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Find the resistance between A and B in the following circuit:

enter image description here

My Thoughts:

It is not the typical circuit that I see, but I'll give it my shot. Now part of mind is saying that the resistance should be 30 Ohms, because that is what it is between A and B. But then that would make this whole question too easy, and too good to be true.

But, lets suppose we find the Resistance of the two parallel resistors 30 Ohms, and 30 Ohms. We have:

enter image description here

I apologise in advance for drawing this by hand because I don't know how to draw computer version of circuits.

But still the Resistance between A and B is 30 Ohms. The answer at the back of the book is 10 Ohms, and my book shows no method whatsoever.

Why is the resistance between A and B equal to 10 Ohms?

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  • \$\begingroup\$ What ways can you take to get from A to B? All these ways the current will also take. It's not just the shortest path in a schematic where the current will flow. \$\endgroup\$
    – Arsenal
    Nov 17 '15 at 7:20
  • \$\begingroup\$ Hint: where does that 15R resistor go? Does it share one or both nodes with the 30R or is it separate? \$\endgroup\$
    – David
    Nov 17 '15 at 7:20
  • \$\begingroup\$ @Arsenal Oh, you mean to say that the current goes from the least resistive path. So lets see, it would go through the parallel resistors and that way around to B (take the longer path). Because 15 Ohms is smaller than 30 Ohms. But how does it give the resistance? Does this mean the resistance is 15 Ohms? \$\endgroup\$
    – M.S.E
    Nov 17 '15 at 7:25
  • \$\begingroup\$ Well like with humans, you will always find some who take the harder path as well. So while more of them will choose the path with less resistance, some of them will also go the path with more resistance. Each and every path with a connection will be taken. So you can redraw the schematic to look more "normal", every node which is connected just by a simple line can be moved freely on a schematic. Can you move the top resistor in a way to make the circuit look normal? \$\endgroup\$
    – Arsenal
    Nov 17 '15 at 7:30
  • \$\begingroup\$ @Arsenal Oh I got it :) Takes a bit of an imagination to reconstruct the original circuit by shifting things and making it more clear :) \$\endgroup\$
    – M.S.E
    Nov 17 '15 at 7:33
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All 3 resisters are in parallel & parallel combination gives out equivalent resistance of 10ohms. The equivalent circuit is :-

enter image description here

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  • \$\begingroup\$ How are they in parallel? They aren't, right? \$\endgroup\$
    – M.S.E
    Nov 17 '15 at 7:23
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    \$\begingroup\$ Please don't use abbreviations like "resis" or "ckt", there is enough space to write out the words and prevent misunderstandings. \$\endgroup\$
    – Arsenal
    Nov 17 '15 at 7:24
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    \$\begingroup\$ They are. All 3 resisters are connected to the same nodes on both sides. Try to visualize. \$\endgroup\$
    – Oshi
    Nov 17 '15 at 7:24
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enter image description here

Next time you can use this alphabetic method. if you face a compenent, change character. then you can calculate.So there are three resistor between A and B.

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