1921 .] 
Robinson.—Voltage-drop in Circuits. 
259 
VOLTAGE-DROP IN ALTERNATING-CURRENT 
OVERHEAD DISTRIBUTION CIRCUITS. 
By I. R. Robinson, B.E. 
The calculations of the voltage-drop in alternating-current circuits involve 
the evaluation of the reactance of the circuit considered. Whilst tables 
of the resistance of S.W.G-. sizes of copper cables are available, there do 
not seem to be any tables giving the values of the reactance for S.W.G. 
sizes for 50 cycles per second. The attached tables are presented in the 
hope that they may be of use to others. The opportunity is also taken 
to indicate a method of calculation which, whilst used for a similar problem 
in connection with transformers, can be profitably applied to the problem 
under consideration. 
Electric-power lines may be divided broadly into two classes, trans¬ 
mission-lines and distribution-lines. Such a division is at best an approxi¬ 
mation, and with increasing voltages the transmission-lines of yesterday 
are the distribution-lines of to-day. For the purpose of this paper, however, 
distribution-lines are taken as those in which the capacity and conductance 
between phases may be neglected as having no appreciable effect on the 
voltage-drop. 
For all voltages for distances up to thirty miles the error in neglecting 
the capacity of the lines is about 0-0015 of the sending-end voltage. The 
method of calculation indicated will be suitable for lines of less than thirty 
miles in length. By a simple extension it applies also to lines up to a 
hundred miles in length. 
The following are the symbols used, with their meanings :— 
P is the power in kilowatts ; 
l is the distance in miles ; 
R is the resistance in ohms per mile per phase ; 
L is the inductance in henrys per mile per phase; 
jp = 2 trf — 314-16 for / = 50 cycles ; 
cos 6 is the power-factor at the receiving end ; 
I r is the current at the receiving end ; 
V s is the voltage at the sending end ; 
V r is the voltage at the receiving end. 
For three-phase transmission V s and V r are voltages from phase • to 
neutral, and P is one-third of the total power transmitted (assuming a 
balanced load). 
For single-phase transmission V s and V r are voltages between phases, 
and P is the total power transmitted. In this case the figure given by 
the final equation must be multiplied by 2 to give the voltage-drop. 
The voltage-drop can best be shown by means of the accompanying 
vector diagram. 
In the diagram, OA, the current at the receiving end, is taken as a 
vector of reference. The voltage at the receiving end leads the current 
there by an angle 0 (where cos 0 is the power-factor of the load), and is 
represented by OB. The voltage-drop due to the resistance is in phase 
