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I am sorry but I have no idea on how to rephrase my question, this is the best I could come up with.

But as they say, a picture is worth a thousand words.

Circuit

As you can see, the 2K resistor is "enclosed between the same node" for the lack of a better expression on my behalf, namely node (b). How would I treat this resistor?

To give some background information, this is for my Principles of Electrical Engineering course, all my previous knowledge of circuitry is from my Physics II course, and I must add that my professor did NOT do a good job in explaining basic circuit analysis.

Now back to the subject at hand, we are being asked to find the equivalent resistor and I could do that just fine. The thing is when I looked up the solution manual that the professor handed us, she had bypassed the 2K resistor but offered no explanation as to why she did that and I am assuming it is because the resistor is situated between node (b) on either ends.

Could someone be kind enough and explain to me what is happening and how should I treat such situation in the future?

Thank you in advance.

EDIT: Thanks to everyone who took their time to explain the concept to me. You guys are great. I get it now.

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    \$\begingroup\$ You can look at it as 2 resistors in parallel. One is 2K and the other is 0 ohms. Now, using the formula for parallel resistors, what's the resistance of the parallel combination? What can you replace the 2K resistor with? \$\endgroup\$ – John D Sep 7 '16 at 2:41
  • \$\begingroup\$ The current through the resistor is 0, so you can replace it with an open-circuit if that makes it easier. The voltage across the resistor is also 0, so you can replace it with a short circuit if you prefer. \$\endgroup\$ – mkeith Sep 7 '16 at 4:24
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    \$\begingroup\$ When this kind of doubt come to you a good advice is to give name to all the nodes, then start to reduce nodes that are equals (shorted), and finally redraw circuit. Often all things become clear. \$\endgroup\$ – Antonio Sep 7 '16 at 7:29
  • \$\begingroup\$ @Antonio that is what I usually do and I got to admit it does simplify things A LOT. I simply did not know what it meant to have the same resistor touching the same node in both ends such as is the case here, but now I get it. \$\endgroup\$ – Moe Odeh Sep 7 '16 at 19:18
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If you look at the bottom-right section of your circuit, the 2K resistor is shorted by a wire. This is the same as having the 2K not present since all electricity will flow through the wire. Connecting any passive component like a resistor in parallel with a wire will render that part useless in the circuit.

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You can remove the 2k resistor because any isn't current in it for the short circuit like this image :

enter image description here

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    \$\begingroup\$ +1 for such an easy an straightforward image explanation. I doubt it's necessary to present the last calculation because this website likes the OP to think. \$\endgroup\$ – Bradman175 Sep 7 '16 at 7:20
  • \$\begingroup\$ @arashzgh the drawings did clear up a lot of confusion, thank you for that. \$\endgroup\$ – Moe Odeh Sep 7 '16 at 17:51
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2K resistor is shortcircuited with a wire. Therefore just remove it.

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