Question

1 m copper wire with a radius of 0.5mm and resistance R is stretched to a distance of 2m. What is the fractional change in resistance delta R/R after the wire is stretched? If we repeat the experiment what is the change delta R/R if the wire is made out of aluminum instead?

Answer 1

resistance of copper wire

R 1= rho L/A = 1.68 * 10^-8 ( 1 m)/ pi ( 0.5 * 10^-3 m)^2 = 2.14 * 10^-2 ohm

for 2 m

R2 = rho L/A = 1.68 * 10^-8 ( 2 m)/ pi ( 0.5 * 10^-3 m)^2 = 4.266 * 10^-2 ohm

delR/R = R2-R1/R1 =  4.266 * 10^-2 ohm- 2.14 * 10^-2 ohm/ 2.14 * 10^-2 ohm = 1.0

for aluminumum wire

R 1= rho L/A = 2.65 * 10^-8 ( 1 m)/ pi ( 0.5 * 10^-3 m)^2 = 3.36 * 10^-2 ohm

for 2 m

R2 = rho L/A = 2.65 * 10^-8 ( 2 m)/ pi ( 0.5 * 10^-3 m)^2 = 6.73 * 10^-2 ohm

delR/R = R2-R1/R1 = 6.73 * 10^-2 ohm- 3.36 * 10^-2 ohm/ 3.36 * 10^-2 ohm =1.0