This problem has been vexing me for a couple of hours. The professor blew through the subject pretty quickly today, and as luck would have it, the TA simply didn't show up to her office hours today, so here I am.

Problem:

Work:

I think I've got it pretty correct up until this point. Basically I'm just confused about two things:

1. Because my resistance is negative, I'm going to have a negative time constant, which means my current will increase exponentially. That seems fishy, given that in all other problems I've done involving un-driven RL circuits, the exact opposite happens.

2. What I really am unsure of is what happens after the switch opens up after 0.03 s and how to reflect that in my i(t). Right now I think my i(t) only tracks the current before the switch opens up.

 

I think I've got it pretty correct up until this point. Basically I'm just confused about two things:

1. Because my resistance is negative, I'm going to have a negative time constant, which means my current will increase exponentially. That seems fishy, given that in all other problems I've done involving un-driven RL circuits, the exact opposite happens.

Okay, but you are comparing apples and oranges. The RL circuit is not undriven prior to the switch opening.

2. What I really am unsure of is what happens after the switch opens up after 0.03 s and how to reflect that in my i(t). Right now I think my i(t) only tracks the current before the switch opens up.

Your circuit changes at 30ms. So you need an expression that describes the behavior prior to 30ms and a different expression that describes it after 30ms, being sure that they satisfy the continuity constraints.