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When using lumped circuit abstraction, if we consider two ends of a voltage source connected with ideal wire KVL won't hold; and also if we put two current sources opposite two each other, then the node in between won't obey KCL. Since there is no change in magnetic flux or other lumped circuit abstraction restrictions; what causes the Kirchhoff's laws to be wrong?

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Kirchhoff's Laws are not wrong, the problem is that you constructed an invalid circuit. Remember that when we talk about ideal sources that we are using a mathematical model that has certain specified properties by definition. The definitions of the ideal voltage and current sources say nothing about magnetic flux nor do they care.

In order to make useful circuit models with these ideal element models we must obey certain rules. One of those rules is that you can not connect two ideal voltage sources in parallel if they have different values. Another is that you can not connect two ideal current sources in series if they have different values. It's as simple as that. You must follow the rules if you expect to create a useful circuit model.

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Make the sources the tiniest amount imperfect, perhaps they have an ESR or 1 pico-ohm, and a voltage difference of 1 femto volt, In reality you will never have ideal sources, so parts per million errors can be mixed in while not affecting the actual results,

Resistors on their own have thermal noise voltage, so in any circuit with any resistance there is always a voltage and current change, if you wanted to you could model any non perfect wire as an AC current source in series or voltage source in parallel if you really wanted to keep it tied to real world concepts.

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