Electric Circuit Analysis: Unit I: b. Basic circuits analysis

Average value

Definition, Formula | Basic circuits analysis

Definition: The average value of an alternating current is defined as the D.C. current which transfers across any circuit the same charge as is transferred by that alternating current during the same time.

 AVERAGE VALUE

Definition: The average value of an alternating current is defined as the D.C. current which transfers across any circuit the same charge as is transferred by that alternating current during the same time.

In case of symmetrical wave forms, the average value taken over the complete cycle is zero. In such case, only half cycle is considered for relating average value with maximum value.

In case of unsymmetrical wave forms, the average value must always be taken over the whole cycle. Example of symmetrical wave forms is sinusoidal wave form.

Example for unsymmetrical wave forms: Half wave rectified wave form.

 

1. To Find the Average Value

Method 1 (Mid ordinate method)

This method can be used for both sinusoidal and non-sinusoidal. It is more convenient for non- sinusoidal waves. Refer the figure above.

Iav = i1 + i2 + …. + in / n

As is seen from the above expression, the accuracy of Iav depends upon the number of terms. More the number of terms, greater the accuracy.

Method 2 (Analytical method)


We must know the equation of wave form mathematically to find the average value by analytical method.

 

2. To Find the Average Value of Sinusoidally varying quantity

i = im sin θ

It is a symmetrical wave form. To calculate the average value, only half cycle must be considered.


For a sinusoidally varying quantity, average value Voyant olma

Note

1. In case of rectangular wave form. RM.S. value = average value. The reader is advised to check this analytically.

2. For all other types of wave forms. R.M.S. value is greater than the average value.

3. Moving coil meters indicate average values for the whole cycle.

4. Moving iron meters always indicate R.M.S values.

5. Hot wire ammeter indicates R.M.S. value of the whole cycle.


Electric Circuit Analysis: Unit I: b. Basic circuits analysis : Tag: : Definition, Formula | Basic circuits analysis - Average value