 F, so τ = RC = 1000 × 1×10^−6 = 1×10^−3 s = 1 ms. At t = 3τ, with Vs = 12 V, Vc(3τ) = 12 [1 − e^{−3}] ≈ 12 × (1 − 0.0498) ≈ 11.40 V. So the correct values are τ = 1 ms and Vc(3τ) ≈ 11.40 V.

The key idea is how a series RC charges over time. The time constant τ equals RC, and the capacitor voltage follows Vc(t) = Vs(1 − e^{−t/τ}) as it charges toward the supply Vs.

Compute τ: R = 1 kΩ = 1000 Ω, C = 1 μF = 1×10^−6 F, so τ = RC = 1000 × 1×10^−6 = 1×10^−3 s = 1 ms.

At t = 3τ, with Vs = 12 V, Vc(3τ) = 12 [1 − e^{−3}] ≈ 12 × (1 − 0.0498) ≈ 11.40 V.

So the correct values are τ = 1 ms and Vc(3τ) ≈ 11.40 V.