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14 June, 02:20

An RC circuit takes t = 2.5 ms to charge to 35% of its full charge after it weas connected to a battery, What is the total time it takes for the capacitor of this curcuit to charge to 95% of the full charge?

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  1. 14 June, 04:35
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    Answer: time taken to charge to 95%

    t = - 5.80[ln (1-0.95) ]

    t = 17.38ms

    Explanation:

    For an RC Charging circuit

    Where Vs

    Vc = Vs (1 - e^ (-t/RC))

    Vc/Vs = 1 - e^ (-t/RC)

    -t/RC = ln (1 - Vc/Vs)

    t = - RC[ln (1 - Vc/Vs) ] and RC = k = - t/ln (1 - Vc/Vs)

    Where;

    Vc = voltage across the capacitor

    Vs = voltage supply

    t = charging time = 2.5ms

    k = RC = time constant.

    Vc/Vs = 0.35

    To calculate the time constant k;

    k = - t/ln (1 - Vc/Vs)

    k = - 2.5/ln (1-0.35)

    k = 5.80ms

    time taken to charge to 95%

    t = - 5.80[ln (1-0.95) ]

    t = 17.38ms
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