Effective Value of a Sine Wave.

Electronic Principles
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convenient basis for establishing an effective value of

alternating current, and is known as the "heating effect"

method. An alternating current is said to have an effective

value of one ampere when it produces heat in a given resistance

at the same rate as does one ampere of direct current.

You can compute the effective value of a sine wave of current to

a fair degree of accuracy by taking equally spaced instantaneous

values of current along the curve and extracting the square root

of the average of the sum of the squared values.

For this reason, the effective value is often cat led the "root

mean square" (rms) value. Thus, Ieff = average of the sum of the

squares of Iinst. Stated another way, the effective or rms value

(Ieff) of a sine wave of current is 0.707 times the maximum value

of current (Imax). Thus, Ieff = 1.414 x Ieff.

To identify the source of the constant 1.414, examine figure 66

on the previous page. Assume that the dc in figure 66, view A,

is maintained at 1 ampere and the resistor temperature is 100

C. Also assume that the ac in figure 66, view B, is increased

until the temperature of the resistor is 100 C. At this point,

it is found that a maximum ac value of 1.414 amperes is required

in order to have the same heating effect as a 1 ampere direct

current. Therefore, in the ac circuit the maximum current

required is 1.414 times the effective current. It is important

to remember that relationship, and that the effective value (Ieff)

of any sine wave of current is always 0.707 times the maximum

value (Imax).

Because alternating current is caused by an alternating voltage,

the ratio of the effective