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Math Help - AC circuit intergration by parts equation

  1. #1
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    AC circuit intergration by parts equation

    Could any body help i have been trying to solve the solution to an equation for my maths assignment but doesnt match the given final solution that i have. The equation is:

    Given that L di/dt + Ri = Esin wt and that i=0 when t=0 show that the solution of the equation is given by

    i= [E / R^2 + w^2 L^2](Rsin wt - wL cos wt)+ [ E w L/R^2+w^2 L^2] e ^-Rt/L

    Can any body help me???
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  2. #2
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    Quote Originally Posted by sarnekat View Post
    Could any body help i have been trying to solve the solution to an equation for my maths assignment but doesnt match the given final solution that i have. The equation is:

    Given that L di/dt + Ri = Esin wt and that i=0 when t=0 show that the solution of the equation is given by

    i= [E / R^2 + w^2 L^2](Rsin wt - wL cos wt)+ [ E w L/R^2+w^2 L^2] e ^-Rt/L

    Can any body help me???
    Since it's a show question, two approaches are available to you:

    1. Substitute the given solution into the differential equation and show that equality is obtained,

    or

    2. Solve the differential equation \frac{d i}{dt} + \frac{R}{L} i = \frac{E}{L} \sin (\omega t). You could use the integrating factor method here.

    Please show what you've done and where you get stuck.
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