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Comparison of Direct and Alternating CurrentAuthor: 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 (22). Hence, throughout the cycle of i (instantaneous value of alternating current), Fig. 32, the rate of heat production at any instant is proportional to the value for the corresponding instant on the curve of i^{2}. The average heating value, or effective value^{1}, of the current over a whole cycle is therefore proportional to the average value of the i^{2} curve. The i^{2} 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 i^{2} about the axis of i is I_{m}^{2}/2 above the axis of i. That is, or Effective I = 0.707 I_{m} (31) Thus, the effective value of a sinusoidal current (or voltage) is (or 0,707) times its maximum value.


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