A graphic method for the exact solution of transmission lines

There seems to be a popular superstition among engineers that the voltage and current relations at different points in a transmission line are peculiar and are not governed by Ohms law. This idea is not true. A transmission line is governed by Ohms law just as is any other alternating-current circuit containing resistance inductance and capacity. The only difference from an ordinary circuit is that in a transmission line we must make a correction for the effect of distributed constants. If we change the current flowing through a line by an amount I, there will be a voltage change equal to I Z between the two ends of the line. The Z in this case, however, is corrected for the distributed constants of the line. The hyperbolic formula which are so widely coming into use, since Doctor Kennelly has given us tables of complex hyperbolic functions, are merely short methods of determining this Z as well as certain other constants which we must use. If we start with a certain voltage Eg at the generator; on open circuit, we will have a slightly higher voltage at the receiver, due to the line capacity drawing a leading current through the inductance. As we load the line with a lagging current this voltage rise is counter-acted by the impedance drop. In a similar manner the generator current is equal to the vector sum of the charging current, and the load current which has been multiplied by a constant. It is possible to express these relations by a vector diagram. Drawing a voltage and current diagram on the same sheet and to suitable scales offers a very convenient method of calculation. From such a diagram it is possible to read directly power and power factor as well as condenser kv-a. necessary for voltage regulation.