# Write a Differential Equation that describes the current though inductor.

#### HPage5

Joined Jan 17, 2016
15
Hey all,

Working on a problem involving differential equations. My knowledge of DE's is pretty limited, as I am taking that class this semester too, and they have no coincided yet.

I have attached thumbnails of the given problem, and my work (the closest I've gotten yet).

I had a problem very similar involving RC and I solved that one fairly easily, but this one is throwing me.

My assumptions and method are as follow:

In the problem statement, The switch is in position 1 for a long time, then at t=0 the switch is thrown to position 2.

In that way, I assume there is nothing to account for in the center branch from the middle top node--so therefore I have accounted for nothing in that branch in my node equation. I know that after a long time L becomes a short, or loses all resistance.

Maybe nodal isn't the way go this time? Maybe I should be doing a mesh around the whole outside loop?

Given:

My work:

#### WBahn

Joined Mar 31, 2012
30,034
Look at the very first term of your very first equation. You are trying to write Ohm's Law for R1. But to do that, you need the voltage across R1. Is (v_L - V_S) the voltage across R1? You also have not defined the reference direction for i_L, which is asking for trouble.

#### HPage5

Joined Jan 17, 2016
15
Okay, I reworked it. Either, I did it right this time, or got lucky. Because I ended up with the solution given.

I tried a mesh approach. Going from the bottom left corner up the first branch and around to the right.

Attached is thumbnail of what I have now.

#### WBahn

Joined Mar 31, 2012
30,034
You got lucky -- and had you bothered to track your units you would have discovered that your very first equation is fundamentally wrong. The first two terms have units of amperes, but the third has units of volts. Thus you know that they can't be added together.