Introduction to Electric Circuits

92 Single-phase a.c. circuits

I

I

tO

(a)

IL

I,

[R

I

(b)

v (reference)

Figure 4.29

Dividing through by V we see that

1/Z = ~/[(1/R) 2 + (1/XL) 2] (4.28)

We have seen (Chapter 2) that the reciprocal of resistance (l/R) is called
conductance (G). The reciprocal of reactance (l/X) is called susceptance (B)
and the reciprocal of impedance (I/Z) is called admittance (Y), so that
Equation (4.28) may be rewritten as

Y = ~r 2 + BL 2) (4.29)

In complex form we have the following relationship:

I= IR -- jlL

so that

V/Z = V/R -jV/XL

Dividing throughout by V gives

1/Z = 1/R -jl/XL

and

Y = G -jBL (4.30)

If we divide each phasor in Fig. 4.29(b) by V we obtain the admittance triangle
shown in Fig. 4.30.

G

BL

Figure 4.30

Note that the phase angle r is given by tan -~ (BL/G) = tan

XL = wL, we have

4, = tan -1 (R/toL)

-' (R/XL) and since

(4.31)