Fourier series and currents

Discussion in 'Homework Help' started by Niles, Dec 27, 2008.

  1. Niles

    Thread Starter Active Member

    Nov 23, 2008
    56
    0
    Hi all.

    Please look at the attached circuit. I have to find the current through the inductor given by I_L(t). The only thing I know is the following equation, which I have derived:

    <br />
\mathcal{E(t)} = L\frac{(R_1+R_2)}{R_2}\frac{dI_L}{dt}+R_1I_L.<br />

    I know that ε(t) is given by some function, whose Fourier series I know. Now my question is:

    Is it correct that the complex current through the inductor is given by:

    <br />
I(t) = \sum {\frac{\varepsilon }{Z}\exp ( - i\omega t)},<br />

    where Z is given by:

    <br />
Z =  - i\omega nL\frac{{(R_1  + R_2 )}}{{R_2 }} + R_1,<br />

    and ε is a complex amplitude?

    Thanks in advance.
     
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