First Order RL Circuit: Finding a Current I2(0-)

[johnsmith7565]

Homework Statement

The switch in the circuit in Fig. P7.1 has been closed for a long time before opening at t=0.

a. Finding i1(0-) and i2(0-). I am stuck on this.

Relevant Equations

Mesh equations

V1r1 + V2r2 + ... + VnRn = 0

I shorted the inductor and performed mesh analysis. The solutions to the linear system were done using a calculator. The book says that the value for i2(0-) should be 15 mA but I'm getting -2mA. What am I doing wrong? I'm completely confused. Maybe mesh isn't the most efficient way to find I2 but it should work, right?

 

[Baluncore]

Currents are flowing at t=0, before switch is opened.
Short inductor, to find the voltage on the central node ?
Remove the short from the inductor after DC solution.
Then Ohms law to find initial currents i1 and i2 ?
What is inductor current ?
Switch opens, but current through inductor continues.
What are the currents i1 and i2 now ?

 

[johnsmith7565]

Currents are flowing at t=0, before switch is opened.
Short inductor, to find the voltage on the central node ?
Remove the short from the inductor after DC solution.
Then Ohms law to find initial currents i1 and i2 ?
What is inductor current ?
Switch opens, but current through inductor continues.
What are the currents i1 and i2 now ?

I’m going to do the first part of your question first.

Here is the node voltage equation:

(v-40)/500 + v/2000 + v/6000 = 0

Using a calculator I get v=30 V.

By ohms law: i2(0-) = -30/2000 = -0.0015 A. That’s right.
I1(0-) = 30/6000 = 0.005 A which is right. Why do I get the correct answers using the node voltage method but not by using the mesh method? That’s what confuses me.

 

[Baluncore]

I think you may have reversed the direction of i2 on the diagram.
Maybe you have as much trouble reading your writing as I do.