If the voltage sources A and B were ideal and identical then source A would "see" a resistance RC in the range 100 Ohm .. infinity, and source B would see a resistance RD in the same range, with the constraint RC * RD / (RC + RD) = 100 Ohm.

If A and B were not ideal but identical then each source would deliver the same current as if a 200 Ohm resistor were connected to each source alone.

If A and B were ideal sources but not identical the circuit were "impossible" (infinite current through both sources).

If A and B were real sources (each one adequately modelled as an ideal source plus a series resistor RA resp. RB) and were not identical, generally, the additional current delivered by source A when the 100 Ohm resistor RE is added would be

(VA * RB^2 + VB * RA * RB) / ((RA + RB) * (RB * RE + RA * (RB + RE))), and for source B accordingly after the necessary changes of indices and signs.

To have an interesting discussion, we first need an interesting question and then - interesting answers... written by interesting authors. I think these requirements are fulfilled here:)

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This question provoked my interest because it is closely related to the BJT differential pair, where the outputs of two emitter followers ("voltage sources") are connected in parallel to a common emitter resistor. I would present my reasoning in the form of imaginary experiments - my favorite technique of understanding and explaining basic circuit phenomena.

If the voltage sources A and B were ideal and identical... I propose to build this circuit in the following sequence:

First, imagine we connect the ideal voltage source A to the 100 ohm resistor R. As a result, the current IA = VA/R will flow through the resistor.

Then let's connect the second ideal voltage source B in parallel to the same resistor. What will happen? I think nothing... Why? Just because the two voltages are absolutely equal... so there is no voltage difference... there is no current flowing... The voltage source A will continue "seeing" only the resistor R... and nothing else... it will not see the voltage source B...

Now let's swap the roles first connecting the ideal voltage source B to the 100 ohm resistor R. As a result, the current IB = VB/R will flow through the resistor.

Then let's connect the ideal voltage source A in parallel to the same resistor. Again nothing will happen because the two voltages are absolutely equal... There is no voltage difference... there is no current flowing... and the voltage source B will continue "seeing" only the resistor R... and will not see the voltage source A...

Very interesting - as though, this configuration possesses a memory... like a latch?!? And we can switch this latch by disconnecting for a moment one or the other source?

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What is absolutely certain in this "ideal" configuration is that the current flowing through the resistor R is I = VA/R = VB/R... but what is not clear is where the current is taken from (voltage source A, B or both).

Hi Cyril,

I agree that including time renders the question even more interesting.

On first glimpse, I completely agree with your imaginary experiment, and I have the impression that Faraday's law is at the bottom of the proposed fact that after connecting the second source both currents remain unchanged (V / 100 and 0).

On second thought, I'm uncertain about the definition of circuits involving ideal elements: Does it make sense to connect an ideal source with an ideal resistor by real conductors, having finite dimensions and hence a magnetic field?

If so, after connecting the first source the current will increase according to V / R * (1 - exp(- t * R / L)). In this case, we have not a binary latch but an analogous one: We can store any possible current distribution by connecting the second source at the right moment, provided the experiment takes place in a noiseless world!

The other case is hard to imagine: Both sources and the resistor had to be point-like, and at the same location. In this case, I don't know which mechanism could keep the currents from fluctuating randomly, always summing up to V / 100, of course.

Based on the difficulty presented by several elements occupying the same location, I'm inclined to vote for the first case.

But on the whole, I feel that the art of idealization includes the ability to neglect certain properties of an element without pondering too much on the physical consequences. ;-)