The Power factor is an expression of energy efficiency. It is usually expressed as a percentage—and the lower the percentage, the less efficient power usage is.

Power factor (PF) is the ratio of power in work. It is measured in kilowatts (kW), to apparent power, measured in kilovolt amperes (kVA). Apparent power is also known as demand. It is the measure of the amount of power used to run machinery and equipment during a certain period. It is found by multiplying (kVA = V x A). The result is expressed as kVA units.

PF expresses the ratio of true power used in a circuit to the apparent power delivered to the circuit.

To calculate the power factor, you need a power quality analyzer or power analyzer that measures both working power (kW) and apparent power (kVA), and to calculate the ratio of kW/kVA.

The power factor formula can be expressed in many other ways:

PF = (True power)/(Apparent power)

OR

PF = W/VA

Table of Contents

**Power in AC circuits:**

The three main components in an AC circuit that can affect the relationship between the voltage and current waveforms, by defining the total impedance of the circuit are the resistor, the capacitor, and the inductor.

The impedance of an AC circuit is equivalent to the resistance calculated in DC circuits. Impedance is generally defined as the ratio of the voltage and current phasor’s produced. Phasor’s are straight lines drawn in such a way as to represents a voltage or current amplitude by its length.

We can use the 90^{o} phase difference as the sides of a right-angled triangle, called an impedance triangle, with the impedance being the hypotenuse as determined by Pythagoras theorem.

Note that impedance, which is the vector sum of the resistance and reactance, has not only a magnitude (Z) but it also has a phase angle (Φ), which represents the phase difference between the resistance and the reactance. In a DC circuit, the power (P) is measured in watts. It is equal to the current squared (I^{2}) times the resistance (R).

Real Power P = I^{2}R

Reactive Power Q = I^{2}X Volt-amperes Reactive

Apparent Power S = I^{2}Z

**Real Power in AC Circuits**

**Real power** (P) is also known as true or active power. It performs the “real work” within an electrical circuit. Real power is measured in watts. It defines the power consumed by the resistive part of a circuit. It is always calculated as I^{2}*R, where R is the total resistive component of the circuit.

Real Power P = I^{2}R = V*I*cos(Φ) Watts, (W)

Since there is no phase difference between the voltage and the current in a resistive circuit, the phase shift between the two waveforms will be zero (0).

## Apparent Power in AC Circuits

The product of the RMS voltage, V applied to a circuit and the RMS current, I flowing into that circuit is called the “volt-ampere product” (VA). It is given the symbol S and whose magnitude is known as apparent power.

**Energy consumption** is the use of the power of a system by making use of supply.

** The energy consumption formula is articulated as,**

*E*_{(kWh/day)} = *P*_{(W)} × *t*_{(h/day)} / 1000_{(W/kW)}

Where,

E is energy in kilowatt-hours(kWh),

P is power in Watts,

t is hours

**3 phase power formula**

### Real Power

The Line to line voltage:

*W _{applied} = 3^{1/2} U_{ll} I cos Φ*

* = 3 ^{1/2} U_{ll} I PF *

*Where,*

*W _{applied} = real power (W, watts)*

*U _{ll} = line to line voltage (V, volts)*

*I = current (A, amps)*

*PF = cos Φ = power factor*

The Line to neutral voltage:

*W _{applied} = 3 U_{ln} I cos Φ *

*Where,*

*U _{ln} = line to neutral voltage (V, volts)*

**Resistive loads** convert current into other forms of energy, such as heat

**Inductive loads** use magnetic fields like motors, solenoids, and relays

Power of a Lens is one of the most important concepts in ray optics. The detailed concept of this topic is given below so that learners can understand this chapter more effectively.

## Power of a Lens Formula

The SI unit of power is diopter. Another thing you should keep in mind is that for a converging lens the optical power is positive and for a diverging lens, it is negative.

For example, if the focal length of a lens is 20cm, converting this to meters, we get 0.2m To find the power of this lens, take the reciprocal of 0.2 and we get 5. This means that you can calculate the power of a lens using radii of curvature of two surfaces and the refractive index of the lens material.

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