Comparison of Direct and Alternating Current

Author: E.E. Kimberly

As explained on page 8, when an alternating voltage is impressed on a circuit an alternating current flows. An alternating current may be compared to a direct current on the basis of their respective abilities to produce heat in a resistance. The instantaneous rate at which an electric current is capable of producing heat is directly proportional to the square of that current, as indicated by equation (2-2). Hence, throughout the cycle of i (instantaneous value of alternating current), Fig. 3-2, the rate of heat production at any instant is proportional to the value for the corresponding instant on the curve of i². The average heating value, or effective value¹, of the current over a whole cycle is therefore proportional to the average value of the i² curve. The i² wave is seen to be a sinusoid with twice the frequency of the i wave and located above the axis of the i wave.

The average value of a sinusoid is zero about its own axis. Hence, the average value of i² about the axis of i is I_m²/2 above the axis of i. That is,

Thus, the effective value of a sinusoidal current (or voltage) is (or 0,707) times its maximum value.

Fig. 3-2. Comparison of Direct and Alternating Current

1	The effective value of current is the square root of the average i2 value and so is sometimes called the root-mean-square (rms) value. An alternating current or voltage is always specified by its effective value unless it is definitely stated otherwise. Maximum values are indicated by the subscript m, as in Im and Em. Average values are indicated by the subscript av, as in Iav and Eav.