Why does the capacitance of a coaxial cable depend on its length but not its impedance?
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Capacitance of the cable comes into play at low enough frequencies that the whole cable can be considered to be at the same time. In such a case, it’s trivial that capacitance scales with length, since larger capacitor plates -> more capacitance.
At high frequencies, due to the velocity factor of the cable (in coax signals travel at approx 0.6 times the speed of light in vacuum) signals don’t have time to travel through the whole cable before the start of the cable is already at a different voltage, so signals [propagate as waves](https://i.stack.imgur.com/gOPmO.jpg) down the length of the cable. The waves don’t “see” anything other than the part of the cable immediately near them – or signals reflecting and coming back from the end and meeting them – (because of that 0.6c limit) so the impedance becomes independent from the cable as a whole.
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