### Power Factor Calculator:

This power factor calculator is handy for analyzing alternating current (AC) flowing in circuits. You probably already know that you can model direct current (DC) with the help of Ohm’s law. For AC, this task is not so simple because such circuits have both real and reactive power.

This calculator helps you find the values of different types of power in a circuit and gives you a power factor formula that expresses the relationship between real and apparent power.

Go through these guiding principles and rules to find the result in seconds.

- Find the current, real power and reactive power of the power triangle.
- Get the sum of the squares of the real power and the reactive power.
- Use the square root of the sum to get the apparent power.
- Divide the true power by the apparent power to check the power factor.
- Divide the actual power by the square of the current to get the resistance value.

Before learning about power factor, you should get an idea about terms like real power, reactive power, apparent power and power triangle.

### The Power Triangle:

Since the apparent power can be found by the vector addition of real and reactive power, we can use a graphical method called the power triangle to represent these three values in triangular form.

Each side of the triangle represents one of the three forms of power transmitted in an AC circuit. The legs of the right triangle represent real and reactive power, and the hypotenuse – apparent power.

One of the consequences of using the power triangle is that we can easily establish a mathematical relationship between the three values using the Pythagorean Theorem:

Power Triangle /Power Factor formula:

Power factor is P_{(w)} in watts and divided by the apparent power s_{(VA) } in Volts per Ampere is equal to the cos φ.Hence the power factor formula can be written as

Power factor =P_{(w)}/s_{(VA)} =cos φ

S^{2} = p^{2} +Q^{2}

### Power Factor

It is the ratio of real power and apparent power.If there is no reactive power in the circuit m then the power factor is 1.

Power factor =P/s

P/s =cos φ

Power factor = cos φ

The formulas to compute the resistance, reactance and impedance are along the lines

P=I^{2} * R

Q= I^{2 } * X

S = I^{2} * Z

Z^{2} = R^{2} + X^{2}

Where

P=is the real power in watts

Q=is the reactive power in watts

S=is the apparent power in VA

φ = is the phase angle

R=is the resistance in ohm

X = is reactance in ohm

I= is current in Ampere

Z = impedance in ohm

### Example:1

If 20 A of electric current is flowing through the circuit and its real power is 150W, and reactive power is 54 VAR, Find its power factor, resistance, impedance?

### Answer:

Given that

Current =20A

Real power P=150 w

Reactive power Q =54 VAR

Apparent power S^{2} = p^{2} + Q^{2}

S^{2} =150^{2} + 54^{2}

S =127.08VA

Power Factor = p/s

=150 /127.08

=84.72

Power Factor = cos φ

84.72 = cos φ

Φ =0.9947 degree

Resistance R =P /I^{2}

=150 / 20^{2}

=0.375

Reactance X = Q /I^{2}

=54/ 20^{2}

=0.135

Impedance Z = S /I^{2}

=127.08 /20^{2}

=31.77

Therefore,power factor is 84.72, resistance is 0.375 ohm, reactance is 0.315 ohm, impedance is 31.77degrees

### Example:2

Calculate the power factor 25 w, and reactive power 15 VAR.Find the Pythagorean theorem?

### Answer:

P=25 W

Q =15 VAR

By using formula

S^{2} = p^{2} + Q^{2}

=25^{2} + 15^{2}

=29.15476 VA