SOLUTION

When a single-circuit transmission line is connected to a voltage source at t = 0, the whole length of the line is not energized all at once; there must be a time lag before the disturbance initiated at one point can be observed at the distant point in the line.

This is due to the presence of distributed constants (inductance and capacitance in a loss-free line). The process is equivalent to launching a voltage wave, which travels along the length of the line at a certain velocity (almost equal to the velocity of light) and reaches the distant end after a period of time.

The voltage wave is usually accompanied by a current wave. These two waves, which are related to each other by the characteristic impedance or resistance of the line, must reach the distant end in a finite time and, in general, must meet a discontinuity as a result of which total or partial reflection will take place.

Then, for a finite line, the voltage and current at any point (including the ends) are the result of the superimposed incident and reflected waves. In this chapter, we shall study the propagation of transient voltage and current waves along the transmission lines which may be caused by switching or lightning and which may subject the electrical systems to dangerous overvoltages.