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Sine Waves and RMS

An AC voltage oscillates sinusoidally in time, with a peak value and an angular frequency that depends on the frequency. Because it changes sign, we use the RMS value to state a steady equivalent voltage that delivers the same power as an equivalent DC voltage. The 230 V mains voltage is always an RMS value, not the peak value.

u(t)=U_p\sin(\omega t)

sinusoidal voltage with angular frequency \omega

\omega=2\pi f

relation between angular frequency and frequency

U=\dfrac{U_p}{\sqrt2}

RMS value for a pure sine wave

Symbols

$U_p$	peak value	V
$\omega$	angular frequency	rad/s
$f$	frequency	Hz
$U$	RMS value	V

Example

Peak value $U_p=325$ V:

$U=325/\sqrt2\approx230$ V, i.e. the usual mains voltage.

230 V is an RMS value – the peak of the mains voltage is actually about 325 V.

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