Q. The length of a given cylindrical wire is increased by 100%. Due to the consequent decrease in diameter, the change in the resistance of the wire will be

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Solution:

Let the length of the wire be l, radius of the wire be r
Resistance resistivity of the wire
Now is increased by 100%

As length is increased, its radius is going to be decreased in such a way that the volume of the cylinder remains constant.

The new resistance
Change in resistance
% change