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Energy stored in coil with given relationship between current and flux

  1. Aug 12, 2012 #1
    1. The problem statement, all variables and given/known data

    The relationship between the current in an N-turn coil and the flux created by it is given as:

    [tex] \Phi = \frac{ai}{b+ci}[/tex]

    Determine the energy stored in the coil when the current varies from 0 to I.

    2. Relevant equations

    [tex] W = N \int{i d\Phi} [/tex]

    3. The attempt at a solution

    Started by differentiating the given relationship with respect to i, using the quotient rule

    [tex] \frac{d\Phi}{di} = \frac{a(b+ci) - cai}{(b+c{i}^2)} \\ \\
    \Rightarrow d\Phi = \frac{a(b+ci)}{{(b+ci}^2)}di - \frac{aci}{(b+ci)^2}di

    [/tex]

    I then proceed to substitute this expression for [tex]d\Phi[/tex] into the equation for W above, and setup two integrals (one for each term), integrating with respect to i from 0 to I.

    Problem is, the integrations are very complex to do by hand, and they aren't in a general form to lookup in a table. This leads me to believe i've made a mistake somewhere, but i can't seem to find it.

    Any help would be greatly appreciated, thanks.
     
  2. jcsd
  3. Aug 12, 2012 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    You might try integration by parts.
     
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