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A wire of resistance "r" is cut into two equal parts and connected in parallel. What will be the new resistance of the conductor? Draw diagram

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The resistance of a piece of wire is directly proportional to its length as the wire is cut in two equal parts 

 Resistance of each part = r/2

We know that in parallel combination equivalent resistance ;  R = 1/R1 + 1/R2

So , Here R = 1/ r/2  +1/ r/2

                      = 2/r + 2/r

                      = 4/r

Thus, the resistance of the combination is 1/4th of the original resistance.

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