There is no paradox, and verpies is wrong because the inductor does not represent a short the moment it is connected to something, even an ideal voltage source.

Indeed I would be wrong if I wrote this about an inductor connected to a voltage source as in Fig.2 , but I was writing about the circuit stipulated by Tinman, which is the circuit depicted in Fig.3.

The latter circuit is equivalent to the diametrically connected toroidal inductor that MH invented as an example and was analyzing in collaboration with me.

See, something MH said bothered me a bit. He said that a resistance of .000001ohm,  1uohm was virtually seemless to being an ideal inductor. Would you agree with that statement? Not trying to pit you against him. But it would be nice if that statement were to be considered true by you or not and give us your understanding as to why your answer is what it is. 

You can not really go by the absolute resistance alone to intuit if that will make the inductor act close to "ideal" or not. It really comes down to the ratio of the inductance to resistance, i.e. tau.

Yes, I would agree that 1u Ohm with 5H is sufficient to get good results when compared to an ideal inductor.

Let's explore if tau could be a good indicator of what inductance to resistance ratio is acceptable as an "ideal" inductor for our particular application. So let's look at MH's example, and use 1u Ohm as the inductor's series resistance: 5H/1u = 5Ms. That's a little less than 3/4 of a year. That is a ratio of 5M. Maybe this is excessive? We can also do some tests to see what might be reasonable: With R=10m Ohm, the end current after 3s is 2.389A, which is pretty close to 2.4. The L/R ratio for this case is 500. So we could establish this as a minimum ratio to achieve near-ideal results. If your L/R ratio is 500 or greater, you will achieve very close to ideal results.

Another example: if your inductance is 100mH, then you can have a maximum of 200u Ohm before it won't be so close to ideal when using the previous ratio of 500:1.

For interest sake, let's see how far we would be off with a ratio of 100:1. So with L=5H, that would be 50m Ohm. That gives us an average current of 2.34A, so the error is 2.5% or so? What is your desired tolerance? If 5% is acceptable, then perhaps we could go to a ratio of 50:1. Let's see: L=5H, R=100m Ohm. This gives us an average current of 2.28A, which is about a 2.28, exactly 5% error. If that is close enough, then we need only ensure a 50:1 L/R ratio to get results within 5% of ideal.

I agree with you on the no current flow at t/0 of an ideal inductor. 

So do I and I even came to the same conclusion in a step-by-step analysis of a resistive inductor here.

If resistance is zero, and no losses, then that underlying ideal inductor mechanism should be lossless and 100% efficient also. And if that mechanism is lossless then the the inductor should continuously impede an emf presented at the input.    

That's a reasonable thinking but note that constant and continuous impediment does not mean complete impediment.  The lack of complete impediment means that the current is not frozen and can increase with time.

That's why when an ideal voltage source is suddenly inserted into an ideal but finite deenergized inductor (as in Fig.2), the current through the inductor increases linearly from zero to infinite current in infinite time - not instantaneously.

PW says that a straight wire has inductance, and I agree, no matter how tiny the inductance is.

I agree with that too.

So it may be that the ideal straight wire may not be able to pass current if the inductance mechanism is 100% efficient.

but when this wire shares the inductor's flux and when the coupling coefficient (k) approaches unity, then this wire, and its inductance, becomes a part of the inductor and closes/completes it losslessly.

Why isnt the CEMF ideal also when it comes to the ideal inductor?

Because the CEMF is a function of reactance, not of resistance.

An ideal inductor must have zero resistance but it does not need to have an infinite inductance (nor infinite reactance).

I was agreeing with this as far as the wire resistance of a normal inductor being in series with the inductor, but when you got to the point where you stated "that entire circuit is closed by an ideal wire just like with an ideal inductor devoid of resistance" you lost me.

Are you referring to some circuit in particular or are you stating that the equivalent model for every inductor includes a short circuit across its terminals?

The model for a normal inductor has the wire resistance in series with the inductor.  The model for an ideal inductor removes that series resistor (or places its value at zero).  There is no short circuit across either inductor.

PW

Is this not the model below?
Regarding MHs question,will there not be an alternating current flow?
If we take into account that MH thinks DC means a steady state flow of current in one direction,then we would have to use the AC model to satisfy MH

Brad

You have an ideal voltage source and an ideal coil of 5 Henrys.  At time t=0 seconds the coil connects to the ideal voltage source. For three seconds the voltage is 4 volts.  Then for the next two seconds the voltage is zero volts. Then for two seconds the voltage is negative three volts, and then for the next six seconds the voltage is 0.5 volts.  Then after that the voltage is zero volts.
What happens from T=0 when the ideal voltage is connected to the ideal coil?.

After reading all of what has been posted from everyone here-->

At T=5 seconds,MHs device explodes.


Brad

Why is that Brad?

Why is that Brad?

Very simple Poynt.

As we have agreed on,while the ideal voltage source has a value of 0 volts,the current will continue to flow through this ideal inductor loop.
At T=5 seconds,the voltage source wants to instantly reverse that current flow direction.
So we have an ideal 5 Henry coil,with current flowing in say a CW direction around the loop.
At T= 5 seconds,the coil is instantly supplied negative 3 volts from an ideal voltage source.
At that instant,you have to infinite current values trying to flow in opposite directions.

Lets use MHs water flow in pipes analogy.
We have water flowing through a pipe at a set rate. We then try to change that flow of water to the opposite direction in an instant. The instantaneous pressure would be infinite if nothing gave out--but something will.

Here in this situation that is !ideal!,and no energy can be dissipated either by the ideal inductor,or the ideal voltage source,you have to wonder what will happen at the instant of the collision of the two meeting apposing current flows.

In order for the current to stop flowing,it must be dissipated into a load-one that can dissipate the energy of that current flow. Normally this can be done just through the resistance of the winding wire it self,but here we have ideal wire that cannot do this.

So at T=5 second's,something has got to give.

Brad