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.