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

In summary, an inductor is an electrical component that stores energy in the form of a magnetic field. When current flows through an inductor, it creates a magnetic field that opposes changes in current, known as inductance. The relationship between current and inductance is described by Faraday's law of induction. The inductance of an inductor can impact the flow of current, with higher inductance causing slower changes in current. Inductors have various practical applications, including filtering unwanted signals, regulating current flow, and controlling electricity in household appliances and electronic devices.
  • #1
Chunkysalsa
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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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  • #2
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
 
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FAQ: How Should You Solve an Inductor Current Problem Using Differential Equations?

What is an inductor?

An inductor is an electrical component that is designed to store energy in the form of a magnetic field. It is made up of a coil of wire that creates a magnetic field when an electric current passes through it.

How does current flow through an inductor?

When an electric current flows through an inductor, it creates a magnetic field around the coil. This magnetic field opposes any changes in the current, causing it to increase or decrease gradually. This is known as inductance.

What is the relationship between current and inductance?

The relationship between current and inductance is described by Faraday's law of induction, which states that the induced electromotive force (EMF) in a closed circuit is directly proportional to the rate of change of the magnetic flux through the circuit. In simple terms, the higher the current, the greater the inductance.

How is current affected by the inductance of an inductor?

The inductance of an inductor can have a significant impact on the flow of current. If the inductance is high, it will resist any changes in the current, causing it to take longer to reach its maximum value. On the other hand, a lower inductance will allow the current to reach its maximum value more quickly.

What are some practical applications of inductors?

Inductors are commonly used in electronic circuits to filter out unwanted signals and to store energy. They are also used in power supplies to regulate current flow and in motors and generators to control the flow of electricity. Inductors are also found in many household appliances, such as refrigerators and washing machines, as well as in computers and other electronic devices.

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