How to Solve for i(t) in a Circuit with a Step Function Source and an Inductor

[Cocoleia]

Homework Statement

I am given that vs(t)=25u(t)-10 and the following circuit

Homework Equations

The Attempt at a Solution

I would set the 12H and 8H as short circuits and then try to use KVL to find the current, but this doesn't work. I know that the answer is: 90-150e^-5t mA

 

[jedishrfu]

What level of study? What other rules have you been given?

Did your book have a step by step solved example?

 

[Cocoleia]

What level of study? What other rules have you been given?

Did your book have a step by step solved example?

2nd year university level, I wasn't given any rules for this question. My book has some solved examples, but they are different from this one. I just don't know where to start on solving this problem

 

[jedishrfu]

Check this lesson:

http://people.seas.harvard.edu/~jones/es154/pages/nicetut/book4/Lcircuits.html

It uses KVL and KCL to solve it.

 

[gneill]

Before doing anything I'd suggest simplifying the circuit first, making a Thevenin equivalent out of the resistor network. That would leave you with a single loop containing a (scaled) source function, one resistor, and one inductor.

Then consider the implications of the source function having a non-zero component that predates time t = 0. Hint: it might be helpful to find the steady state conditions for t < 0 and t >>0. How will the transition between those states look (what form will it take graphically)?