Fourier series and currents

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

  1. Niles

    Thread Starter Active Member

    Nov 23, 2008
    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.