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Trip1
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Homework Statement
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.
Homework Equations
[tex] W = N \int{i d\Phi} [/tex]
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.