CBSE Class 12-science Answered

Derivation of root mean square voltage formula:

At any time, t, the voltage is given by

E = E_o sin?t

Squaring

E² = E_o² sin²?t

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

Giving

E² = ½E_o² - ½ E_o² 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 = ½E_o².

Thus, the ROOT MEAN SQUARE VOLTAGE will be E_RMS = E_o/?2 = 0.707E_o

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