# Determining current in a branch having no resistor [closed]

In context to the diagram below , it is quite easy to find the current flowing through section AD , which turns out to be 2A , however , I cannot determine the current in any other branches with Kirchoff's Voltage Law . The branches AB,CD,DE and FA have no resistance across them so whenever I take those branches in any of the the possible loops , the potential drop/rise will always be 0 so the terms involving 'I' never appear and consequently they are indeterminable.So how do I find the magnitude of 'I' ?
In this particular case I can guess than I=1A with junction rule and the symmetry of the circuit - the batteries have same emf, so what if the emfs aren't same ? then the original problem comes up again.

## closed as off-topic by John Rennie, Jon Custer, GiorgioP, stafusa, ZeroTheHeroJun 29 at 11:44

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• Each branch will contribute 1A. I + I = x and x = 2A and I=I. – PhysicsDave Jun 1 at 17:08

As modeled, it's totally undetermined. $$I$$ could be any finite value, positive or negative, with no limits.

In the real world, it would be determined by the non-ideality of the two voltage sources. They won't both be exactly 10.000000 V, and they will both have non-zero equivalent internal resistance. Exactly how much would depend on how these sources are physically implemented.

what if the emfs aren't same?

Then you have a mathematically contradictory model. Say source BC has 10 V, and source FE has value 7 V. Then your schematic is equivalent to writing the equation

$$10\ {\rm V}=7\ {\rm V}$$

which is simply a mathematical false statement.

In the real world, the contradiction would be resolved by the sources having non-zero equivalent internal resistance.

• @ADITYAPRAKASH, no, I'm following the conventions you established in your schematic. $x$ is 2 A. The current flowing through one source is $I$ and through the other source $I-x$ (flowing in the positive terminal of the source). $I$ could be -1000 A, +2,000,000 A, or any other finite value. – The Photon Jun 1 at 16:17