How Should You Solve an Inductor Current Problem Using Differential Equations?

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SUMMARY

The discussion focuses on solving an inductor current problem using differential equations, specifically for the scenario where a switch closes at t=0. The correct solution for the inductor current is identified as 6 - e^(-t/6) A. Participants explore various methods, including Kirchhoff's Voltage Law (KVL) and Thevenin equivalents, to derive the solution. Ultimately, the consensus is that employing a system of equations is necessary for accurate results, particularly when dealing with complex circuits.

PREREQUISITES
  • Differential equations, specifically in the context of electrical circuits
  • Understanding of inductor behavior in circuits
  • Knowledge of Kirchhoff's Voltage Law (KVL)
  • Familiarity with Thevenin's theorem for circuit simplification
NEXT STEPS
  • Study differential equations applied to electrical circuits
  • Learn how to derive inductor current using KVL
  • Research Thevenin equivalents and their applications in circuit analysis
  • Explore advanced circuit simulation tools for verifying theoretical results
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in analyzing and solving inductor current problems using differential equations.

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Homework Statement



Find inductor current for t > 0
http://img192.imageshack.us/img192/5814/unledgo.png
Switch is initially open and closes at t=0+

The professor wants us to solve these only using the Diff Eq approach. On other questions I would just do a KVL with the inductor loop and solves the resultant ODE. However with this one I would have to do a system of equations. I'm not to sure if that's what I'm supposed to do or even how to do that math.

I also tried taking the inductor out and doing a thevenin equivalent. I get the correct time constant this way but the constants of integration are way off.

I really just don't know how to approach this problem.

fyi I'm told the answer is 6 - e^(-t/6) A,whoops sorry for the typo in title, been a tiring day.
 
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Well since i drew up that schematic to post here I figured I'd run the simulation as well. So I haven't found my error yet but it looks like doing a thevenin equivalent should yield me the correct answer.

Is this the best way to approach this problem though? I still feel like I'm missing some key idea here and my book is absolutely terrible at everything but pretty pictures.EDIT:
Figured out the problem
 
Last edited:

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