# Power factor

#### rougie

Joined Dec 11, 2006
410
Hello forum,

I have been reading some lectures in this site and I have a question about obtaining the apparent power, true power, reactive power and the power factor of an actual AC circuit.

Basically I am wondering if someone can take a quick look and evaluate or validate that what I am doing is okay.

Let's say I have an 120VAC, 60HZ, RL circuit comprising a 60 ohm resistor and a 160 milli-henry coil. This circuit will have two outputs that will connect to a micro controller. Please view attached schematic. One of the ouputs will read the instantaneous current and the other will read the instantaneous voltage (both at the source of the AC circuit). To read the voltage and current, we will build a small circuit that will convert these values to an analog voltage signal so that the micro controller can read them. Therefore, we do not care about *how* the instataneous voltage and current are read... for example purposes, for now, we just know that the micro controller is able to read those values.

So, if we are able to read the instantaneous voltage and current values into the micro controller, then we should be able to calculate the RMS voltage and currents. So for the sake of this example, lets say we are reading an rms current and voltage of:

I = 1.41A
V = 120 VAC

In doing so, I can calculate the total AC impedence by doing:

ZT = 120/1.41A = 85.10 ohms

By having the total impedence, I can calculate the apparent power by doing:

S = I²Z = (1.41²) x 85.10 = 169.256 va

Also, since we are able to read the instantaneous voltage and current of the AC circuit, we are definitely able to detect the pahse angle between the current and voltage. We can the convert this angle to degrees. Assume we have a 45° angle. Refering to the trigonometric triangle, we can then figure out the true and reactive powers by doing:

119.2 watts = 169.256 * cosine 45° <<< true power

119.9 vars = 169.256 * sine 45° <<< reactive power

Also, we can simply calculate the power factor of this circuit by doing:

0.703 = 119.2/169.256

Is what I am doing correct? All feedback is appreciated.

ross

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