Question

Derive an expression for Avg.value of ac voltage?

Answer 1

Derivation of root mean square current formula:
At any time, t, the voltage is given by
E = Eo sinωt
Squaring, we get E² = Eo² sin²ωt
But, from trigonometry, sin²α = ½(1 - cos2α)

Using this we get, E² = ½Eo² - ½ Eo² cos2ωt

But the average of cos 2ωt over a complete cycle is zero.
Thus, 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


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