# The ratio of the peak value of a wave to its RMS value is defined as:

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SSC JE EE Previous Paper 9 (Held on: 29 Oct 2020 Evening)
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1. Form factor
2. Peak factor
3. Mean value
4. Average factor

## Answer (Detailed Solution Below)

Option 2 : Peak factor
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ST 1: Basic Electrical Engineering
3623
20 Questions 20 Marks 20 Mins

## Detailed Solution

Explanation:

The form factor is defined as the ratio of the RMS value to the average value of an alternating quantity.

F.F. (Form factor) = $$\frac{{R.M.S\;Value}}{{Average\;Value}}$$

Crest Factor ‘or’ Peak Factor is defined as the ratio of the maximum value to the R.M.S value of an alternating quantity.

C.F. ‘or’ P.F. = $$\frac{{Maximum\;Value}}{{R.M.S\;Value}}$$

IMPORTANT EVALUATIONS:

 WAVEFORM SHAPE MAX. VALUE AVERAGE VALUE RMS VALUE FORM FACTOR CREST FACTOR SINUSOIDAL WAVE $${A_m}$$ $$\frac{{2{A_m}}}{\pi }$$ $$\frac{{{A_m}}}{{\sqrt 2 }}$$ $$\frac{{\frac{{{A_m}}}{{\sqrt 2 }}}}{{\frac{{2{A_m}}}{\pi }}} = 1.11$$ $$\frac{{{A_m}}}{{\frac{{{A_m}}}{{\sqrt 2 }}}} = \sqrt 2$$ SQUARE WAVE $${A_m}$$ $${A_m}$$ $${A_m}$$ $$\frac{{{A_m}}}{{{A_m}}} = 1$$ $$\frac{{{A_m}}}{{{A_m}}} = 1$$ TRIANGULAR WAVE $${A_m}$$ $$\frac{{{A_m}}}{2}$$ $$\frac{{{A_m}}}{{\sqrt 3 }}$$ $$\frac{{\frac{{{A_m}}}{{\sqrt 3 }}}}{{\frac{{{A_m}}}{2}}} = \frac{2}{{\sqrt 3 }}$$ $$\frac{{{A_m}}}{{\frac{{{A_m}}}{{\sqrt 3 }}}} = \sqrt 3$$ HALF-WAVE RECTIFIED WAVE $${A_m}$$ $$\frac{{{A_m}}}{\pi }$$ $$\frac{{{A_m}}}{2}$$ $$\frac{{\frac{{{A_m}}}{2}}}{{\frac{{{A_m}}}{\pi }}} = \frac{\pi }{2}$$ $$2$$