A sine wave has a peak value of 100V. What are the average value and rms value?

Question

A sine wave has a peak value of 100V. What are the average value and rms value?

Answer 1

The RMS value for an AC sine wave will be the peak value divided by the square root of 2 or approximately

Pk/1.414 = 70.7V

The average value is defined as the average value of a half-cycle, not a full cycle, since that will be zero. For a sine wave I believe it is 63.7% of the peak value, so our answer would be 67.3VAC. Low-cost non-RMS voltmeters typically measure the average value, then mutiply it by 0.707/0.637 to get the RMS value on the assumption that the signal is a sinewave. If the signal is not a sine wave, an averaging meter will report an incorrect "RMS" value because the ratio of average to RMS varies with the shape of the signal.

[REPOST] The average value is what you get when you rectify and then RC filter the input. This is the method used in averaging meters. True RMS meters will essentially sample the input hundreds or thousands of times per cycle, square each value, sum them, divide by the number of samples to get the average square, and then take the square root of the result and report it. This is what RMS means, "root mean square", and represents the power the signal will deliver to a load, no matter what the wave shape may be.

[RE-REPOST] Okay, to the obviously less-informed person who gave me a thumbs-down, here's some back-up. The 63.7% I quoted is correct.

http://www.xantrex.com/web/id/325/docserve.asp

Answer 2

Gary is correct. The average value is .637 x peak value. Average is based on peak, not peak-to-peak. RMS is .707 x peak or 1.11 x average value.

Answer 3

Since the sine wave is always going above and below zero by the same amount its average is zero.

Its RMS (the effective value) is .707 x its peak value.

Answer 4

vmax=100
average v=(2/pi)*vmax
=(2/3.1416)*100
=0.636*100
=63.6
rms v=(vmax)/(2^0.5)
=(vmax)/(0.707)
=141.44