Which of the following is a correct representation of peak value in an AC circuit?
Answer & step-by-step solution
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.
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.
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.
AC परिपथ में पीक मान का सही निरूपण निम्नलिखित में से कौन-सा है?
उत्तर और चरणबद्ध हल
पीक फैक्टर AC तरंग के अधिकतम (पीक) मान को RMS मान से जोड़ता है। परिभाषा से पीक फैक्टर = V_peak/V_rms, अतः V_peak = पीक फैक्टर × V_rms। साइन तरंग के लिए पीक फैक्टर √2 है।
विस्तृत हल (मूल भाषा में)
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.
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.
AC પરિપથમાં પીક મૂલ્યનું સાચું નિરૂપણ નીચેનામાંથી કયું છે?
જવાબ અને પગલાવાર ઉકેલ
પીક ફેક્ટર AC તરંગના મહત્તમ (પીક) મૂલ્યને RMS મૂલ્ય સાથે જોડે છે. વ્યાખ્યા મુજબ પીક ફેક્ટર = V_peak/V_rms, તેથી V_peak = પીક ફેક્ટર × V_rms. સાઇન તરંગ માટે પીક ફેક્ટર √2 છે.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
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.
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.
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