In the last lesson, two points were described:
1.
How a sinusoidal voltage waveform (ac) is generated?
2.
How the average and rms values of the periodic voltage or current waveforms, are
computed?
Some examples are also described there. In this lesson, the representation of
sinusoidal (ac) voltage/current signals by a phasor is first explained. The polar/Cartesian
(rectangular) form of phasor, as complex quantity, is described. Lastly, the algebra,
involving the phasors (voltage/current), is presented. Different mathematical operations –
addition/subtraction and multiplication/division, on two or more phasors, are discussed.
Keywords
: Phasor, Sinusoidal signals, phasor algebra
After going through this lesson, the students will be able to answer the following
questions;
1.
What is meant by the term, ‘phasor’ in respect of a sinusoidal signal?
2.
How to represent the sinusoidal voltage or current waveform by phasor?
3.
How to write a phasor quantity (complex) in polar/Cartesian (rectangular) form?
4. How to perform the operations, like addition/subtraction and multiplication/division
on two or more phasors, to obtain a phasor?
This lesson forms the background of the following lessons in the complete module of
single ac circuits, starting with the next lesson on the solution of the current in the steady
state, in R-L-C series circuits.
Symbols
i
or i(t)
Instantaneous value of the current (sinusoidal form)
I
Current (rms value)
Maximum value of the current
m
I
−
I
Phasor representation of the current
φ
Phase angle, say of the current phasor, with respect to the reference phasor
Same symbols are used for voltage or any other phasor.
Representation of Sinusoidal Signal by a Phasor
A sinusoidal quantity, i.e. current,
t
I
t
i
m
ω
sin
)
(
=
, is taken up as an example. In Fig.
13.1a, the length, OP, along the x-axis, represents the maximum value of the current
,
on a certain scale. It is being rotated in the anti-clockwise direction at an angular speed,
m
I
, and takes up a position, OA after a time t (or angle,
t
θ
=
, with the x-axis). The
vertical projection of OA is plotted in the right hand side of the above figure with respect
to the angle
. It will generate a sine wave (Fig. 13.1b), as OA is at an angle,
with the
x-axis, as stated earlier. The vertical projection of OA along y-axis is OC = AB =
Version 2 EE IIT, Kharagpur