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(a) 100%(b) 50%(c) 300%(d) 200%
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it's answer should be option no. c
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Answer:
C) 300%
Explanation:
Resistivity = R = p L/A where p is the resistivity / specific resistance
Let the length be l and the radius = r
Since l is increased by 100% thus,
l' = l+100/100l
= l`= 2l
Due to an increase in length, the area must decrease as volume remains constant
Al = A`l`
Hence, A` = A/2
New Resistance R` = pl`/A` = 4pl/A
Change in resistance = 3pl/A or 300 %
Therefore, the consequent decrease in diameter the change in the resistance of the wire will be 300%
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