If length of a given wire increases by 10% due to stretching, the resistance of the wire increases by

Options

A. 0.21
B. 0.2
C. 0.1
D. 0.05

Answer

A

Explanation

Here l.=l+ 10% of l=1.11. As volume of wire remains unchanged, so the new cross-section area
`A. = (Al)/(l.) = (Al)/(1.1l) = (A)/(1.1)`
` therefore ` New resistance `R. = (rho l.)/(A.) = (rho (1.1l))/((A//1.1)) = 1.21 (rho l)/(A) = 1.21 R`
` therefore (Delta R)/(R ) = (R. - R)/(R ) = 0.21 = 21%`