Effective or RMS Value

The effective or root mean square value of a periodic signal is equal to the magnitude of a DC signal which produces the same heating effect as periodic signal when applied across the load resistance. Consider a periodic signal, v (t), then

The RMS value of the sine wave is found out to be
 

The mains voltage of 230 V in the UK is its RMS value. A multimeter measures RMS voltages while an oscilloscope measures peak amplitudes. Hence the mains voltage when displayed on the oscilloscope will read 230 × √2 = 325.27 V

All the above expressions are independent of phase angle φ.

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