Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 293

TABLE 11.2
AC Sine Wave Conversion Table

Multiply the Value: by to Obtain:

Peak 2 Peak-to-peak

Peak-to-peak 0.5 Peak

Peak 0.637 Average

Average 1.637 Peak

Peak 0.707 RMS (effective)

RMS (effective) 1.414 Peak

Average 1.110 RMS (effective)

RMS (effective) 0.901 Average

11.7.11.9 Average Value
Because the positive alternation is identical to the negative alternation, the average value of a com-
plete cycle of a sine wave is zero. In certain types of circuits however, it is necessary to compute the
average value of one alternation. Figure 11.57 shows that the average value of a sine wave is 0.637
x peak value:

Average value = 0.637 × peak value (11.55)

or

E avg = E m × 0.637

where
E avg = Average voltage of one alternation.
E m = Maximum or peak voltage.

Similarly,

I avg = I m × 0.637 (11.56)

where
I avg = Average current in one alternation.
I m = Maximum or peak current.

Table 11.2 lists the various values of sine wave amplitude used for the conversion of AC sine
wave voltage and current.

11.7.11.10 Resistance in AC Circuits
If a sine wave of voltage is applied to a resistance, the resulting current will also be a sine wave.
This follows Ohm's law, which states that the current is directly proportional to the applied voltage.
Figure 11.58 shows a sine wave of voltage and the resulting sine wave of current superimposed on
the same time axis. Notice that as the voltage increases in a positive direction the current increases
along with it. When the voltage reverses direction, the current reverses direction. At all times, the
voltage and current pass through the same relative parts of their respective cycles at the same time.
When two waves, such as those shown in Figure 11.58, are precisely in step with one another, they
are said to be in phase . To be in phase, the two waves reach their maximum and minimum points at
the same time and in the same direction. In some circuits, several sine waves can be in phase with
each other; thus, it is possible to have two or more voltage drops in phase with each other and in
phase with the circuit current.