Hi everyone , i have a question about a the circuit shown in the attachmens (prolem image)

Given :
1- the circuit in the problem image
2- the switch has been closed for a long time and then opend at t=0

problem :
get the current through the inductor before opening the switch

Solution :

making an equivalent circuit for t<0 as show in the solution image, treating the the inductor like a short ciruict then it wil carry all the current from the current source , so the current through the inductor is 5A (or -5A considnering the refrence arrow).

My qustion :

i have no problem with treating the inductor as an short circuit while t<0 but i can't understand why erasing the 40V battery and the 4 ohm resistor from the equivalent circuit ? if there is no battery in the original circuit then there will be a short circuit across the 4 ohm resistor then we can get it out of the equivalent circuit but the battery is there so why treating it like it is not there ? shouldn't it make an amount of currents that affect the current passing through the inductor ??

thank you

 

With the switch closed, how can any current from the battery make it to the inductor. You have the battery and resistor on the left and the rest of the circuit on the right and they are connected by a single node, which means you have no circuit for current to pass between the left part and the right part.

 

For t<0 the switch is closed. This connects the 4 Ohm resistor to the negative side of the battery. In this condition there is current flowing through the 4 Ohm resistor. None of this current will be directed through the inductor.

The circuit can be redrawn to more clearly show this. Both the resistor and inductor can be independently shown to be connected to the bottom line in the drawing.

 

Zero amps throuh the inductor, reason no Voltage = no Current,

10 amps through the 4 ohm resistor..

 

For t<0 the switch is closed. This connects the 4 Ohm resistor to the negative side of the battery. In this condition there is current flowing through the 4 Ohm resistor. None of this current will be directed through the inductor.

The circuit can be redrawn to more clearly show this. Both the resistor and inductor can be independently shown to be connected to the bottom line in the drawing.

you mean the circuit can be drawn like this ?

 

For t<0, yes.

 

thank you all guys , you made my life a lot easier, i really appreciate it

 

Zero amps throuh the inductor, reason no Voltage = no Current,

10 amps through the 4 ohm resistor..

no voltage = no current?

On what do you base that?

If there is no current through the inductor, where does the 5 A from the current source go? Through the 16 Ω resistor? If so, then what's the voltage across the resistor? If that is non-zero, then how is there no voltage across the inductor?

 

Ok Einstein, where is the 5amps coming from?

 

Ok Einstein, where is the 5amps coming from?

Oh, I don't know....



Seems to me that a 5 A current source might, possibly, output, oh, say 5 A.

But that's just a wild guess.

 

So there must be another voltage source then, hey!

 

So there must be another voltage source then, hey!

Even if the current source has a voltage source imbedded in it, that does not make your statement that there is zero amps flowing in the inductor correct, does it?

And you do NOT need voltage in order for current to flow. Have you never heard of a superconducting magnet in persistent mode? Without any power source at all they will maintain current in the magnet for months will only a slight reduction due to parasitic losses.

 

Still doesn't explain where the 5amps is coming from does it.

 

Still doesn't explain where the 5amps is coming from does it.

It doesn't matter where it's coming from. The issue is where is it going?

It is coming from the 5 A current source. That is all that is needed for this problem.

You stated that there is zero amps in the inductor. You have not corrected that answer, so presumably you are standing by it. Fine. I asked you where the 5 A from the current source is going, if not through the inductor. You refuse to answer than question. Why?

 

I want to know why there isnt a voltage source listed for the 5amps supply, there must be two voltage sources, if there is only one voltage source then the current has to be zero.

 

So in other words, you don't understand what a current supply is.

 

If you want the 5 Amp current source to become a voltage source, change it to it's thevenin equivalent.

 

You could do that in this case only because a parallel resistance is given that you could absorb into the equivalent model. But this problem doesn't need that resistor there and, with it gone, the answer to the specific question asked doesn't change.

In general, you can't convert an ideal voltage source into a Norton equivalent or an ideal current source into a Thevenin equivalent -- the existence of an equivalent requires a non-zero, but finite, source impedance.