rms value

[bhuvaneshnick]

i have learned what is rms value just before . its has been stated like"power dissipated with rms voltage is same power dissipated by equivalent dc voltage".i understand this point. Later question arose to me why we need rms value of signal and i accommodate myself that is to make analyses simple.

But i want strong answer why we are interested in Rms value.?

 

[MrAl]

i have learned what is rms value just before . its has been stated like"power dissipated with rms voltage is same power dissipated by equivalent dc voltage".i understand this point. Later question arose to me why we need rms value of signal and i accommodate myself that is to make analyses simple.

But i want strong answer why we are interested in Rms value.?

Hello there,

Interesting question and one that should be asked.

What do you already know about voltage? Think about this for a minute. If i say to you, i have a 1.5v battery, you probably think of a small AA cell or something like that, but just concentrating on the voltage itself 1.5v is rather low, so with high resistance it can not produce much current. Now i say i also have a 12v battery. You might think of a car battery, but 12v is a higher than 1.5v so you know it can produce more current in a somewhat higher resistance. What if i also have a 120v battery? You think about how much higher that is than the other two, and how it is even dangerous because it can produce significant current even in higher resistances than either 1.5v or 12v.

So far you have noticed that the different voltages, 1.5, 12, and 120v, have different overall characters. The higher ones can produce more current than the lower ones, and thus more power. So you are able to get a feel for the relationship between the voltage level (the number itself) and the common experience you might see in a real life application.

Now we move to the instantaneous voltage. That means the voltage can change with time, and any time we look at it, it can have a different value. For example, at t=1 second it might be 1.5v, at t=2 seconds it might be 12v, and at t=3 seconds it might be 120v. Also, the dwell period at each of these intervals might be different. At 1 second it might dwell for 1 full second, then at t=2 seconds it might dwell for 0.1 seconds (before return to zero) and at t=3 seconds it might stay at 120v for 0.001 seconds and then fall back to zero. So now how do you relate this waveform to the common experience, in a way that is similar to the way you were able to do with the fixed constant voltage sources?
It gets much harder now, because you see that the voltage only stays at 120v for very short time, and 12v for a short time, and stays at 1.5v for a relatively long time. This means the average signal will be closer to 1.5v, but maybe a little higher because of other voltages. The peak is 120v, so that tells you the maximum voltage is quite high. But how do we get an idea how much power this signal can produce? We want a quick and simple estimate so that we can compare it to other waveforms, maybe one where the 120v signal lasts for 1 full second.

If we take the average, we miss out on some information contained in the higher voltage, and if we take the peak we get a value that is too high. But if we take the RMS value of the waveform, we know the power it can produce in a resistor of some fixed value because the power can then be calculated with the familiar law:
P=V^2/R

In other words, if we use any other type of measurement we get a power estimate that is either too high or too low, but the RMS measurement at least gives us the power that will be produced in a resistance, which will be the same as a DC voltage of the same value.

It is still an estimate when the load is not a resistance however, but many types of loads are either resistive or mostly resistive, so the RMS value gives us something to compare to other signals that makes sense. If we compare any other measurements we'll get a false sense of what to expect. Comparing the RMS values of two signals we get something that makes sense because a higher value produces more power than a lower value.

You might have also noticed now that voltage itself is not as 'real' as energy. Nothing can ever happen with voltage alone, we also need a current to get something to happen. To know if something is going to happen or not with a signal measurement means we have to be able to measure the energy or power, and these depend on BOTH voltage and current. Having a single number (instead of having to know both the current and the voltage) allows us to quickly compare two signals as to what they might actually be able to do in real life. The RMS value helps us to be able to do that.

To sum up using one of your own words, the RMS value is a 'stronger' type of measurement than a simple peak or average measurement.

 

[KeepItSimpleStupid]

I'll add one thing. When "we" speak of the RMS value, we generally think of measuring an AC or periodic voltage. 12 VDC is indeed 12 VRMS too, but we usually never think of it that way.

Most meters when measuring AC, ASSUME the input is a sine wave, average it and multiply it by a constant so that the reading would be RMS. When the waveform is NOT a sinusoid, the value has little meaning.

TRMS meters accept an arbitrary, periodic waveform and compute the RMS value. SOME meters allow RMS(DC+AC) usually the RMS value of the AC component only, RMS(AC).

Meter specs include valid frequencies and crest factors allowed.

