Short transmission lines are defined as overhead lines with a length of less than 80 km and an operating voltage of up to 20 kV. Due to the shorter length and lower operating voltage of short transmission lines, the charging current is relatively low.
As a result, the effect of the line capacitance on the circuit behavior is extremely small and can be neglected. This is because the capacitance of a transmission line is proportional to the length of the line. For a short transmission line, the capacitance is very small, so it has a minimal effect on the circuit behavior.
In a short transmission line, the distance between the sending and receiving ends is relatively small, so the time it takes for the voltage and current waves to travel down the line is very short. As a result, the source at the sending end sees only the impedance of the load at the receiving end, and not the characteristic impedance of the line.
This is because the voltage and current waves travel at the speed of light, which is approximately 3 x 108 meters per second. For a short transmission line, the length of the line is typically much shorter than the time it takes for the voltage and current waves to travel down the line. As a result, the load impedance has a much greater influence on the circuit behavior than the characteristic impedance of the line.
In contrast, for a medium or long transmission line, the length of the line is much longer, so it takes a longer time for the voltage and current waves to travel down the line. In this case, the characteristic impedance of the line has a greater influence on the circuit behavior, and the load impedance is less significant.
In addition, the capacitance of a transmission line is proportional to the length of the line. For a short transmission line, the capacitance is very small and can be neglected. However, for a medium or long transmission line, the capacitance is much larger and must be taken into consideration when analyzing the circuit.
Overall, the decision to neglect the line capacitance in short transmission lines is based on the relative time it takes for the voltage and current waves to travel down the line and the corresponding influence of the load and line impedances on the circuit behavior.