The current in a 25-mH inductor is given by the expressions i(t) = 0 t 0 Find th

Question

The current in a 25-mH inductor is given by the expressions i(t) = 0 t 0 Find the voltage across the inductor and the expression for the energy stored in it. Round the answers to 3 significant digits. V t 0 J t 0

Explanation / Answer

a. v = L.di(t)/dt     t < 0:    i(t) =0        v = 0     t > 0:    i(t) =10(1-e^-t) E-3                i'(t) = 10e^-t E-3 v = Li'(t)= 25E-3 * 10E-3 e^-t = 250E-6 e^-t                v = 250 e^-t    V b w = 1/2 Li^2     t < 0:    i(t) =0        w = 0     t > 0:    i(t) = 10(1-e^-t)E-3         i^2 = 100E-6(1-e^-t)^2                w = 1/2 Li^2 = 1/2 * 25E-3 * 100E-6 * (1-e^-t)^2                    = 1.25(1-e^-t)^2     J

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