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18 July, 16:34

Find the time t2 that it would take the charge of the capacitor to reach 99.99% of its maximum value given that r=12.0ω and c=500μf.

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  1. 18 July, 18:52
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    Given that,.

    R = 12 ohms

    C = 500μf.

    Time t = ? When the charge reaches 99.99% of maximum

    The charge on a RC circuit is given as

    A discharging circuit

    Q = Qo•exp (-t/RC)

    Where RC is the time constant

    τ = RC = 12 * 500 * 10^-6

    τ = 0.006 sec

    The maximum charge is Qo,

    Therefore Q = 99.99% of Qo

    Then, Q = 99.99/100 * Qo

    Q = 0.9999Qo

    So, substituting this into the equation above

    Q = Qo•exp (-t/RC)

    0.9999Qo = Qo•exp (-t / 0.006)

    Divide both side by Qo

    0.9999 = exp (-t / 0.006)

    Take In of both sodes

    In (0.9999) = In (exp (-t / 0.006))

    -1 * 10^-4 = - t / 0.006

    t = - 1 * 10^-4 * - 0.006

    t = 6 * 10^-7 second

    So it will take 6 * 10^-7 a for charge to reached 99.99% of it's maximum charge
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