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question is not clear. RMS is .707 of peak. If you're asking about sums of currents or voltages represented by sine waves and they don't have the same frequency then the sum's RMS value is the square root of the sum of the squared amplitudes of the two waves. The squared amplitudes are proportional to the power in each current or voltage and the result represents the sum of the powers.
If the two sine waves have the same frequency then the sum's RMS value is the sum of the two RMS values. The physical circuit has to add power to the signal. (if the amplitudes are equal the resultant will have 4 times the power)
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CoachThe RMS value of a sine wave is the "Effective" or "Working" value of a sine wave. That is, the amount of power produced by a amount of current (Amperes). So for example, in your house, the power you would read is say, 120 Volts RMS. In actuality, you are getting 170 volts (if you round it). This 170 volts is the voltage you would get at the "Peak" (90 degrees into the sine wave). A way to find the RMS is done by this.
RMS= Peak Voltage X .707
The rms value of an ac voltage tells you the dc voltage that would produce the same power in a resistive load.
Power is I2R, so if I is varying with time, the average power over time is proportional to the average value of I2. The square-root of the average value of I2 tells you the current that would produce the same power if it were dc.
RMS voltage is always quoted for ac power supplies. For a sine-wave the rms value is 1/sqrt(2) times the peak voltage.
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