Engineering Differential equation to represent circuit

[TigerBrah]

**edit** This problem has been solved.For the circuit shown in the figure, find a differential equation the relates the input current i₁(t) to the output voltage e₀(t). Note that you cannot take a KVL across a current source because you cannot figure out the voltage drop across it.

the circuit:

http://www.flickr.com/photos/70948910@N08/6412941773

my work so far:

http://www.flickr.com/photos/70948910@N08/6413318181/Am I on the right track? We never had any problems with a current source during the lectures, and I don't know if I can set the voltages of parallel branches equal like that.

Any ideas will be greatly appreciated! It has been very tough getting in touch with my professor over Thanksgiving break and this assignment is due tomorrow.

 

[gneill]

Hi TigerBrah, welcome to Physics Forums.

You're doing pretty well with the problem, but I think you'll want to keep R2 in the equations (rather than substituting e_o), since R2 influences the current in its branch. If you solve for the differential equation for the branch current, multiplying it through by R2 will give you the equation for the output voltage.

Another approach would be to use mesh currents. The first loop's mesh current is set by the input current, so you only have one loop to deal with.

Yet another approach would be to convert i_i(t) and R1 into a Thevenin equivalent voltage source and series resistance. Then you'd have a simple voltage divider to solve!

 

[TigerBrah]

Thanks gneill!

Using Mesh Currents is definitely the fastest way. I reworked the problem and got almost the same answer as above, but I also caught a mistake. My last term should be divided by R1.

I was also able to check my work using a secondary method we learned in class using Laplace transformations.

I appreciate your help!

 

[gneill]

Hey, glad to help