A copper wire is stretched to make it 0.1 % longer. The percentage change in its resistance is ...... (Assume that the volume of the wire remains constant.)

Options

A. increase by 0.2 %
B. decrease by 0.2 %
C. decrease by 0.05 %
D. increase by 0.05 %

Answer

A

Explanation

increase by 0.2 %
Suppose the length of the wire is l and area of cross-section is A.
The resistance of a wire, = R = `(rho l)/(A)`
` therefore R = (rho l^(2))/(Al) = (rho l^(2))/(V) `.... (1)
`therefore (dR)/(dl) = (rho)/(V) (2l) `
`therefore dR = (2 rho)/(V) l dl " " ` .... (2)
Taking ratio of equations (2) and (1),
`(dR)/(R) = ((rho)/(V) 2ldl)/((rho)/(V)l^(2))`
`therefore (dR)/(R) = 2 (dl)/(l)`
Percentage change = `(dR)/(R) xx 100 %`
= 2 `((dl)/(l) ) xx 100 %`
= `2 (0.1 %) = 0.2 %`
Thus, the resistance of the wire increases by 0.2 % .