# Derive an expression for Root Mean Square Value of Alternating Current

## Root Mean Square Value of Alternating Current:

The RMS or the effective value of an alternating voltage or current is a steady voltage or current that when passing or flowing through a given resistance for a given time produces the same amount of wastage of energy as produced by the alternating current flowing through the same resistance for the same time. From a heating point of view IRMS = IDC. If we know the maximum value of current or voltage then the RMS value of current or voltage can be calculated as follows:

IRMS = Im/√2 = 0.707 Im // For sinusoidal wave form.

∴ ERMS = 0.707 Em

The voltmeter and ammeter, we generally used to measure the R.M.S value of alternating voltage and current respectively when connected to an AC supply. Again from a heating point of view, the RMS value of alternating current is equivalent to direct current (IRMS = IDC).

Conclusion: For this reason, the knowledge of the RMS value of alternating current is so much important in Electrical Engineering.