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On 3/19/14 5:26 AM, Adam Munich wrote:
Jim is correct; more information about that can be found here:
https://en.wikipedia.org/wiki/Root_mean_square
It's kind of like the average value of a function, but squared like
variance, such that you don't end up with a situation where your "rms
average" is meaningless. (ie standard function for "average value" of a 50%
square wave would be zero!).
RMS is more like standard deviation: square root of the mean squared
deviation.
However, there's a more rational reason for using RMS. Two signals with
the same RMS current or voltage will dissipate the same power in a load.
Consider a DC current of 10 Amps, flowing through a 100 Ohm resistor:
It dissipates I^2*R watts or 10^2 * 100 = 10kW
Now consider a DC current of 20 amps that is pulsing on and off 10 times
a second with 50% duty cycle.
WHile the current is on, the power is 20^2*100 or 40kW, and while the
current is off, the power is zero. So the *average* power is 20kW, even
though the average current is the same 10 Amps (half the time it's 20,
half the time it's zero).
It turns out that the pulsed DC current has an RMS value of, you guessed
it, 14.14 Amps (14.14^2*100 = 20kW)
If the duty cycle were 10%, it would be different. You'd be dissipating
4kW, and the average current is 5 Amps.
This "square of the voltage or current" thing shows up a lot:
the"action" (which is what makes a fuse blow) is I^2*t, because, after
all, fuses are all about thermal properties, and power & energy goes as
the square of the current.
So a resistance heater or lightbulb will work the same with the same RMS
current/voltage, independent of the actual waveform. If it's 120V rms,
it matters not whether it is 120V DC or 170V peak AC sinusoid or
something else.
In fact, the classic "true RMS" meter uses thermal approaches to measure
the power/voltage/current. It measures the temperature of a resistor
through which the current is passing, and is calibrated by measuring the
DC current which creates the same heating.
Most *meters* measure average (or peak) voltage or current, and then
just have a scale calibrated that is assuming sinusoidal waveform. For
instance, a bridge rectifier feeding a analog DC meter: the meter
mechanically averages the voltage coming out of the bridge.