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.

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.