RMS (Root-mean square) value

In Fig. (a), the resistor R is connected as the load of the DC power supply of the voltage, V. The current in this circuit is V / R, and the power consumed by the power supply is V² / R.
Fig. (b) shows the case of a simple AC power supply Vsin ωt. The current also changes with time and is expressed by (V/R)sinωt. In addition, the power consumption also varies with time and is represented by the function (1－cos 2ωt)/2. On average, it is (1/2) V² / R, and when this is converted to the case of the DC in (a), the voltage corresponds to the direct current of V / √2. This voltage is the root-mean square value.
Fig. (c) shows the case of square wave voltage. When voltage V and a voltage of 0 are applied at equal intervals, the average power consumption is (1/2) V² / R as in (b). In this case as well, the effective (root-mean square) voltage converted into DC is V / √2. However, the time average of this square wave is V/2. Thus, the average voltage and the root-mean square value voltage are different.