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Home Q & A Board Science-Related Homework Help Physics
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smmunday smmunday
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11 years ago
Why is the peak voltage higher than the RMS voltage?
I know about the equation Vpeak = ?2 x Vrms, but can someone please explain briefly the physics behind it.
Thanks.
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#1
11 years ago
AC, alternating current, varies over time in a sinusoidal manner - the voltage goes up and down around a mid-point, tracing a sine curve in time (Imagine a graph of voltage versus time.  Remember your trigonometry?).  The RMS, Root Mean Square, is the average over time of the square of the voltage.  This 'average' falls somewhere below the peak of the sine wave curve. Hence, the RMS voltage is lower than the peak.
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finallyfinally
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11 years ago
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#3
11 years ago
RMS (Root Mean Square) is the heating equivalent.

Intuitively, since the sine wave spends only a small portion of it's time at the peaks, and most of it's time below those peaks, the overall effect of the wave would be expected to be significantly less than the peak, and it is, as you note.

The actual physics, you square the sine wave to get a sine squared wave, then integrate it over one cycle, and average it over that cycle.
v = ? (Vp)²sin²?tdt
between t = 0 and ?t = 2?
going through the math you get
v = Vp/?2
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#4
11 years ago
If you don't understand why peak voltage is higher than RMS voltage that means you either don't understand what "peak" means, or what "RMS" means, or both. If you understand the terms then you automatically understand why peak voltage is higher.
Get a piece of graph paper, draw one cycle of a sine wave on it with amplitude = 1, take a number of equally spaced points along the X axis and using a calculator calculate the square of the voltage at each point. Now plot the squares on the same graph. You'll see you get a new sine wave, frequency double the original, amplitude 0.5V, with a DC offset of 0.5V. Now find the mean voltage of this sinewave, which is the average of all the points. I'll tell you the answer - it's 0.5V. Now find the square root of the mean - it is 0.7071
Peak voltage is what it says - the peak of the waveform, which is 1.000V.

Now you know why peak voltage is higher than RMS voltage.

Try the same exercise for a square wave. You'll find that peak voltage = RMS voltage.
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