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I crossed out the middle because it felt like it wouldn't make sense. (Mostly because i felt like conservation of current was violated.) But im not sure why it wont go through at that particular section. I thought whenever you have junction the current must go each pathway but why not in this case?

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Your intuition is correct, but explaining why clearly might be trickier.

Current only flows in a loop. There is no loop that includes your crossed out path.

If you wanted to consider that your crossed out path was in fact two conductors, and current flowed out and back along the same wire, then conservation of charge for each of the left hand and right hand bunch of nodes nodes means that the leftwards and rightwards current through that path are equal, and therefore cancel out to zero.

Or more simply, conservation of charge on each bunch of nodes means that no current flows between them.

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  • \$\begingroup\$ Your answer is actually very good. \$\endgroup\$ – MaximGi Mar 14 '16 at 9:10
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    \$\begingroup\$ @MaximGi I know it's right, the problem I have for something that fundamental, is that if you don't just grok it, it can be very difficult to convince \$\endgroup\$ – Neil_UK Mar 14 '16 at 9:13
  • \$\begingroup\$ OP, Neil UK explained this well. In case you want the circuit theory jargon for this concept it's called the cut-set form of Kirchoff's current law. \$\endgroup\$ – The Photon Mar 14 '16 at 17:08

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