This question was previously asked in

UP Jal Nigam E&M 2016 Official Paper

Option 4 : kVAr

**Capacitors for power factor correction are rated in kVAr.**

__Important Points__

__Power Factor:__

- The overall power factor is defined as the cosine of the angle between the voltage and current.
- In AC circuits, the power factor is also defined as the ratio of the real power flowing to the load to the apparent power in the circuit. Hence power factor can also be defined as the ratio of watts to volt-amperes.
- It is also defined as the ratio of resistance to the impedance of the circuit.
- The capacitor is used for power factor improvement.

Power Triangle:

The power factor easily analyzed by the power triangle of the AC circuit.

If each side of the current triangle is multiplied by voltage V, then we get the power triangle as shown.

Power factor = cos ϕ

OA = VI cos φ and represents the active power in watts or kW

AB = VI sin φ and represents the reactive power in VAR or kVAR

OB = VI and represents the apparent power in VA or kVA

OB2 = OA2 + AB2

(kVA)2 = (kW)2 + (kVAR)2

\(cosϕ = \frac{{OA}}{{OB}} = \frac{{kW}}{{kVA}}\)

The lagging reactive power is responsible for the low power factor.

From the power triangle it is clear that the smaller the reactive power component, the higher is the power factor of the circuit and vice-versa.

Power Factor Improvement:

Considered an inductive load taking a lagging current at power factor cos ϕ1.

In order to improve the power factor of the circuit, we have to connect the capacitor in parallel with the inductive load as shown,

Where,

Ic = current flow through the capacitor that leads the supply voltage by 90°.

I = current flow through the inductive load that lags behind the supply voltage by angle ϕ1.

I' = Resultat current that lags or leads the supply voltage by angle ϕ2 depends on the magnitude of Ic.

The phasor diagram of the circuit can be drawn as,

From the phasor,

\(I_c=Isinϕ_1-I'sinϕ_2\)

Capacitor required to improve power factor from cos ϕ1 to cos ϕ2 given by,

\(C = \frac{{{I_c}}}{{\omega V}}\)