Replacement of the cable in the test circuit by these two components and application of the test voltage would result in the identical current and phase angle as observed when using the cable. As long as the frequency of the applied AC voltage does not change, impedance measurements would be identical for both the capacitor-resistor combination and the infinitely long cable. If the infinitely long cable is cut to some finite length and the far end of this cable is connected to a capacitor-resistor combination which is assembled and found to be equal to the characteristic impedance , an astounding discovery is made. Cut the cable to any length and if the termination at the far end is unchanged and the frequency is unchanged, no difference in the measured impedance will be noticed. The impedance of inductors and capacitors is dependent on frequency.
L is inductance in henries.
It can be seen by the equation that inductive reactance increases when frequency increases. It can be seen by this equation that capacitive reactance decreases when frequency increases. Figure 3 . Relative dielectric constant vs. frequency . If the capacitance does not vary with frequency, the Zo varies inversely with the square root of the frequency and has a phase angle which is -45 o near DC and decreases to 0 o as frequency increases.