A resistive wire is stretched till its length is increased by 100%. Due to the consequent decrease in diameter, the change in the resistance of a stretched wire will be

Options

A. 3
B. 2
C. 1
D. 0.5

Answer

A

Explanation

300 %
Let length of wire is l and area is A.
R = `(rho l)/(A)`
New length of wire l. = l + 100% l = 21 and area is A..
`therefore (R.)/(R) = (rho l. )/(A.) (A)/(rho1) = (A)/(A.) (l.)/(l) = ((l.)/(l) )^(2) = ((2l.)/(l) )^(2) = 4 `
`R. = (rho l.)/(A.)`
`therefore R. = 4R = R + 3R = ((4R - R)/(R) xx 100 ) % `
`= ((3R)/(R) xx 100 )% ` = 300 %
Percentage change in resistance = 300%