Basic AC Theory AC GENERATION ANALYSISWhen a voltage is produced by an AC generator, the resulting current varies in step with thevoltage. As the generator coil rotates 360°, the output voltage goes through one complete cycle.In one cycle, the voltage increases from zero to E_{max} in one direction, decreases to zero, increasesto E_{max} in the opposite direction (negative E_{max}), and then decreases to zero again. The value ofE_{max}occurs at 90° and is referred to as peak voltage. The time it takes for the generator tocomplete one cycle is called the period, and the number of cycles per second is called thefrequency(measured in hertz).One way to refer to AC voltage or current is by peak voltage (E_{p}) or peak current (I_{p}). This isthe maximum voltage or current for an AC sine wave.Another value, the peak-to-peak value (E_{p-p} or I_{p-p}), is the magnitude of voltage, or current range,spanned by the sine wave. However, the value most commonly used for AC is effective value.Effective value of AC is the amount of AC that produces the same heating effect as an equalamount of DC. In simpler terms, one ampere effective value of AC will produce the sameamount of heat in a conductor, in a given time, as one ampere of DC. The heating effect of agiven AC current is proportional to the square of the current. Effective value of AC can becalculated by squaring all the amplitudes of the sine wave over one period, taking the averageof these values, and then taking the square root. The effective value, being the root of the mean(average) square of the currents, is known as the root-mean-square, or RMS value. In order tounderstand the meaning of effective current applied to a sine wave, refer to Figure 4.The values of I are plotted on the upper curve, and the corresponding values of I^{2} are plotted onthe lower curve. The I^{2} curve has twice the frequency of I and varies above and below a newaxis. The new axis is the average of the I^{2} values, and the square root of that value is the RMS,or effective value, of current. The average value is ½ I_{max}^{2}. The RMS value is then, which is equal to 0.707 I_{max}.2I^{2}_{max}2OR22I_{max}There are six basic equations that are used to convert a value of AC voltage or current to anothervalue, as listed below.Average value = peak value x 0.637 (7-1)Effective value (RMS) = peak value x 0.707 (7-2)Peak value = average value x 1.57 (7-3)Effective value (RMS) = average value x 1.11 (7-4)Peak value = effective value (RMS) x 1.414 (7-5)Average value = effective (RMS) x 0.9 (7-6)The values of current (I) and voltage (E) that are normally encountered are assumed to be RMSvalues; therefore, no subscript is used.Rev. 0 Page 5 ES-07

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