Analysis of the AC power generation process and of the alternating current we use in almost every aspect of our lives is necessary to better understand how AC power is used in today's technology.

EO1.3 DEFINE the following terms in relation to AC generation:

a. Radians/second

b. Hertz

c. Period

EO 1.4DEFINE effective value of an AC current relative to DC current.

EO 1.5Given a maximum value, CALCULATE the effective (RMS) and average values of AC voltage.

EO 1.6Given a diagram of two sine waves, DESCRIBE the phase relationship between the two waves.

Effective Values

The output voltage of an AC generator can be expressed in two ways. One is graphically by use of a sine wave (Figure 3). The second way is algebraically by the equation

e = E_max,sin cot, which will be covered later in the text.

Figure 3 Voltage Sine Wave

When a voltage is produced by an AC generator, the resulting current varies in step with the voltage. 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, increases to E_max in the opposite direction (negative E., ), and then decreases to zero again. The value of E_max occurs at 90 and is referred to as peak voltage. The time it takes for the generator to complete one cycle is called the period, and the number of cycles per second is called the frequency (measured in hertz).

One way to refer to AC voltage or current is by peak voltage (E_P) or peak current (I_p). This is the maximum voltage or current for an AC sine wave.

Another value, the peak-to-peak value (E_p-por 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 equal amount of DC. In simpler terms, one ampere effective value of AC will produce the same amount of heat in a conductor, in a given time, as one ampere of DC. The heating effect of a given AC current is proportional to the square of the current. Effective value of AC can be calculated by squaring all the amplitudes of the sine wave over one period, taking the average of 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 to understand 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 I² are plotted on the lower curve. The I² curve has twice the frequency of I and varies above and below a new axis. The new axis is the average of the I² values, and the square root of that value is the RMS, or effective value, of current. The average value is ¹/₂ I_max². The RMS value is then

There are six basic equations that are used to convert a value of AC voltage or current to another value, as listed below.

The values of current (I) and voltage (E) that are normally encountered are assumed to be RMS values; therefore, no subscript is used.

Figure 4 Effective Value of Current

Another useful value is the average value of the amplitude during the positive half of the cycle. Equation (7-7) is the mathematical relationship between I_av, I_max , and I.

Equation (7-8) is the mathematical relationship between E_av ,E_max , and E.

Example 1: The peak value of voltage in an AC circuit is 200 V. What is the RMS value of the voltage?

Example 2: The peak current in an AC circuit is 10 amps. What is the average value of current in the circuit?