# How to Measure Power - AC

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• Last Post 23 August 2017
Chris posted this 25 June 2017

This topic is to help measure AC Sinusoidal Power and be as accurate as possible.

First, this only works with Sinusoidal Wave forms, irregular or square wave forms are not measured this way, and if done so will not yield accurate results.

Measure Current using a Current Shunt, sometimes known as a Current Viewing Resistor (CVR) or more commonly known as a Current Sensing Resistor (CSR). This turns Current into a Voltage Wave Form, something we can see on the oscilloscope. A simple Circuit follows, where we measure the Current (I) that is in the Circuit, the Lamp will carry the same current we sense across the Resistor. This is Kirchhoff's Current Law, where all nodes in a Circuit must carry the same Current. The value of the Current is determined by Ohms Law, where the Voltage across R1, this is the Voltage Drop, is V/R = I, Voltage / Resistance = Current. Example:

• We measure a 0.1 Volt Drop across the Resistor R1.
• Total input Voltage is 10 Volts.
• The Resistance of R1 is 0.1 Ohms:

So, the Current in the Circuit is: 0.1 / 0.1 = 1 Ampere.

We have a Voltage Drop in our Resistor, and this is dissipated as Heat, so there is Power being used here, this can be calculated as: V2 / R = P so 0.12 / 0.1 = 0.1 Watts dissipated in the CSR

Thus, the Total Power in the load: 9.99 Watts

Steps:

• Take Voltage Measurement, Use RMS Values from your Scope.
• Take the Current Measurement, again use RMS Values from your Scope.
• Measure the Phase Angle between the two Wave Forms. The following Video is a good resource:

Note: Some say you should use Mean Values. It is up to you, and may be worth comparing the two values. The RMS should work out to be the mean anyway, as this is the entire point of RMS, Root Mean Square, the RMS difference from Peak Values is the Mean.

Make sure you check your scope probes, make sure you account for the magnification, either 1x 10x or more.

The equation for calculating AC Sinusoidal Power is: V x I x Cos(Theta) where Theta is the Phase angle in Radians.

As a quick and easy resource, I have added an AC Power Calculator to my website: AC or Sinusoidal Power Calculator

By using this calculator, it makes for a quick easy painless measurement.

Note: My calculator takes Degrees and not Radians. Also, try to use Precision Sensing Resistors, they are very cheap, and worth the investment!

Hope this helps!

Chris

Chris posted this 25 June 2017

Hi Vasile - Yes, A Resistor in the Circuit will introduce extra Impedance, this is an extra Load, if you like, and must be accounted for.

Rule of Thumb: Use a low valued Resistor, to reduce the extra Circuit Impedance as much as possible, but not too low or it will be very hard to get accurate measurements. I like a 0.1 Ohm Precision Resistor. The reason, If I set my scope probe to 10x, all I need do is take my Current reading as 1 x on the scope.

For example: 1 Volt across a 1 Ohm Resistor will see 1 Amp in the Circuit - Ohms Law. But a 0.1 Ohm Resistor with a 0.99 Ohm Load, with 1 Volt across the Load's is 1/10th the value  So, we know, because Ohms Law is your Friend, that 1 Amp is flowing in the Circuit, because 1 Volt across 1 Ohm is 1 Amp, but we are only measuring at a 10th of the Resistance in the Circuit. A Diagram to help: XMM1 measures the total Voltage Drop at 1 Volt, with a small rounding error. This is correct, it is measuring the Amperage at 1 Amp as the Voltage across 1 Ohm is 1 Amp. However, XMM2, the 0.1 Ohm Current Sensing Resistor (CSR) is only 1/10th the total resistance, and this is correctly measuring 100mv because the Resistance is 1/10th the total value.

So, you can see, using a 0.1 Ohm Precision Resistor and setting the Scope to 10x, gives me the correct value of current, it does the Math for me and all I do is read off the screen.

Note: This is a DC Example, and AC is the topic. I recommend using a scope to do the measuring, so you can see the wave forms. You can use a Digital Multi Meter, but the problem is, if you do not have a Sinusoidal Wave Form then your measurements may be in vein.

Some years ago, I built what I call Measurement Blocks, cheap and easy. Although these Through Hole Current Resistors are not labelled "Precision" they are remarkably accurate! ±1%  I also have these: These are Precision, and I use them for an extra check on my small tolerance stuff.

This makes life easy, The only thing is making sure there is no Ground Loop, which is easy with some practice.

I hope this helps!

Chris

Chris posted this 27 June 2017

Hi Vasile - Please keep in mind that Hall Effect Current Probes can have their own set of problems. They are not always a more accurate way to measure Current.

Its worth noting that some I have used do have issues like Phase Angle Delays which can mean a big difference in Accuracy. Some are just not accurate at all.

Also, some are. So it is worth knowing both methods to verity the result of the other.

Chris

Chris posted this 23 August 2017

I have been taking a look at this discussion as I think it is very important and noticed an error.Isn't R2 suposed to be 0.9 Ohm and not 0.99Ohm as you have writen?so as to sum up with R1 to 1Ohm?

I am glad you are paying attention Vasile.

Yes, exactly! 0.9 and 0.99 are not the same number! This introduces a 0.99 - 0.1 = 0.89 of an error. The "Rounding Error" I indicated at.

Chris

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Weeks High Earners:
The great Nikola Tesla: Ere many generations pass, our machinery will be driven by a power obtainable at any point of the universe. This idea is not novel. Men have been led to it long ago go by instinct or reason. It has been expressed in many ways, and in many places, in the history of old and new. We find it in the delightful myth of Antheus, who drives power from the earth; we find it among the subtle speculations of one of your splendid mathematicians, and in many hints and statements of thinkers of the present time. Throughout space there is energy. Is this energy static or kinetic? If static, our hopes are in vain; if kinetic - and this we know it is for certain - then it is a mere question of time when men will succeed in attaching their machinery to the very wheelwork of nature.

Experiments With Alternate Currents Of High Potential And High Frequency (February 1892).

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