Peak factor directly relates the maximum (peak) value of an AC waveform to its RMS value. By definition, Peak factor = V_peak / V_rms, so V_peak = Peak factor × V_rms. For a sine wave the peak factor is √2.
Formula / Key Relation
Peak factor = Vpeak / Vrms
Therefore:
Vpeak = Peak factor × Vrms
For a sinusoid:
Vpeak = √2 Vrms
Detailed Explanation
Concept & ReasoningThe RMS value represents the DC-equivalent heating value of an AC quantity, whereas the peak value is the maximum instantaneous magnitude. Peak factor (also called crest factor) is defined as the ratio of peak value to RMS value. Rearranging that definition immediately gives the required representation. Form factor is a different ratio: RMS value divided by average rectified value, so it cannot be used to obtain the peak value directly unless additional waveform information is known.How to Solve It in the ExamRemember: peak factor connects PEAK ↔ RMS; form factor connects RMS ↔ average rectified value.Important Exam PointWrite…
Concept & Reasoning
The RMS value represents the DC-equivalent heating value of an AC quantity, whereas the peak value is the maximum instantaneous magnitude. Peak factor (also called crest factor) is defined as the ratio of peak value to RMS value. Rearranging that definition immediately gives the required representation. Form factor is a different ratio: RMS value divided by average rectified value, so it cannot be used to obtain the peak value directly unless additional waveform information is known.
How to Solve It in the Exam
Remember: peak factor connects PEAK ↔ RMS; form factor connects RMS ↔ average rectified value.
Important Exam Point
Write the definitions of peak factor and form factor before manipulating them; this prevents mixing the two ratios.
Related Revision Path
This question sits in the revision path Basic Electrical Engineering → AC Fundamentals → Waveform Factors .
Quick Trick
Remember: peak factor connects PEAK ↔ RMS; form factor connects RMS ↔ average rectified value.
Common Mistake
Do not confuse peak factor with form factor. For a sine wave they are approximately 1.414 and 1.11 respectively.
Exam Tip
Write the definitions of peak factor and form factor before manipulating them; this prevents mixing the two ratios.
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