Electrical Engineering/circuit

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circuit
circuit  

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original  
i have Solve the circuit given in picture and when I reach step 4(my work given) I found the 6&2 ohm are in series I connected them and at last making equivalent parallel with4 and then the equivalent in series with 16 got the answer 18.66,in book answer is 19ohm mean like connecting 2&4 in series and solving further. .my method was right or not?any general rule relative to this?

Answer
Your picture diagrams were not clear enough to read and I could not follow through your calculations.

But, it is a simple problem of reduction through equivalent resistances. I think you did not reduce the resistances correctly.  You cannot alter the circuit. If two resistors are in parallel you can replace it with the equivalent.  If two resistors are in series they can be added.  It is just a matter of making the proper reductions.

Please go through your analysis again starting with the two top resistors on the right side of the diagram; it must be started there in order to continue with the reduction.  

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