Let's look at this post by Lawrence Tseung:

** When to use rms value for comparison? **

There appears to be some misunderstanding of rms value and exactly when to use it.

The answer is as follows:

1. The term rms stands for root mean square. For a true sine wave, there will be values on the positive side and the same values will appear on the negative side. If we take the mean or average value, the result is zero.

2. Since we cannot compare two zero sine waves with the mean value, the industry devised the concept of root mean square. Essentially, the value is taken (either positive or negative) and then the value is multiplied by itself or squared.

3. For a positive number (e.g. 5), the squared value is 25 positive. For a negative number (e.g. -5), the squared value is also 25 positive. Thus, only the actual numeric value is effectively used.

4. In sampling a waveform, there may be many (e.g. 100) sampling points. There will be 100 squared numbers. The mean of these 100 squared numbers is taken. Then the square root function is applied.

5. Thus different sine waves can be compared with the rms value.

Once we understand the basic method, we know that we should apply this technique in the case when the voltage or current has positive and negative components. In fact, even if we are not sure, we can use the rms value for comparison purposes. We cannot go wrong in all cases!

Thus when the PhysicsProf and his experienced University colleague displayed their screen shots, they chose to display the rms Power value. **That is the CORRECT and scientifically acceptable display.**

**Hope this explanation helps all.** Science is reason and understanding. Science is not dogma or the belief or experience of an individual or a group of individuals no matter their position or background.

The concept of RMS is a somewhat confusing topic among both amateurs and professionals. In short, RMS is an equivalent DC value. The following will hopefully clearly illustrate why the last 3 paragraphs in the above quote should be reconsidered.

Using a very basic example of a 60Hz sine wave, let's look at two different methods of measuring the

**REAL** power in the simple circuit shown in the pictures. Utilized are separate voltage and current sources so that the phase relationship between them can be readily changed. The two wave forms are initially in perfect phase, and are multiplied together to produce an instantaneous power trace, just as would happen with our scope measurement. This exercise could readily be done to equal validity on the bench with real circuitry and test equipment, but it is much easier and more precise to accomplish with a circuit simulation.

The following first example uses two DMMs (not shown) with a simple circuit such as the top one shown in the schematic

**rms_ave_01.gif**. The current would be measured with a DMM in series with the circuit. With R1 as a pure resistance, and no reactive components present, the phase relationship between the voltage and current is "zero", therefore the DMM method is valid in this case.

**Given: (60Hz sine wave, continuous, non-reactive circuit) ("p" is "peak") (RMS values as measured with a standard or RMS-capable DMM)**1) Voltage: 10Vp = 7.07V

_{RMS}2) Current: 200mAp = 141.4mA

_{RMS}3) Power: V

_{RMS} x I

_{RMS} =

**1W** =

**REAL** power in R1.

So, we have taken the RMS of the voltage and current, and their product gives us the

**REAL** power dissipated in R1. Note that we have not performed any computation on the resulting power value, it was derived only from the voltage and current. With a purely resistive circuit where no phase shift occurs, two DMM's can be used to accurately measure the V and I values.

Let's now compare this measurement with one made using the oscilloscope method, where we sample the voltage and current wave forms of each generator (

**V1** and

**I1**) at a sufficiently high rate.

1) Voltage: The scope is set to indicate the RMS value of the displayed wave form voltage measurement, and it displays 7.07V

_{RMS}2) Current: The scope is set to indicate the RMS value of the displayed wave form current measurement, and it displays 141.4mA

_{RMS}3) Power: The scope is set to multiply in real time, the voltage and current wave forms to produce a third wave form trace showing us the instantaneous power. The scope is set to indicate the

**RMS** value of the displayed wave form power computation, and it displays

**1.22W**4) The scope is set to indicate the

**MEAN** value of the displayed wave form power computation, and it displays

**1.00W**Note that the

**MEAN** setting produced the correct result of

**1W**, whereas the

**RMS** setting did not. The following pictures illustrate this example, as well as the results with a progressive increase in the phase differential between the voltage and current. Rather than

**MEAN**, the abbreviation

**AVG** is used to denote "average" which is the terminology used in PSpice, and which is the equivalent to "MEAN".

**In Summary:****rms_ave_01.gif** illustrates the two generators used throughout these last tests, and indicates that the phase relationship between the voltage and current is zero in this first case. The amplitudes are set to the same values as the example with the DMM's.

**rms_ave_02.gif** illustrates the instantaneous power trace at the top (green trace) and the resulting RMS and AVG computations. This again illustrates the example given above where the phase is zero and the AVG computation gives the correct result.

**rms_ave_03.gif** illustrates the voltage and current with a 45º phase differential.

**rms_ave_04.gif** illustrates the instantaneous power trace at the top (green trace) and the resulting RMS and AVG computations. Note that the instantaneous power trace now deviates slightly below the 0 mark, but still exhibits a 2Wp-p swing. The bottom plot clearly indicates the discrepancy between the RMS and AVG computations, the RMS being

**1W** and the AVG being

**0.707W**. The reader may recall that the power factor for phase-shifted wave forms is: PF=COS (q), where "q" is the phase angle. In this case we have PF=COS (45) and

**PF=0.707**, so the AVG computation is correct in this case also.

**rms_ave_05.gif** illustrates the voltage and current with a 90º phase differential.

**rms_ave_06.gif** illustrates the instantaneous power trace at the top (green trace) and the resulting RMS and AVG computations. Note that the instantaneous power trace now deviates evenly below and above the 0 mark, but still exhibits a 2Wp-p swing. The bottom plot clearly indicates the discrepancy between the RMS and AVG computations, the RMS being

**0.707W** and the AVG being

**0.00W**. In this case we have PF=COS (90) and

**PF=0.00**, so

**the AVG computation is again correct**. The RMS computation has provided a gross error in terms of indicating the REAL power in the circuit.

Whether or not the RMS computation on an instantaneous power wave form can and should be used for comparisons, or even at all, is left to the reader.

.99