Question

Two wires are identical, except that one is aluminum and one is tungsten. the aluminum wire has a resistance of 0.22 ω. what is the resistance of the tungsten wire?

Answer 1

The resistance R of a piece of wire is given by

`R=\rho (L)/(A)`
where
`\rho` 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
`R_T` (the resistance of the tungsten wire) and
`R_A` (the resistance of the aluminum wire):

`(R_T)/(R_A)= (\rho_T (L)/(A) )/(\rho_A (L)/(A) )`

the two wires are identical, so L and A are the same for the two wires and simplify in the ratio, and we get:

`R_T = (\rho_T)/(\rho_A) R_A`

By using the resistivity of the aluminum:
`\rho_A=2.65 \cdot 10^(-8) \Omega m` and the resistivity of the tungsten:
`\rho_T = 5.6 \cdot 10^(-8) \Omega m`m we can get the resistance of the tungsten wire:

`R_T = (\rho_T)/(\rho_A) R_A = ( 5.6 \cdot 10^(-8) \Omega m)/(2.65 \cdot 10^(-8) \Omega m) (0.22 \Omega) = 0.46 \Omega`