Why does the capacitance of a coaxial cable depend on its length but not its impedance?
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Capacitence comes from the area, proximity and intermediary material of the two conductors. The longer the conductors the more area to create higher capacitence. The cable also have inductance which depends on the thickness and length of the conductor, so the longer the cable the higher the inductance.
Impedence comes from the ratio of capacitence and inductance. So as the length of the cable increase the capacitence and inductance increase at the same rate so the ratio is going to stay the same.
Another way to look at it is that the impedance is the apparant resistance of the signal at the wavefront. Making the cable longer does not change the wavefront, it just make it go longer. So the impedance does not change.
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