The impedance of a Une is expressed by two quantities r and
x; these two are also at right angles to each other. Thus the
impedance might be written as Z == r -f jx, and we realize that
the numerical value of Z or ^ = vV -.- x^.
Since, however, the reactance con-
sumes an e.m.f. 90 degrees ahead of
the current, the diagram should be
constructed as in Fig. 11. In other
words, X is negative, which fact should
be shown in the imaginary equation by

using the minus sign.
Thus, the impedance should be written as

Z = r — jx.
The voltage consumed by the line impedance r — jx when
a lagging current, i -f ji^, is flowing, is IZ = {i -h ji.) (r - jx),
which multiplied gives

ir -f i^x -h J (2/ — ix).
For lagging current and condensive reactance we get

(i + /i\) (r -h jx) = ir - i^x + / (i/ + ix).
For leading wattless current and inductive reactance we get

(i — jij) (r — jx) = ir + i^x — j (i^r + ix).
TRANSMISSION LINE 27

The actual numerical value of a complex expression a ±jb
is always

Since a ± jb really represents the hypothenuse of a triangle
having a anxl b as sides, it matters not whether a or 6 are posi-
tive or negative.
