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I was trying to analyse an ideal transformer with one ideal independent voltage source on each winding.

I got a relationship between those voltage sources but it contradicts the fact that both voltage sources are independent of each other and there should not be any such relationship between them.

Here is my solution:

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What is the reason behind this contradiction?

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    \$\begingroup\$ You can't make such a circuit out of ideal components. It is not physical. You have two ideal entities forcing different voltages on the same point. \$\endgroup\$ – Eugene Sh. Nov 13 '20 at 15:11
  • \$\begingroup\$ If both voltage sources are the same value, frequency and phase then you can do it (for N=1). I don't see how you got the turns ratio to be negative though \$\endgroup\$ – Andy aka Nov 13 '20 at 15:20
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    \$\begingroup\$ The reason ideal components are ideal and cannot exist in reality is because a a contradiction can always be found somewhere when using them. If you find a contradiction with ideal components, it doesn't mean that there is something wrong with your work. \$\endgroup\$ – DKNguyen Nov 13 '20 at 15:52
  • \$\begingroup\$ You can find contradiction if you apply Kirchoff's law after you put an ideal 5V battery across an Ideal 10V battery as well. Or if you put a zero ohm resistor across a voltage source and calculate the voltage across the resistor using ohm's law. Lesson: Never linger too much on "Ideality". Let's think real. \$\endgroup\$ – Mitu Raj Nov 13 '20 at 17:19
  • \$\begingroup\$ What is M? what does MdI_1/dt accoutn for? \$\endgroup\$ – Buraian Mar 6 at 22:28
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A shorter version of this would be to replace an ideal 1:1 transformer with wires.

The result is the same: two independent sources in a fight.

An ideal transformer with a coupling constant of unity just reflects the voltage on one port to a scaled version on the other, at the same time that it reflects current. Because it is infinitely stiff in this regard, if you excite it with an ideal voltage source, you have to treat the other side as an ideal voltage source.

Ditto, if you excite one side with an ideal current source, you must treat the other side as an ideal current source.

When you use ideal components, you need to observe some rules to avoid conflicts like this (or you need to accept infinite currents and/or voltages). That's just how it is.

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To better understand the transformer behavior, insert 0.1 ohms in the left side, in series with the ideal voltage source.

And replace the right side source with a 100 ohm resistor.

Now vary that 100 ohms, and observe the current from the left side source, and observe the voltage across that 0.1 ohm resistor.

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