Question

A copper wire and aluminum wire of same length have same resistance. Specific resistance of aluminum is more than that of copper. Which of the following statement is correct

• A. Mass of copper and aluminium wire are same.
• B. Mass of copper wire is more than that of aluminium wire.
• C. Mass of copper wire is less than that of aluminium wire.
• D. none of these

Answer 1

The correct option is D none of these

Let resistance of copper wire be=$R_c$

resistance of aluminium wire be=$R_a$

Given, $R_c=R_a$ and $L_c=L_a$

But, ${\rho }_a>{\rho }_c$ (specific resistance)

Now Since,

$R_c=R_a$

$\frac{{\rho }_c{L}_c}{A_c}=\frac{{\rho }_a{L}_a}{A_a}$

$\frac{{\rho }_a}{{\rho }_c}=\frac{A_a}{A_c}$

$⟹{\rho }_a>{\rho }_c(\because {\rho }_a>{\rho }_c)$

$⟹{\mu }_a>{\mu }_c$

Since density is unknown to us.

Therefore this does not conclude anything about their masses.