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

how long does it take to reduce the capacitor’s charge to 10 μc?

Answer:

Q = CV

V = Q/C = 30µ/20µ = 1.5 volts initial

final, V = 3/20 = 0.15 volts

voltage on a cap, discharging

v = v₀e^(–t/τ)

v₀ is the initial voltage on the cap

v is the voltage after time t

R is resistance in ohms,

C is capacitance in farads

t is time in seconds

RC = τ = time constant

τ = 20µ x 1.4k = 28 ms

v = v₀e^(–t/τ)

0.15 = 1.5e^(–t/28m)

e^(–t/28m) = 0.1

–t/28m = -2.303

t = (28ms)(2.303) = 64.5 ms

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