Now, when measuring the signal's mean power with a resistor & thermometer we don't always know anything about the signal pattern — i.e. we don't always know if it's d.c., a sinewave, or more complicated. All we know are a power and a resistance. A given measured average power, P, could be produced by any signal pattern whose average squared voltage was 
. The three signals (d.c., sinewave, & complicated) shown in figure 4.1 can now all be said to have the same ‘size’ if they produce the same amount of power — i.e. when
Hence this technique of measuring a mean power gives us a way to compare the sizes of signals without having to worry about the details of their variations.
From equation 7 we can now define a voltage, 
, calculated from the measured power
i.e.
This quantity, 
, can be used to represent the size of the signal's voltage no matter what the signal pattern is. The rms stands for root mean square and indicates that it is a value which depends upon the square root of the time average (mean) of the voltage squared. Root mean square voltages (and other quantities, like currents) are a convenient way to represent the signal size since we don't have to bother with the signal's shape. As a result rms voltages and current values are widely used to indicate the sizes of signals. In effect, when we say a given signal has an rms voltage level, 
, we're actually saying that it carries the same power as a steady d.c. voltage of 
volts. For a sinewave we can expect that 
. Since we've already found that 
we can use an oscilloscope to determine a sinewave's rms voltage by noting the peak-to-peak voltage an using
Note, however, that equation 10 is only correct for sinewaves.
Waves like squarewaves or trianglewaves have different 
ratios. Some
waveforms — e.g. the complicated one shown in figure 4.1c on the
previous page — don't even have a unique peak-to-peak value!
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