Question

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%

Answer 1

it's answer should be option no. c

Answer 2

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%