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[n00b alert]

I'm wondering why there's no current across the 4-ohm resistor. Circuit

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    \$\begingroup\$ I'm wondering what's connected to A and B . \$\endgroup\$ – Nick Alexeev Jun 7 '16 at 22:40
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    \$\begingroup\$ Current goes through a resistor, voltage appears across it. \$\endgroup\$ – Barry Jun 7 '16 at 22:47
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    \$\begingroup\$ Does this make anyone cringe :O? Best to study electronic circuitry from the basics. And I'm right now a bit sceptical as to how the 10V battery only has a load of 5Ω which allows a dangerous amount of current, thus creating some significant heat. \$\endgroup\$ – Bradman175 Jun 7 '16 at 23:02
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You can think of A and B as having a resistor of infinite resistance between them. That's one way of defining an open circuit. As a result, the current in the loop containing the infinite resistance is zero. Current will only flow in a closed loop, at least at this level of analysis.

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The node A is not connected to anything. It's left open. Imagine a wire hanging loosely. It will not conduct any current. With resistor or otherwise.

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