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Kelsie Sawayn

Feb 20, 2025

A 20.0μF capacitor initially charged to 30.0μC is discharged through a 1.40kΩ resistor. How long does it take?

A 20.0μF capacitor initially charged to 30.0μC is discharged through a 1.40kΩ resistor. How long does it take to reduce the capacitor’s charge to 3.00μC ?_________ms
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Madie Hilpert

Feb 20, 2025

Q = CVV = Q/C = 30µ/20µ = 1.5 volts initialfinal, V = 3/20 = 0.15 voltsvoltage on a cap, dischargingv = v₀e^(–t/τ)v₀ is the initial voltage on the capv is the voltage after time tR is resistance in ohms, C is capacitance in faradst is time in secondsRC = τ = time constantτ = 20µ x 1.4k = 28 msv = v₀e^(–t/τ)0.15 = 1.5e^(–t/28m)e^(–t/28m) = 0.1–t/28m = -2.303t = (28ms)(2.303) = 64.5 ms... Show More
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