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8 September, 23:32

A 24.0-V battery is connected in series with a resistor and an inductor, with R = 9.40 Ω and L = 6.40 H, respectively. (a) Find the energy stored in the inductor when the current reaches its maximum value. J (b) Find the energy stored in the inductor at an instant that is a time interval of one time constant after the switch

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  1. 8 September, 23:39
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    a) 20.81 J

    b) 8.29 J

    Explanation:

    V = iR + L di/dt

    where

    i = a (1-e^-kt)

    for large t

    i = V/R

    i = 24 / 9.4

    i = 2.55 A

    so

    i = 2.55 (1-e^-kt)

    di/dt = 2.55 k e^-kt

    24 = 24-24e^-kt + 6.4 (2.55) k e^-kt

    24 = 6.4 (2.55) k

    k = 24 / (6.4 * 2.55)

    k = 24 / 16.32

    k = 1.47 = R/L

    so

    i = 2.55 (1-e^ - (Rt/L))

    current is maximum at great t

    i max = 2.55 - 0

    energy = (1/2) L i^2

    E = (1/2) (6.4) 2.55^2

    E = 20.81 Joules

    one time constant T = L/R and e^ - (Rt/L) = 1/e =.368

    i = 2.55 (1 - 0.368)

    i = 2.55 * 0.632

    i = 1.61 amps

    energy = (1/2) (6.4) 1.61^2

    E = 8.29 Joules
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