A copper wire of resistance r is cut in 10 parts of equal length two pieces in series and then five such combination are joined in parallel the new combination will have a resistance
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The resistance of a conductor is directly proportional to the length of the conductor. The resistance of the metallic wire, when it is cut into ten parts of equal length is r=R/10 Two such pieces when joined in series, the equivalent resistance of these two parts =r+r=2r=2R/10 Series resistance of two parts=2xR/10=R/5, 5 such elements are connected in parallel. Therefore the total resistance R' will be
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