Why does the capacitance of a coaxial cable depend on its length but not its impedance?
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Capacitance is based on the word “capacity”. A guy named Faraday discovered that two pieces of metal, separated by a “dielectric” material, can hold a charge for a certain length of time. This is called “capacitance”.
Thus, capacitance is based on how much metal there is, the space between the metals, and what type of dielectric is used. So, then, a coaxial cable will have a slightly different capacitance at 100 feet length then 10 feet. This value for capacitance is “constant”, it does not change, regardless of the signal going thru the cable (DC versus 100MHz, for example)
Impedance is related to how fast/efficiently the capacitor can charge/discharge. If you put a DC signal into a capacitor – it will charge once and stay charged until you remove the DC. If you put a variable signal (like 1MHz) into a capacitor, the circuit will act as though there is a resistor in the circuit, because the capacitor is trying to charge/discharge at that rate. Thus the impedance is dependent on the frequency of the signal, in conjunction with the capacitance of the circuit. Coaxial cables are designed to provide a known impedance at a specific frequency range.
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