Now, we are going to discuss about power factor
For that, we will first consider a simple circuit consisting of an alternating voltage
source across which purely resistive load is connected. For this voltage source, a current will flow through the load
As the load is purely resistive, there will be no phase difference between the voltage
and the current in the circuit. For a purely sinusoidal voltage supplied by the source, let's draw the waveform of both
current and voltage. Here in the picture, the black waveform represents the voltage and red waveform represents the current
Now, if the load is purely inductive instead of resistive, the current lags behind the
source voltage by 90 degrees. It is shown here in this figure
The black waveform here also represents the voltage and red waveform represents the current
Now if the load is purely capacitive instead of resistive, the current leads ahead the
source voltage by 90 degrees. It is shown here in this figure
The black waveform here also represents the voltage and red waveform represents the current
Now imagine, the load has all, resistance, inductance and capacitance. And due to collective effect of these three parameters, the current shifts behind the
source voltage by an angle theta. It is shown here in this figure
The black waveform here also represents the voltage and red waveform represents the current
Now come to the resistive load circuit. Here, if we multiply voltage waveform with current waveform, we will get the power waveform
Let's do that. For that, we will consider the voltage waveform as Vmax sin omega t and current waveform as
Imax sin omega t and if we multiply them, we will get power P equals Vmax sin omega
t into Imax sin omega t. This may be rewritten as P equals Vmax into Imax by 2 into 2 sin omega t sin omega t
This implies P equals Vmax into Imax by 2 into 2 sin square omega t
This can be rewritten as sin square omega t plus cos square omega t minus within bracket
cos square omega t minus sin square omega t. Or, P equals Vmax into Imax by 2 into within bracket 1 minus cos 2 omega t
And this is power waveform. Now let's plot this expression of power waveform along with voltage and current waveform in
same figure. Here you see, the power waveform does not have any negative part, although the corresponding
voltage and current waveform do have equal positive and negative part. Now let's find the average value of this power and for that, we have to integrate the power
waveform equation 0 to 2 pi and divide it by 2 pi
Look here, this will ultimately come as Vmax into Imax by 2
Now come back to the circuit where the load has all, resistance, capacitance and inductance values
And due to the collective effect of these three parameters, the current shifts behind
the source voltage by an angle theta as we have already shown
Here, as the current shifts behind the source voltage by an angle theta, the waveform equation
of that can be represented as Imax sin omega t minus theta
By multiplying voltage waveform Vmax sin omega t and current waveform Imax sin omega
t minus theta, we get instantaneous power P equals to Vmax sin omega t into Imax sin
omega t minus theta. After simplifying this equation, we get the final power waveform here as P equals Vmax
into Imax by 2 into within bracket cos theta minus cos 2 omega t minus theta
Now let's plot this expression of power waveform along with voltage and current waveform in
same figure. Here you see, the power waveform has a negative part
Now let's find the average value of this power and for that, we have to integrate the power
waveform equation 0 to 2 pi and divide it by 2 pi
Look here, this will ultimately come as Vmax into Imax by 2 into cos theta
So far, we have calculated only average power of a purely resistive load and an arbitrary
load with same sinusoidal voltage and current with same magnitude peak. Now let's come to the actual definition of power factor
Power factor is a measure to the degree to which a given load matches that of a pure resistance
That means it can be considered as the ratio of average power of an arbitrary load to the
average power of a purely resistive load for same sinusoidal voltage and current with same
magnitude peak. Hence, here the power factor would be Vmax into Imax by 2 into cos theta by Vmax into
Imax by 2 which is nothing but simple cos theta. Hence, power factor can be defined as cosine of the angle between voltage and current in
any load. But it is true only for sinusoidal alternating signal. But for other form of signals, it is determined by the ratio of average power of an arbitrary
load to the average power of a purely resistive load for same sinusoidal voltage and current
with same magnitude peak. Hope we could give you a basic idea of power factor
Thank you