Question #ce955

1 Answer
Cosmic Defect
Dec 8, 2017

R_2 = 9R_1R2=9R1

Explanation:

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

R = \rho L/AR=ρLA, where \rhoρ is the resistivity which is a material property. The other two are geometrical parameters. LL is the length and AA 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

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