Partial RL Circuit: Solving for Current in Inductor with Kirchhoff's Rules

[Ithryndil]

Homework Statement

A current pulse is fed to the partial circuit shown in Figure P32.25. The current begins at zero, then becomes Imax = 7.0 A between t = 0 and t = 200 µs, and then is zero once again. Determine the current in the inductor as a function of time. Let L = 1.0 mH and R = 100 . (Use t as appropriate.) Figure

Homework Equations

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The Attempt at a Solution

I know I need to use Kirchhoff's rules for this. I am not quite sure how to go about setting this up...I know I will have:

Emf - IR - L(dI/dt) = 0

Since there is no Emf this becomes:
L(dI/dt) = - IR

I am not sure where to go from here. I have the correct answer for $$0\leq$$ $$t$$ $$\leq200\mu s$$ being:

$$I(t) = 7(1 - e^{-100000t})$$

I also am not sure how to proceed with finding the current for t > 200 microseconds.

 

[Ithryndil]

I know that Iresistor must be:

Iresistor (I2) = Iinitial(I1) - Iinductor(I3).

However, whenever I use that I can't ever seem to get the actually statement they are getting for Iinductor. I get this DE:

L(dI3/dt) = -I2*R.

When I solve that I get:

I3 = I1 + e^(-Rt/L)

That expression doesn't seem right, and is not right.

 

[hyperon]

Since there is no Emf this becomes:
L(dI/dt) = - IR

This is the DE you need. The boundary condition is just continuity with the earlier function you found.

 

[Ithryndil]

I am not sure I follow what you mean about the earlier function. Are you talking about Kirchhoffs rule with the Emf in it?