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

Options

A. `300 %`
B. `200%`
C. `100 %`
D. `50%`

Answer

A

Explanation

(a) If suppose initial length `l_(1) = 100` then `l_(2) = 100 + 100 = 200`
`(R_(1))/(R_(2)) = ((l_(1))/(l_(2)))^(2) = ((100)/(200))^(2) implies R_(2) = 4 R_(1)`
`(Delta R)/(R ) xx 100 = (R_(2) - R_(1))/(R_(1)) xx 100 = (4 R_(1) - R_(2))/(R_(1)) xx 100 = 300 %`