Average And Rms Value Of Alternating Current And Voltage - Practice Questions & MCQ

Average or Mean value:

The average voltage (or current) of a periodic waveform whether it is a sine wave, square wave or triangular waveform is defined as the quotient of the area under the waveform with respect to time. In other words, the averaging of all the instantaneous values along time axis with time being one full period (T).

The average value of alternating quantity for one complete cycle is zero. 

The average value of ac over half cycle (t=0 to T/2) 

$
i_{a v}=\frac{\int_{\frac{T}{2}}^0 i d t}{\int_{\frac{T}{2}}^0 d t}=\frac{2 i_0}{\pi}=0.637 i_0=63.7 \% \text { of } i_0
$

Similarly $V_{a v}=\frac{2 V_0}{\pi}=0.637 V_0=63.7 \%$ of $V_0$
Peak to peak value:
The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak.

$
\text { Peak to peak value }=V_0+V_0=2 V_0
$
 

Form factor and peak factor :

The ratio of r.m.s value of ac to its average during half cycle is defined as form factor. The ratio of peak value and r.m.s value is called peak factor.

$$
\text { Form Factor }=\frac{V_{\mathrm{rms}}}{V_{\mathrm{avg}}}
$$

or a sinusoidal waveform:
$V_{\mathrm{rms}}=\frac{V_m}{\sqrt{2}}$
$V_{\text {avg }}=\frac{2 V_m}{\pi}$
hus, the form factor for a sine wave is:

$$
\text { Form Factor }=\frac{\frac{V_m}{\sqrt{2}}}{\frac{2 V_m}{\pi}}=\frac{\pi}{2 \sqrt{2}} \approx 1.11
$$