Question Detail
Question
A 10 µF capacitor is charged by a 24 V battery through a 400 kΩ resistor. After 1s, what is the voltage across the resistor?
Correct Answer
Option D is the correct answer.
Detailed Explanation
In an RC charging circuit, the voltage across the resistor as a function of time is given by VR(t) = Vbattery * e(-t/RC). Given: C = 10 µF = 10 x 10-6 F = 10-5 F, R = 400 kΩ = 400 x 103 Ω = 4 x 105 Ω, Vbattery = 24 V, t = 1 s. First, calculate the time constant τ = RC: τ = (4 x 105 Ω) * (10-5 F) = 4 s. Now, calculate the voltage across the resistor at t = 1 s: VR(1s) = 24 V * e(-1s / 4s) = 24 * e(-0.25) VR(1s) ≈ 24 * 0.7788 ≈ 18.69 V. The closest option is 18.7 V.
Hint
Recall the formula for voltage across the resistor in an RC charging circuit: VR(t) = Vbattery * e(-t/RC). Don't forget to calculate the time constant first.