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The circuit is the following:

schematic

simulate this circuit – Schematic created using CircuitLab

What is the equivalent resistance seen across Nodes 1 and 2? I am told it is R4 + R5. That means everything to the left is cut out.

1) Why can't current flow from across R3 to the left, into the short wire and bifurcate through the resistors R1 and R2, and back out through R3?

2) Why can't current flow across R3, into the short, and back out through the short?

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    \$\begingroup\$ Please justify why on earth that you think current can simultaneously flow in opposite directions through R3? Can a water pipe transport water in both directions simultaneously? \$\endgroup\$ – Andy aka Jun 10 '20 at 12:31
  • \$\begingroup\$ Can current flows both directions through a component at the same time? \$\endgroup\$ – user253751 Jun 10 '20 at 15:05
  • \$\begingroup\$ @user253751 Nope, due to the polarity of current, charges can only flow one way. Glad this question could be of use to you. \$\endgroup\$ – cccube Jun 12 '20 at 19:05
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No, the correct answer does not mean that "everything to the left is shorted out". In this case it is quite the opposite. There is no complete path for current to flow through "everything to the left" back to either Node1 or Node2. If no current can flow through these elements then they can not have any effect on the rest of the circuit. Therefore, they can be ignored.

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1) and 2) are not circuits. If current cannot flow in a circuit, it does not flow at all.

Why current must flow in a circuit is a different question...

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  • \$\begingroup\$ Why current must (usually) flow in a loop: electronics.stackexchange.com/questions/294940/… \$\endgroup\$ – cccube Jun 10 '20 at 13:08
  • \$\begingroup\$ (Conbentional) Current flows from higher positive potential to lower negative potential. There must be a complete path. Node 1, R4, R5 and Node 2 form a complete path. Whether a current flows depends on a potential being applied to Node 1 and 2. Rest of the circuit is a dead-end. \$\endgroup\$ – StainlessSteelRat Jun 10 '20 at 17:02

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