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?

  • $\begingroup$ 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). $\endgroup$
    – Kyle Oman
    Aug 21, 2013 at 16:51
  • $\begingroup$ Thanks, for formatting my question. I hope that will help me to get my answer. $\endgroup$ Aug 21, 2013 at 16:57
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    $\begingroup$ 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. $\endgroup$
    – Kyle Kanos
    Aug 21, 2013 at 17:09
  • $\begingroup$ 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. $\endgroup$
    – udiboy1209
    Aug 21, 2013 at 19:02

1 Answer 1


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

  • $\begingroup$ BTW, I can't understand the concepts of different potentials. How can we know from the diagram that it has 3 different potentials? $\endgroup$ Aug 23, 2013 at 17:36
  • $\begingroup$ 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. $\endgroup$ Aug 24, 2013 at 1:45

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