Understanding Power Factor and Load Impedance

[p75213]

Homework Statement

I understand power factor is defined as (average power)/(apparent power) or cos(theta v - theta i) where theta v = load voltage and theta i = load current. Also the power factor angle is equal to the load impedance.

I don't understand how the 2 definitions of power factor equal each other or why the power factor angle equals the load impedance.

I know it's a tall order but I would appreciate it if somebody could answer these questions. Alternatively a good website or book that explains this fully.

 

[technician]

Your first statement means PF = Cos of the angle between V (the supply voltage) and the current vectors.
It does not equal the impedance but the angle between the impedance and the resistance vectors is the same as in my first sentence.
Hope this helps you to picture the vectors and the angle

 

[2milehi]

See if this helps

 

[p75213]

This is what I was after.

 

[DeeNos]

Power factor is an important concept in electrical engineering and it is essential to understand its relationship with load impedance. Let's start by defining power factor and load impedance.

Power factor, as you correctly stated, is the ratio of average power to apparent power. It is a measure of how effectively a circuit uses electrical power. A high power factor indicates that the circuit is using most of the supplied power to do useful work, while a low power factor indicates that a significant portion of the supplied power is being wasted.

On the other hand, load impedance is a measure of the opposition a circuit presents to the flow of alternating current (AC). It is a combination of resistance and reactance and is represented by a complex number. The load impedance can be thought of as the "resistance" to the flow of power in the circuit.

Now, let's look at the two definitions of power factor and how they relate to each other. The first definition, (average power)/(apparent power), can also be written as (Vrms)(Irms cosθ)/(Vrms)(Irms), where Vrms and Irms are the root mean square values of voltage and current, respectively, and θ is the phase angle between them. This definition is based on the concept of real power, which is the actual power being used to do work in the circuit.

The second definition, cos(θv - θi), is based on the concept of apparent power, which is the product of voltage and current without taking into account the phase difference between them. The power factor angle, θv - θi, is the phase difference between the voltage and current in the circuit.

Now, let's consider a purely resistive load, where the load impedance is equal to the resistance of the circuit. In this case, the phase angle between voltage and current is 0 degrees and the power factor angle, θv - θi, is also 0 degrees. Therefore, the two definitions of power factor are equal.

However, in a circuit with a reactive load, where the load impedance has both resistance and reactance components, the phase angle between voltage and current is no longer 0 degrees. This results in a difference between the two definitions of power factor. In this case, the power factor angle, θv - θi, is equal to the load impedance angle, which is the angle formed by the resistance and reactance