Re: RMS vs Average Value
It is simple mathematical average value as said above.
It is used to determine the average power in an alternating current. Since the voltage in an A/C system oscillates between + and -, the Average value is zero. The RMS or "nominal" voltage is related to the average of the absolute value (or average vector magnitude) of the current, and is about 70% of the peak value.
As you have asked for the sine wave case. It needs a lil bit more explanation.
There are 3 different ways to quantify the magnitude of a sine wave.
1-Peak voltage 2- peak-peak voltage 3-RMS voltage
Peak voltage tells you how far the voltage swings, either positive or negative, from the point of reference(In case of sine wave this point of reference is the DC level). Peak voltage is only a moderately useful way of measuring voltage when trying to express the amount of work that will be done when driving a specified load. As AC voltage(assume sine wave) is constantly changing and is at or near the highest and lowest points in the cycle for only a tiny fraction of the cycle, the peak voltage is not a good way to determine how much work can be done by an AC power source.
2- Peak-Peak voltage:
As you can guess from the name,it tells you how far voltage swings from one peak value to the next.It is rarely used for measuring voltages in case of sine wave. It is probably more useful in the case of a non-symmetrical wave form.
3- RMS voltage:
RMS voltage is absolutely the most common way to measure/quantify AC voltage. It is also the most useful since it will give you the ability to exactly(more or less) predict how much work will be done by an AC voltage(source)unlike the case of peak voltage. The RMS value(voltage) of a pure sine wave is approximately .707*peak voltage. All voltmeters generally gives the RMS voltage of the wave form.
From where the name RMS came: If you try to find out the average value of a sine wave,it will be equal to ZERO(DC) because of equal positive and negative half of sine wave in one complete cycle but this ZERO value is not correct(since when an AC voltage/current wave osciallte it perform some work and avrage work cant be ZERO). To get the right average value,
S:sine wave is first squared (so that both halves of sine wave become +ve),
M:after this average is being taken just like normal averaging way
R:In the end to remove the Effect of square which has been done in first step, Square root is being taken to get actual Average value(amount of work being done)
If you read it in reverse order you will get 'RMS'(Root mean square) name.
If you are wondering about the number 0.707,this is how it comes.
If you take one cycle of Sine wave with a peak power of '1volt' and measures the instantaneous voltage at regular time intervals on this sine wave. Then 'squares' all of the voltages at each point and adds the squared values together and then calculates the average (mean) from the squared values and finally in the end calculate the square root of the average (mean) value you will get the value of 1(peak value)*0.707 (1volt* 1/square root of 2).
If you have sinewave with a peak value other than 1volt simply replace 1 with that peak value in above equation and you will get true average value of sine wave.
Hope it helps.
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