According to the Canon website, and just about every other source on the web, the f/ #of a lens is calculated as [focal length] / [physical aperture diameter]. This fraction is simplified to 1/[f/ #]. This is why most lens barrels have the f/# written as 1:__.
So, if the maximum physical aperture remains constant, as the focal length changes as a lens zooms, the aperture value (f/ #) must change. However, many high end "constant aperture" zoom lenses are available. If the f/ # does not change as the lens zooms, the lenses physical aperture must increase. Right?
Ex.- Canon 70-200mm f/2.8 L IS.
At 70mm- 70/a = 1/2.8, a = 196
At 200mm- 200/a = 1/2.8, a = 560