# series RL analysis using Laplace

• Mar 23rd 2013, 11:08 AM
Mckiseldeck
series RL analysis using Laplace
Hi Guys,
Could anyone offer some assistance please?

I have a question which states the following:
L[v(t)] = V(s) = 1/(1+s^s)(1-e^(pi*s)
if an inductor (1 H) and a resistor (1 Ohm) are connected in series then show that the resulting current is,

i(t)=sigma(n=0,infinity).f(t-n*pi)
where f(t) =(sin(t)-cos(t)+e^(-t))u(t)

i am able to analysis the circuit to give the following:
L[di/dt] +L[Ri]=L[v(t)]
giving I(s)=1/(s+1)(s^2+1)(1-e^(pi*s))

using partial fractions it becomes:
I(s)=(1/(1-e^(-pi*s)))*0.5*((-s/(s^2+1))+(1/(s^2+1))+(1/(s+1))

I am really not sure where to go next, I am sure that 1/(1-e^(-s*pi)) is some kind of geometric series but other than that I am stumped!<br><br>I would really appreciate it if someone could point me in the right direction.
Regards,

Mckiseldeck
• Mar 23rd 2013, 06:57 PM
chiro
Re: series RL analysis using Laplace
Hey Mckiseldeck.

Have you considered using repeated applications of the convolution theorem?
• Mar 24th 2013, 07:57 AM
Mckiseldeck
Re: series RL analysis using Laplace
Quote:

Originally Posted by chiro
Hey Mckiseldeck.

Have you considered using repeated applications of the convolution theorem?