First let me state my inferences on these:
If the frequency increases, the reactive component increases. So Power factor = Resistance/Impedance decreases. Thus Power factor decreases -> which means the current drawn is more, considering load is inductive in nature
But we know I = V/ 2*pi*f*L . So if frequency increases, the current drawn decreases as per this relation.
What am I missing here?
Hello there,
As Carl was saying, the relationships here depend on how the circuit is arranged, the topology of the circuit. We can look at two cases and see what happens. The simplest two cases are the series RL and the parallel RL so we'll do that.
First, the impedance of the parallel circuit is:
Zp=(j*w*L*R)/(R+j*w*L)
and the impedance of the series circuit is:
Zs=R+j*w*L
The phase shift for the parallel circuit is:
THp=-atan(R/(w*L))
and the phase shift for the series circuit is:
THs=-atan(w*L/R)
Since the power factor is cos(TH) where TH is the phase shift between current and voltage, the power factor for the series circuit is:
PFs=R/(sqrt(R^2+w^2*L^2)
while for the parallel circuit we have a power factor:
PFp=w*L/sqrt(R^2+w^2*L^2)
Now we are in a position to evaluate the power factor directly in either the series or parallel case.
Starting at zero frequency, for the series case we get:
PFs(0)=R/R=1
and at infinite frequency we get:
PFs(inf)=0
and for the parallel case at zero frequency we get:
PFp(0)=0
and for infinite frequency we get:
PFp(inf)=1
Now we can compare the two sets of information.
We immediately see that the power factor for zero and infinite frequencies are reversed for the series and parallel RL circuits.
Now we look at the current...
The current in the series circuit is:
Is=1/sqrt(R^2+w^2*L^2)
and in the parallel circuit it is:
Ip=sqrt(R^2+w^2*L^2)/(w*L*R)
The current in the parallel circuit for zero and infinite frequencies is:
Ip(0)=infinite
Ip(inf)=1/R
The current in the series circuit for zero and infinite frequencies is:
Is(0)=1/R
Is(inf)=0
So you can now compare these limits and see that the responses are different.
Listing the values all on one line for parallel in order of PF for zero and inf freq, then current for zero and inf frequencies, followed by the series case on the next line:
0,1,inf,1/R (parallel)
1,0,1/R,0 (series)
We can see that the results are sort of swapped except for the current which is either infinite or zero, but the 1/R currents are also swapped. So the two circuits have a basic difference in that both their power factors AND current responses are swapped.