To find RMS or effective values of some important waveforms

TO FIND RMS OR EFFECTIVE VALUES OF SOME IMPORTANT WAVEFORMS

RMS value of half wave rectified waveform :

2. Average value of half-wave rectified alternating current :

As the waveform is not symmetrical, we should take full cycle to find average value.

For a half wave rectified wave form

RMS value = 0.5 × maximum value

Average value = 0.318 × maximum value

Form factor of a half wave rectified alternating current

Kf = RMS value / Average value

= 0.5 × maximum value / 0.318 × maximum value

Kf = 1.57

3. RMS value and average value of a full wave rectified sinusoidal wave form

For a full wave rectified sine wave form,

4. To find RMS value average value, K_f and K_a for a saw-tooth wave form

Note

1. As mentioned earlier, RMS and average values can also be computed by the following formulae

RMS value = √Area of the squared wave / base

Average value = Area under the curve / base

As an example let us take the saw-tooth wave form as shown above. The shape of the squared wave form is as shown below. Take only one cycle.

Area of the wave form under the curve (triangle)

Note 2:

The saw-tooth wave form may be of the shape shown in fig.1.139. The equation is obtained by intercept formula. Here also

V_ms = 0.577 V_m

V_av = 0.5 V_m

5. To find the RMS value of a semi circular current wave which has a maximum value of 'a'

Solution:

The equation of the semi circular wave is

For a circular wave,

RMS value = 0.816 Maximum value