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Initial Wire
Copper has a resistivity of 1.68x10^-8 ohm meters. If the length of a copper wire is 1 m and its cross-sectional area is 1 cm squared, the resistance of the wire is 1.68x10^-4 ohms. To obtain this resistance, first multiply the length by the resistivity -- this results in a quantity of 1.68x10^-8 ohm m squared -- then divide by the cross-sectional area. Since 1 cm is equal to 1x10^-2 m, 1 cm squared is equal to 1x10^-4 m squared. Therefore, dividing 1.68x10^-8 ohm m squared by the cross-sectional area of 1x10^-4 m squared yields a resistance of 1.68x10^-4 ohms.
Stretching Without Change in Cross-Sectional Area
Suppose the wire could be stretched to 2 m without changing the cross-sectional area. This will double the resistance of the wire. First, multiply the new length by the resistivity; this results in the quantity 3.36x10^-8 ohm m squared. Dividing by the same cross-sectional area of 1x10^-4 m squared yields a new resistance of 3.36x10^-4 ohms.
Current and Cross-Sectional Area
When a wire of a given length conducts electric current, the number of electrons that can travel through the wire is limited by the diameter of the wire; a larger-diameter wire permits more electrons to flow. The cross-sectional area of the wire, therefore, is inversely proportional to the resistance -- the greater the cross-sectional area, the lower the resistance of the wire.
Expected Change in Cross-Sectional Area
If you stretch a wire but the volume remains constant, the cross-sectional area will change. As the length increases, the cross-sectional area must decrease in order to keep the volume constant. If you double the length of the wire, the cross-sectional area is reduced by half. This, in turn, increases the resistance even more. The numerator of 3.36x10^-8 ohm m squared that results from the doubling of the wire then must be divided by 0.5x10^-4 m squared. This results in a resistance of 6.72x10^-4 ohms. In this case, stretching quadruples the original resistance.