Q. In order to increase the resistance of a given wire of uniform cross section to four times its value, a fraction of its length is stretched uniformly till the full length of the wire becomes times the original length. What is the value of this fraction ?

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Solution:

Suppose fraction of the length of resistance is stretched to -times.
Then its new length is given as

Resistance is given as

[ is the volume of wire]

[As remain constant]
The final resistance becomes four times so we use

Solving above two equations we get

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