Question

The r.m.s. current in an AC circuit is 2A. If the wattless current be $\sqrt 3 $A, what is the power factor of the circuit?
$ A.\dfrac{1}{2} \\
  B.\dfrac{1}{3} \\
  C.\dfrac{1}{{\sqrt 3 }} \\
  D.\dfrac{1}{{\sqrt 2 }} \\
$

Answer 1

Hint – In order to get this problem solved we need to use the relation between r.m.s. and wattles current in which the phase angle $\phi $ is included then obtain the power factor by applying the formula of power factor I equal to rms current multiplied by sin$\phi $.

Complete step-by-step solution-
RMS current:- For the simplest point, tell me to measure the current (or potential difference) at small time intervals. Square every value, add the squares (which are all positive) and divide by the number of samples to find the average square or the average square. And take the square root of it. This is the average square root value (rms). RMS current is equal to root 2 times the amplitude of the current.
Wattless current:- Current flow in the AC circuit without any net dissipation of power is called wattless current. Therefore, the fact that at a very high frequency, the inductor in the circuit is almost an open circuit.
It is given that r.m.s. current is 2A.
Wattles current is $\sqrt 3 $A.
We know the relation that ${I_{wattless}} = {I_{rms}}\sin \phi $.
On putting the values we get the equation as:
$ \sqrt 3 = 2\sin \phi \\
  \sin \phi = \dfrac{{\sqrt 3 }}{2} \\
  \phi = {60^0} \\ $
Hence, the phase angle is 60 degrees.
We also know that power factor = $\cos \phi $
So, putting the value of angle as 60 we get power factor as $\dfrac{1}{2}$.
So, the correct option is A.

Note – Whenever you get to solve such problems think about the formulas we can use to get the problem solved. We need to know about the terms like power factor, wattless current and rms current. These are the topics which are intensively highlighted in the chapter of alternating current.