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15 July, 21:11

A) The current that goes through a 100 mH inductor is given as

i (t) = 6 - 2e^-2t A t > = 0

Find the voltage v (t) across the inductor.

b) The voltage v (t) = 5sin (5t) V is applied across the terminals of a 200 mH inductor. The initial current through the inductor is i (0) = - 10 A. Find the current i (t) through the inductor for t > 0.

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  1. 15 July, 21:25
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    A) V (t) = 0.4e^-2t

    B) i (t) = (25tsin5t+10) A for t>0

    Explanation:

    Formula for calculating voltage across an inductor is expressed as:

    V = Ldi/dt

    Given L = 100mH = 100*10^-3

    If i (t) = 6 - 2e^-2t A t > = 0

    di/dt = (-2) (-2) e^-2t

    di/dt = 4e^-2t

    If t ≥ 0

    V (t) = 100*10^-3 * (4e^-2t)

    V (t) = 0.1*4e^-2t

    V (t) = 0.4e^-2t for t≥0

    B) Applying the same formula as above

    V = Ldi/dt

    Vdt = Ldi

    V/L dt = di

    On integration

    Vt/L = i + C

    When t = 0, i = - 10A

    Substituting the values into the formula

    V (0) / L = - 10 + C

    0 = - 10+C

    C = 10

    To get the current i (t) through the inductor for t>0,

    Since Vt/L = i + C

    Given V (t) = 5sin5t Volts

    L = 200mH = 200*10^-3H

    C = 10

    On substituting

    (5sin5t) t/0.2 = i + 10

    25tsin5t = i + 10

    i (t) = (25tsin5t-10) A for t>0
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