As Mr Al says, a lot of stuff revolves around power and efficiency. e.g. . AC power in, DC out at what efficiency?

 

[bhuvaneshnick]

AC power in, DC out at what efficiency?

i dont get what you trying to say?

It is still an estimate when the load is not a resistance however, but many types of loads are either resistive or mostly resistive

when we need to compare to voltage in terms of power its okay.if suppose the load is capacitor or inductor(not resistive load anyway) does rms works?

You might have also noticed now that voltage itself is not as 'real' as energy

i dont understand this line.


Thank you

 

[KeepItSimpleStupid]

AC in DC out (an example):

Here **broken link removed** is a spec sheet and note the column, efficiency. We have an AC power in and and DC power out, so you can compute it.

It is still an estimate when the load is not a resistance however, but many types of loads are either resistive or mostly resistive

A pure inductor and capacitor only exist in theory.[/quote]

 

[MrAl]

i dont get what you trying to say?



when we need to compare to voltage in terms of power its okay.if suppose the load is capacitor or inductor(not resistive load anyway) does rms works?



i dont understand this line.


Thank you

Hi,

In the case of the pure inductance or capacitance or even a reactive load with resistance, we can not compute the power from the RMS voltage measurement alone. Thus RMS is just an estimate, and it's only when the load is purely resistive to be exact. If the load is pure inductance or cap, then RMS wont tell us anything except that when we finally do get around to connecting a real load, we'll see real power show up, and most applications at some point will have some sort of power loss and that's the resistive part. So we can still understand that 240vrms will produce more power in that future load than 120vrms will. It will follow the square law.

When the current is in phase with the voltage, the load is said to dissipate "real" power. When the current is out of phase with the voltage we usually call this "apparent" power. So the real power is the real power, and the apparent power is the real power plus the reactive power, and the reactive power is not real power because it doesnt do anything...it's just stored.

 

[KeepItSimpleStupid]

I don't like the word "estimate" ut the second paragraph of MrAL is spot on.

The first waveform here https://ccipower.com/support/resources/technical-reference/control-firing-modes is typical in industrial process temperature control.
This is an application where TRMS is needed. Typically a resistive load is used for heating. We want P=V*I to work when measured independently and it does with RMS values and a resistive heater.

Motors and switched mode power supplies are much more complicated to get power computations to work.

So again if we know that the RMS voltage and RMS current and we use we can use the power factor from the specs and use P= V*I*pf for power.

The deal is:
a) P- V* I for DC circuits and AC circuits with a resistive load,
b) P=V*I*cos(theta) or P=V*I*pf for sinusoidal voltages and currents

Note that theta is 0 or cos (0) = 1 so P=V*I*1 is not a different formula for DC.

The application of (b) needs to be used with care.
c) the pf of arbitrary loads can be computed, BUT the signal MUST be periodic. It can be done using the definitions and knowing v(t) and i(t) and some other computations. Apparent power is Vrms * I rms. Real power is derived from v(t)*i(t). and apparent power/real power is pf.

 

[KeepItSimpleStupid]

We have been talking about RMS as though it's magic. There is a mathematical formula for it.

Anyway, you start with the voltage, square it and take the square root. This basically FLIPs the waveform, so it stays above zero.

(-I)*(-V+) is positive or energy dissipated and (+V)*(+I) is positive, so energy dissipated. The average value of a sine wave is zero, so that won't help us.
making the voltage always positive will. Now we take the mathematical average of the new waveform. This is the RMS value.

EDIT: Parens

 

[MrAl]

I don't like the word "estimate" [but] the second paragraph of MrAL is spot on.

There are two different views here for RMS. One is the *calculation* of the RMS value, the other is the *application* of that RMS value.

When say "estimate" i am talking about the application. The calculation itself can be exact, but the application can be very inexact yet still provide us with good information especially for comparative purposes.

For example, we have a signal coming in that is 10vrms. We measure it with a super accurate true rms meter, it measures 10.000vrms. The first application is 10vrms with a resistive load, thus the rms value tells us exactly what the power will be. The second application is a resistor and capacitor load and the power factor isnt too bad but not exactly known, and thus the rms value tells us a little about what the power will be but it's not accurate. But then we have a third application with a higher rms voltage, 20vrms, and same cap and resistor, and that tells us that whatever we did get in the second application we will see more of in the third application. And it is more than just knowing the peak voltage for example, which will be less informative.

There are some interesting applications we could look at i guess.