what is rms value and why do we use it?

Question

In my book its written that to express the ac power(from a resistor) in the same form as dc power we use a special value of current called the rms value.
Why do we use rms value for at all ? Why to express ac power in terms of dc power?
Whats so special about it?

Answer 1

RMS is Root mean square.



It is the square root of the average of the squares of a variable.



"Why to express ac power in terms of dc power?"



Power = E^2/R



Where E is the voltage and R is the resistance. An AC voltage is varying between two extremes. If I tell you that the AC is varying between +170V and 170V you can calculate the peak power with the above formula, but that is not the average power dissipation. Calculating the RMS tells us what DC voltage we would need to replace that AC voltage with to get the same average power dissipation.



Through calculus we can find the conversion factor between peak voltage and RMS voltage of a sinusoidal voltage wave, and that conversion factor is √2 /2.



For my 170v peak example the RMS voltage is



170v * √2 /2 ≈ 120v



"also i couldn't understand why most of the time ac voltage value is less than its peak value."



It is ALWAYS less than or equal to it's peak value no matter what the shape of the wave for the same reason the that the average of a set of numbers is always less than or equal to the largest number in the set. If I tell you that the tallest person at our school is 6'5" you know that the average height of everybody at school is less than 6'5".

Answer 2

When the values are oscillating, like a sine or cosine wave, then their average values will be zero. This will not give any idea of the strength, which is amplitude. The amplitude varies from 0 to a maximum value. Energy is proportional to the amplitude square. That varies from 0 t0 a maximum value. To find the average value of energy or amplitude, the RMS value is used. It is useful for ac currents and voltages.

Answer 3

i think of Billruss has the impressive theory yet he gets somewhat mixed up which regrettably finally ends up in a incorrect answer. For a sine wave the RMS fee is the top divided (no longer more suitable!!) via ?2 So the RMS fee of the waveform you specify is 3+4/?2 = 5.828 v