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Recently, I came across a question based on finding electric current of a circuit. Here's the image...

I know, by using the formula $I=V/R$, we can easily calculate the current as $V$ is given and $R$ can be calculated from the diagram. In the book (from where I got the question),

Solve the $R$ (net) by combining the $6 \Omega$ and $2 \Omega$ resistances in parallel, and with both, $1.5 \Omega$ in series and whole parallel with $3 \Omega$.

I didn't get the logic they used. First, I thought of keeping 6, 2 and 1.5 ohm resistors in parallel and with all, the 3 ohm in series. But, that didn't work. Can someone please help me?

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Hi, welcome to physics.SE! I cleaned up the formatting in your answer, have a look at the syntax by clicking "edit" (there's also a section in the site FAQ about formatting math). I also put your picture in directly, which is something you cannot do as a new user (helps prevent spam). –  Kyle Aug 21 '13 at 16:51
    
Thanks, for formatting my question. I hope that will help me to get my answer. –  Subhadeep Dey Aug 21 '13 at 16:57
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Try drawing the circular circuit as a square. It should be pretty clear then why the solution is with 6 & 2 being in parallel and not 6, 2, & 1.5. –  Kyle Kanos Aug 21 '13 at 17:09
    
I get these kind of problems in my textbook too. Don't know why they test us with such strange diagrams of circuits, when all it is a simple series-parallel combination. –  udiboy Aug 21 '13 at 19:02
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1 Answer

You can reduce this to a simple problem by reforming the diagram to appear more meaningful and solvable. First thing to identify is that all points connected by wires without resistance are at same potential since no potential difference is needed for current to flow through them(assumed to have zero resistance). hence, in your diagram, you can identify three regions with three different potentials and then reform the diagram. (the red, blue and the black).
enter image description here
Now to reform the image, you start out by the positive terminal of the baterry which is connected to the red potential. The 2 and 6 ohm resistances connect the red potential to the black while the 3 ohm connects it direct to the blue. Moreover, the 1.5 ohm connects the black and the blue resistances. Its is depicted below wherein you can easily solve for the net resistance or current.Sorry for the poor diagrams.enter image description here

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thanks for helping me! –  Subhadeep Dey Aug 23 '13 at 17:34
    
BTW, I can't understand the concepts of different potentials. How can we know from the diagram that it has 3 different potentials? –  Subhadeep Dey Aug 23 '13 at 17:36
    
Like i said, all points connected by wires only and no resistances are at same potential. There are three such wire segments connecting a few resistors and hence 3 potentials. –  Satwik Pasani Aug 24 '13 at 1:45
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