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insights into all 70% marks i.e. rms, 3dbrolloff, ect

Discussion in 'General Electronics Discussion' started by zachary schexnaydre, Apr 19, 2013.

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  1. zachary schexnaydre

    zachary schexnaydre

    Apr 19, 2013
    Hey guys, i sat through a basic electronics lecture at my local community college and the subject was ac voltage, reading the peak voltage and ect. well the topic came up that a volt meter reads the rms of an ac voltage which is 120 volts. I asked my self why does the meter read at 70% and i came up with a random answer in my head. I thought that if the peak voltage is about 169 volts and the 70% mark is 120 volts that maybe all the numbers from 120 to 169 added together will equal all the numbers below the 70% mark (1 through 120) added together. Come to find out it is extremely close. I used other numbers other than 169 and that top 30% is always within 2 or 3 % with the bottom 70%. I asked several engineers if they have ever seen this concept and they did not, they tried figuring it out using higher mathematics and seemed unsure of their answers. Its funny because me and a few professors now refer to it as Schexnaydre's theorem. So i have a few questions.

    Has anyone ever heard of this concept?
    Is there a name for this concept?
    Also is this taught in text books? Am i over analyzing this?
  2. (*steve*)

    (*steve*) ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd Moderator

    Jan 21, 2010
    Have you done calculus?

    Look up RMS (root mean square).

    For an AC signal that is a sine wave, the same heating effect will be seen in a resistor with a DC voltage equal to approx 70.71% of the peak AC value.

    The magic 1/sqrt(2) value only applies to certain waveforms, sine waves being a conspicuous example.

    The general solution isn't as simple as your calculations, but the concept is similar.
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