RLL Circuit

Thread Starter


Joined Sep 24, 2008
Alright this is the circuit we're given...

We're asked to...

a)"Determine the differential equation that relates the input current x(t) to output current y(t)."

b) Find the characteristic equation for this circuit and express the roots of the characteristic equation in terms of L1, L2, and R.

c) Determine the zero-input response given initial inductor currents of 1 amp each. That is, find yo(t) given iL1(0) = iL2(0) = 1 A.

This is the only problem on my homework that I cannot figure out... I just need some help getting a starting point. Thanks!


Joined Jan 28, 2005
You are correct ameriland. For some reason, I was initially unable to view it but now I can see it just fine.



Joined Aug 9, 2008
Its been a while but this is what I would do.

1. From left to right ignore everything and reassign them basic a, b, c, d.
2. Do Kirchoff's law for current and voltage with the new letters.
3. Take each letter and convert it back into current or voltage.

Example of voltage across an inductor V = Lc di/dt.
(knowing this you can rearrange and integrate to make the equation for current through an inductor. (Instantanious charging/instantaneous discharging)

You will need to do the same for the current.

Here is a series problem solved that helps to understand were I a going with this.


Hope this helps.

Thread Starter


Joined Sep 24, 2008
well yeah... apparently my course is using the same book as you and I found your post, but no one ever really answered it... Did you ever figure it out?


Joined Mar 27, 2008
I remember seeing this. I believe Ratch had helped Vanush with it. Yeah, I just checked. Part of the problem was a lack of info.

There needs to be some clarification as to the source--does your problem use a sinusoidal current source or just x(t)?