Fri September 09, 2011 By: Joshika Saraf

what is the value of Erms?show it by full process.

Expert Reply
Sat September 10, 2011

Derivation of root mean square voltage formula:

At any time, t, the voltage is given by

E = Eo sin?t


E2 = Eo2 sin2?t

But, from trigonometry, sin2? = ½(1 - cos2?)


E2 = ½Eo2 - ½ Eo2 cos 2?t

But the average of cos 2?t over a complete cycle is zero. The average square of the voltage over a whole cycle will be E2 = ½Eo2.

Thus, the ROOT MEAN SQUARE VOLTAGE will be ERMS = Eo/?2 = 0.707Eo

A similar argument will show that the ROOT MEAN SQUARE CURRENT will be Io/?2 = 0.707Io.

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