The resistance R of a piece of wire is given by
[tex]R=\rho \frac{L}{A} [/tex]
where [tex]\rho[/tex] is the resistivity of the material, L is the length of the wire and A is its cross-sectional area.
Using this formula, and labeling with A the aluminum and with T the tungsten wire, we can write the ratio between [tex]R_T[/tex] (the resistance of the tungsten wire) and [tex]R_A[/tex] (the resistance of the aluminum wire):
[tex] \frac{R_T}{R_A}= \frac{\rho_T \frac{L}{A} }{\rho_A \frac{L}{A} } [/tex]
the two wires are identical, so L and A are the same for the two wires and simplify in the ratio, and we get:
[tex]R_T = \frac{\rho_T}{\rho_A} R_A [/tex]
By using the resistivity of the aluminum: [tex]\rho_A=2.65 \cdot 10^{-8} \Omega m[/tex] and the resistivity of the tungsten: [tex]\rho_T = 5.6 \cdot 10^{-8} \Omega m[/tex]m we can get the resistance of the tungsten wire:
[tex]R_T = \frac{\rho_T}{\rho_A} R_A = \frac{ 5.6 \cdot 10^{-8} \Omega m}{2.65 \cdot 10^{-8} \Omega m} (0.22 \Omega) = 0.46 \Omega[/tex]
