Page 339 - Basic Electrical Engineering

Alternating quantities like voltage, current, etc., can be represented either in
the polar form or in the rectangular form on real and imaginary axis. In Fig.
3.38 is shown a voltage, V represented in the complex plane.

The voltage, V can be represented as . This is called the polar form of
representation. Voltage V can also be represented as V = a + jb = V cosϕ +
jV sinϕ. This is called the rectangular form of representation using a j

operator.

Significance of operator j

The operator j used in the above expression indicates a real operation. This

operation when applied to a phasor, indicates the rotation of that phasor in the
counter-clockwise direction through 90° without changing its magnitude. As

such it has been referred to as an operator. For example, let a phasor A drawn
from O to A be in phase with the X-axis as has been shown in Fig. 3.39 (a).

This phasor when represented by jA shows that the phasor A has been rotated
in the anticlockwise direction by an angle 90° and as such its position now is
along the Y-axis. If the operator j is again applied to phasor jA, it turns in the

2
counter-clockwise direction through another 90°, thus giving a phasor j A
which is equal and opposite to the phasor A, i.e., equal to −A. See Fig. 3.39

(a).