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18 June, 22:43

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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  1. 19 June, 02:33
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    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.
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