Question

of these two wires compare? Consider two copper wires of equal cross-sectional area. One wire has 3 times the length of the other. How do the resistivities of these two wires compare? The longer wire has 3 times the resistivity of the shorter wire. The longer wire has 27 times times the resistivity of the shorter wire. The longer wire has 9 times times the resistivity of the shorter wire. Both wires have the same resistivity.

Answer 1

Answer:

Both wires have the same resistivity.

Explanation:

The resistivity of a material depends on the following factors:

1. The nature of the material, i.e., the number density of free electrons of the material.
2. The temperature of the material.

The resistance R of a wire of resistivity $\rho$, length l and cross-sectional area A is given by

$R=\dfrac{\rho l}{A}.$

On varying the length and cross-sectional area of the wire, the resistance of the wire is changed but resistivity does not change as it is an intrinsic property of the material of the wire.

For the two given wires, the length and the cross-sectional area are different, but both the wires are of copper which means the number density of free electrons on both the wires is same and both the wires are placed in same environmental condition, which means the temperature would also be same.

Thus, the resistivities of both the wire are same.