87-3 Effective values of current and voltage The effective value of any periodic current is equal to the value of the direct current which flowing through a resistance R, delivers the same power to R as periodic current does R i R R P=R i Rdt dt T 2R= raid i 2dt V Ddt T The root mean square value Rms of the sinusoidal waveform cos(at-9)dt =l VT 1+c0s2(a-),=1 2 T and V 2
§7-3 Effective values of current and voltage. The effective value of any periodic current is equal to the value of the direct current which flowing through a resistance R, delivers the same power to R as periodic current does. I R i R P I R 2 = i dt T R i Rdt T P T T = = 0 2 0 1 2 i dt T R I R T = 0 2 2 i dt T I T = 0 1 2 The root mean square value dt T V T = 0 1 2 2 2 1 m m T I T = I = 2 m I I = 2 Vm and V = = − T I m t dt T I 0 2 2 cos ( ) 1 + − = T m dt t T I 0 2 1 1 cos 2( ) Rms of the sinusoidal waveform: