# 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:

$
\mathcal{E(t)} = L\frac{(R_1+R_2)}{R_2}\frac{dI_L}{dt}+R_1I_L.
$

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:

$
I(t) = \sum {\frac{\varepsilon }{Z}\exp ( - i\omega t)},
$

where Z is given by:

$
Z = - i\omega nL\frac{{(R_1 + R_2 )}}{{R_2 }} + R_1,
$

and ε is a complex amplitude?