Question

Question #ce955

Answer 1

`R_2 = 9R_1`

Explanation:

The resistance `R` of the wire depends on two factors - its geometry and its material property,

`R = \rho L/A`, where `\rho` is the resistivity which is a material property. The other two are geometrical parameters. `L` is the length and `A` is the cross-sectional area.

When a wire is stretched, its length increases while its cross-sectional area decreases accordingly to keep the volume a constant.

Volume: `\quad V = L_1A_1 = L_2A_2;`
`A_2/A_1 = L_1/L_2` ...... (1)

`R_1=\rhoL_1/A_1;\qquad R_2=\rhoL_2/A_2`

`R_1/R_2 = (L_1/L_2)(A_2/A_1) = (L_1/L_2)^2 = (1/3)^2 = 1/9`

`R_2 = 9R_1`