Than we can add a new pair of resistors, and the input resistance of the circuit will not change - adding one more pair to an infinite network does not make any difference. A further simplification is that, for large N , R 1 is much less than R 2 . According to our result, the resistance on one end of an infinite long cable is the geometric mean of the two resistances characterizing the cable. The best conditions for transmitting power are achieved by using a 50 W output resistance source, and a 50 W load. When the currents and voltages are time dependent we have to worry about the time variations of the energy stored in the electric and magnetic fields around the conductors.
Life gets rather complicated for a general time dependent signal.
We will discuss that in the next chapter. The best way to treat an arbitrary time dependent signal is to assume that it is in fact part of a periodic sequence. For periodic signals we have a theorem stating that As long as the circuits are linear, all periodic signals can be treated as a superposition of sine waves with proper phases and amplitudes . The mathematical process of determining the phases and amplitudes is called a Fourier transformation. The amplitude as a function of the frequency is called the spectrum of the signal.