Question:

What is the effective resistance across this capacitor?

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A 0.02 microF capacitor is given a charge Q0. After 15 s, the capacitor's charge is 0.5Q0. What is the effective resistance across this capacitor? Answer in units of M­.

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  1. "Answer in units of M" huh?  Resistors are in ohms.

    Charge goes to half, voltage also goes to half

    v = v₀[1 - e^(-t/RC)]

    v/v₀ = 1 - e^(-t/RC)

    0.5 = 1 - e^(-15/R(0.02uF))

    0.5 = e^(-15/R(0.02uF))

    ln of both sides

    -0.693 = -15/R(0.02uF)

    15*R*0.02uF = 0.693

    R = 0.222 Mohm or 222 kohm

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