A 20 μF capacitor initially charged to 30 μC is discharged through a 1.5 kΩ resistor. Part A How long does it take to reduce the capacitor's charge to 10 μC? Express your answer with the appropriate units.

Question

Physics

Martha Huber

17 December, 02:08

A 20 μF capacitor initially charged to 30 μC is discharged through a 1.5 kΩ resistor. Part A How long does it take to reduce the capacitor's charge to 10 μC? Express your answer with the appropriate units.

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Answers (1)

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Kasey Thompson · Answer 1

it will take 36.12 ms to reduce the capacitor's charge to 10 μC

Explanation:

Qi = C*V

then:

Vi = Q/C = 30μ/20μ = 1.5 volts

and:

Vf = Q/C = 10μ/20μ = 0.5 volts

then:

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 1.5k = 30 ms

v = v₀e^ (t/τ)

0.5 = 1.5e^ (t/30ms)

e^ (t/30ms) = 10/3

t/30ms = 1.20397

t = (30ms) (1.20397) = 36.12 ms

Therefore, it will take 36.12 ms to reduce the capacitor's charge to 10 μC.