If someone ask you whether
current and voltage are vector or scalar quantity the obviously you will answer
that they are scalar quantity. Next, the question arises if current and voltage
are scalar quantity then why do we represent then in form of vector which is
famously known as Phasor? We will discuss here this aspect.

Vectors are physical
quantity which have magnitude, direction and above all which follows the
triangle law of addition of two vectors. As current have both magnitude and direction
but they do not follow the triangle law of addition of two vectors, hence
current is a scalar. Same argument applies with voltage.

While representing a vector,
it is represented by an arrow pointing toward a particular direction and the

**.***length of the arrow is proportional to the magnitude of the vector*
Now coming to Phasor.
Electrical
quantities such as voltage and current are scalar quantities. However, their
values changes over time in a sinusoidal way.

V = V

_{m}Sinwt
If we see this voltage on
Voltage and Time axis, we find that magnitude of voltage varies from –Vm to +Vm
with respect to time. Now consider the figure below.

In the figure a vector is
drawn from the origin making an angle of wt with the time axis and rotating in
anti clockwise direction.

**If we take the projection of the vector on Voltage axis, we observe that we get the instantaneous value of the Voltage V = VmSinwt. It is normal practice to take the length of Phasor as the R.M.S value of the Voltage / Current while in vector, length is directly proportional to magnitude of the vector.***Mind that this vector is rotating with some frequency, that is why it is Phasor. Normal Vector do not rotate.*
Anything that behaves like
this can be represented by phasors, which are really just representations of
sinusoids.

Thus Phasors are generally
rotational representation of sinusoidally varying quantities. The phase
differences in various sinusoidal quantities can be represented in space
respectively by single elements rotating at angle difference with each other
but their frequency should be same else they cannot be represented on a single
diagram. Their projection on the reference axis gives the value of the
individual quantities at an instant of time.

**Hope it might help you. Thank you!**

## No comments:

Post a Comment