# RLL Circuit

#### ameriland

Joined Sep 24, 2008
3
Alright this is the circuit we're given...

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!

#### hgmjr

Joined Jan 28, 2005
9,029
Did you intend to attach a diagram? If not, it would be helpful if you would do that.

hgmjr

#### ameriland

Joined Sep 24, 2008
3

#### hgmjr

Joined Jan 28, 2005
9,029
You are correct ameriland. For some reason, I was initially unable to view it but now I can see it just fine.

hgmjr

#### SIcam

Joined Aug 9, 2008
61
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)
http://www.ecelab.com/inductance-equations.htm

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.

http://commons.bcit.ca/math/examples/elex/differential_eqns/index.html

Hope this helps.

#### ameriland

Joined Sep 24, 2008
3
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?

#### silvrstring

Joined Mar 27, 2008
159
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)?

#### Vanush

Joined Apr 19, 2008
46
The question is supposed to be solved in the time domain