I was studying the power in Alternating current. The formula to calculate the power in alternating circuit is
$$P = VI \cos{\Phi} $$
where, $V$ and $I$ are RMS values of voltage and current and $\Phi$ is the phase difference between voltage and current.
Let's take a simple AC circuit connected to a resistor (or any appliance).
Here The power through the resistor is
$$P = VI$$
as the impedance is equal to $R$ and the value of power factor is 1.
But, if we connect an inductor in parallel, the value of power factor will decrease due to increase in $\Phi$. and the current will increase (Overall, Power will remain constant).
Does that mean that we can reduce power factor to get more current? I'm confused about this. Is there also any value of power factor?
Best Answer
Your formula for power, $P = VI \cos{\Phi}$, gives the average (over a period) rate at which electrical energy is converted into heat.
The difference between a resistor and an inductor is that over a whole period a resistor is taking electrical energy from a voltage source and converting it into heat whereas for a quarter of a period an inductor is taking electrical energy from a voltage source and converting it into stored energy in a magnetic field and then for the next quarter cycle the inductor is giving back the energy to the voltage source as its magnetic field (stored energy) is reducing so on average over half a period there is no net transfer of energy between voltage source and inductor.
In terms of averages over a period, $\langle P\rangle_{\rm resistor, period} = V_{\rm RMS}I_{\rm RMS}$ and $\langle P\rangle_{\rm inductor, period} = 0$
So in this situation $P=V\times I\cos \Phi = V I_{\rm R}$ as $V$ and $I_{\rm R}$ are in phase with one another, and the $I_{\rm L}$ plays no part in the average power dissipation as $V$ and $I_{\rm L}$ are $\pi/2$ out of phase.
So power is only dissipated if there is a projection of current onto the $V$ axis.