Question

A copper wire and aluminum wire of the same length has the same resistance. The specific resistance of aluminum is more than that of copper. Which of the following statements is correct?
A. Mass of copper and aluminum wire is the same.
B. Mass. of copper wire is more than that of aluminum wire.
C. Mass of copper wire is less than that of aluminum wire.
D. none of these

Answer 1

Assume the mass, length, and area of the two wires. Find the resistance of the two wires using the mathematical expression of the resistance. Equate them to find the relation between their respective areas. Now calculate the ratio of the mass of the two wires.

Complete step by step answer:
We know that the resistance of the wire is given by:
$R = \rho \dfrac{l}{A}$
Here R is the resistance, l is the wire's length, A is the cross-sectional area of the wire, and $\rho$ is the wire's resistivity.
We will now use subscript 1 for aluminum and subscript 2 for copper.
We will now equate the resistances of the two-wire since they are the same as given.
$\begin{array}{l} \Rightarrow {R_1} = {R_2}\\\ \Rightarrow {\rho _1}\dfrac{{{l_1}}}{{{A_1}}} = {\rho _2}\dfrac{{{l_2}}}{{{A_2}}}\\\ \Rightarrow \dfrac{{{\rho _1}}}{{{\rho _2}}} = \dfrac{{{l_1}}}{{{l_2}}} \end{array}$
Since no information is given about the cross-sectional area and density of the wire, we cannot move further in the calculation. Therefore, we cannot determine the ratios for the mass of the two wires.

Therefore, the correct option is (D).

Additional Information: Resistivity varies from one material to another. The resistivity of a material varies in direct resonance with the temperature. The resistance of two wires of different materials can be made to be the same. But resistivity of two materials can never be the same.

Note: In actual practice, the aluminum wire mass is less than the mass of the copper wire for the same length and cross-sectional area. Electrical lines are long wires carrying a high value of current. If the overhead lines' mass is too much, the power cable will form an arc and can disrupt other lines in the vicinity. Aluminum wire is preferred for these conditions.