For a pure sinusoidal AC voltage, the RMS value is obtained by multiplying the peak value by __________.
\(\frac{1}{\sqrt{2}}\)
The RMS (root-mean-square) value of an AC waveform is its effective value, the value that produces the same heating in a resistor as an equal steady DC.
For a pure sinusoid this effective value is found by squaring the wave, averaging over a cycle and taking the square root.
Carrying out that calculation for a sine wave gives \(V_{rms}=\dfrac{V_{peak}}{\sqrt{2}}\).
So the peak value must be multiplied by \(\dfrac{1}{\sqrt{2}}\approx0.707\) to obtain the RMS value.
Multiplying by \(\sqrt{2}\) does the reverse, converting RMS back to peak, so that option is inverted.
Multiplying by \(1\) would leave the peak unchanged, and \(\dfrac{1}{2}\) is the factor between peak and the average of a full-wave-rectified sine, not the RMS factor.
Hence, the answer is \(\frac{1}{\sqrt{2}}\).
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