A 20 μF capacitor initially charged to 30 μC is discharged through a 1.5 kΩ resistor. How long does it take to reduce the capacitor’s charge to 10 μC?

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Study for the UCF PHY2054 General Physics Exam. Use flashcards and multiple-choice questions complete with hints and explanations. Boost your understanding and get exam-ready!

Multiple Choice

A 20 μF capacitor initially charged to 30 μC is discharged through a 1.5 kΩ resistor. How long does it take to reduce the capacitor’s charge to 10 μC?

Explanation:
Discharging through a resistor makes the capacitor’s charge decay exponentially with a time constant RC. The charge follows Q(t) = Q0 e^{-t/(RC)}. Here Q0 is 30 μC, the target is 10 μC, and the resistance and capacitance give RC = (1.5×10^3 Ω)(20×10^-6 F) = 0.03 s. The fraction remaining is 10/30 = 1/3, so e^{-t/(RC)} = 1/3. Taking natural logs, t = RC ln 3 ≈ 0.03 s × 1.0986 ≈ 0.03296 s, which is about 33 ms.

Discharging through a resistor makes the capacitor’s charge decay exponentially with a time constant RC. The charge follows Q(t) = Q0 e^{-t/(RC)}. Here Q0 is 30 μC, the target is 10 μC, and the resistance and capacitance give RC = (1.5×10^3 Ω)(20×10^-6 F) = 0.03 s. The fraction remaining is 10/30 = 1/3, so e^{-t/(RC)} = 1/3. Taking natural logs, t = RC ln 3 ≈ 0.03 s × 1.0986 ≈ 0.03296 s, which is about 33 ms.

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