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?

The resistance R of a piece of wire is given by

where  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  (the resistance of the tungsten wire) and  (the resistance of the aluminum wire):


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


By using the resistivity of the aluminum:  and the resistivity of the tungsten: m we can get the resistance of the tungsten wire:

Planck decided to assume that atoms could only vibrate at certain frequencies that were whole numbers eg 2f, 3f and so on. others used to think that atoms vibrate continuously