A 20.0μF capacitor initially charged to 30.0μC is discharged through a 1.40kΩ resistor. How long does it take?
A 20.0 μF capacitor, initially charged to 30.0 μC, is discharged through a 1.40 kΩ resistor. How long will it take for the capacitor's charge to decrease to 3.00 μC? Please provide your answer in milliseconds.
1 Answers
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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