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

AI Thread Summary
The discussion revolves around calculating the initial current I2(0-) in a first-order RL circuit after shorting the inductor. The original poster is confused because their mesh analysis yields -2 mA, while the textbook states it should be 15 mA. A participant suggests using node voltage equations instead, which correctly calculate I2(0-) as -1.5 mA and I1(0-) as 5 mA. The discrepancy may stem from a possible error in the direction of current I2 in the diagram. The conversation emphasizes the importance of method selection and accuracy in circuit analysis.
johnsmith7565
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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
IMG-3091.jpg
IMG-3092.jpg


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?
 
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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 ?
 
Baluncore said:
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.
 
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.
 

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