If an a.c, i = i0 sin ωt , passes through a resistance R, the instantaneous rate of heat production is
P = i2 R
The ‘average’ rate of production of heat, over one complete cycle of current, is then given by
Now if one passes a direct current, of strength irms , in a resistance R, the rate of heat production will again be i\(^2_{rms}\) R . Thus the root mean square value, of an a.c., is equal to that direct current, which produces the same (total) heat, in a given resistance (in a time equal to the time period of the a.c.) as the given alternating current does over its one complete cycle. Hence, the root mean square value, of an a.c., is also called as the ‘effective value’ or the ‘virtual value’ of the given a.c. The measurable value of an a.c. is thus its r.m.s value, or ‘effective (or virtual) value’. The ammeter or voltmeter designed to measure a.c., would directly give the relevant r.m.s value. In our houses, alternating current is supplied at 220 V. It means that
