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So far I calculated total resistance and it is 4.66 ohms and there is 12 volt voltage across them, what is the best way or HOW to calculate current for each resistor ?

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Hi Hooman - this is a site for conceptual questions about physics, not general homework help. If you can edit your question to ask about the specific physics concept that is giving you trouble, I'll be happy to reopen it. See our FAQ and homework policy for more information. –  David Z Feb 24 '13 at 6:40
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closed as too localized by David Z Feb 24 '13 at 6:40

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3 Answers

This can also be solved using mesh analysis.

Mesh analysis breaks down the circuit into one or more "loops", or "meshes". In this example notice ther are 3 meshes. This will result in a 3 by 3 linear system. Through linear algebra, the solution to the system will be the three mesh currents. The three mesh currents will be all you need to know all of the currents through each resistor. Remember that if a resistor lies between two different meshes, the current through it will be the difference between the two mesh currents (e.g. the current through the 4$\Omega$ which lies between mesh 1 and mesh 2 is $i_1-i_2$).

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Hi Zetta - our homework policy disallows giving complete answers to homework-like questions. Accordingly, I'm temporarily deleting this. –  David Z Feb 24 '13 at 6:42
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For this kind of circuit, it's helpful to simplify down to one total resistance to calculate the current with $V=IR$, However, you can draw multiple diagrams when simplifying the resistance. After finding the total current, you can use that total current along with a voltage divider. Eventually if you continue with this, you will have a voltage at every node and thus be able to calculate the current at all paths.

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When two resistors are connected in series, the voltage on each of them is proportional to the relevant resistance, if two resistors are connected in parallel, the current in each of them is inversely proportional to the relevant resistance. That should be enough to calculate the current for each resistor.

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