Consider the following statements regarding complex power:
1. Apparent power is the magnitude of complex power.
2. Reactive power can be negative.
3. Power factor is defined as ratio of real power to reactive power.
Which of the above statements is/are correct?
Answer & step-by-step solution
In sinusoidal steady state, complex power combines real and reactive power as S=P+jQ. Power factor is the ratio P/|S| and equals cosφ for sinusoidal voltage and current. Key relation: S=P+jQ; |S|=√(P²+Q²); PF=P/|S|=cosφ.
Exam focus: Draw the power triangle before choosing a power-factor relation. Common trap: Do not confuse P/Q with power factor.
Statement-wise Verification
- Statement 1 - Correct.
Apparent power is the magnitude of complex power.
Its magnitude |S| is apparent power in VA - Statement 2 - Correct.
Reactive power can be negative.
Inductive loads conventionally have positive Q and capacitive loads negative Q. - Statement 3 - Incorrect.
Power factor is defined as ratio of real power to reactive power.
The correct principle is: Power factor is the ratio P/|S| and equals cosφ for sinusoidal voltage and current.
Core Concept
In sinusoidal steady state, complex power combines real and reactive power as S=P+jQ. Its magnitude |S| is apparent power in VA, while P is measured in W and Q in var. Inductive loads conventionally have positive Q and capacitive loads negative Q. Power factor is the ratio P/|S| and equals cosφ for sinusoidal voltage and current.
Formula / Key Relationship
S=P+jQ; |S|=√(P²+Q²); PF=P/|S|=cosφ.
Why the Other Options Are Wrong
Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 1. Option C is incorrect because it omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 3.
Exam Shortcut / Approach
Draw the power triangle before choosing a power-factor relation.
Common Mistake
Do not confuse P/Q with power factor.
Quick Revision
Complex Power and Power Factor is linked with Complex Power, AC Fundamentals and Basic Electrical Engineering. Draw the power triangle before choosing a power-factor relation.
कॉम्प्लेक्स पावर के संबंध में निम्नलिखित कथनों पर विचार कीजिए:
1. आभासी शक्ति (Apparent power) कॉम्प्लेक्स पावर का परिमाण है।
2. प्रतिक्रियाशील शक्ति (Reactive power) ऋणात्मक हो सकती है।
3. पावर फैक्टर, वास्तविक शक्ति और प्रतिक्रियाशील शक्ति के अनुपात के रूप में परिभाषित है।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
साइनसॉइडल स्थायी अवस्था में S=P+jQ। पावर फैक्टर P/|S| है और साइनसॉइडल वोल्टेज-करंट के लिए cosφ के बराबर है। मुख्य संबंध: |S|=√(P²+Q²); PF=P/|S|=cosφ।
परीक्षा फोकस: पहले पावर त्रिभुज बनाएँ। सामान्य गलती: P/Q को पावर फैक्टर न समझें।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Apparent power is the magnitude of complex power.
Its magnitude |S| is apparent power in VA - Statement 2 - Correct.
Reactive power can be negative.
Inductive loads conventionally have positive Q and capacitive loads negative Q. - Statement 3 - Incorrect.
Power factor is defined as ratio of real power to reactive power.
The correct principle is: Power factor is the ratio P/|S| and equals cosφ for sinusoidal voltage and current.
Core Concept
In sinusoidal steady state, complex power combines real and reactive power as S=P+jQ. Its magnitude |S| is apparent power in VA, while P is measured in W and Q in var. Inductive loads conventionally have positive Q and capacitive loads negative Q. Power factor is the ratio P/|S| and equals cosφ for sinusoidal voltage and current.
Formula / Key Relationship
S=P+jQ; |S|=√(P²+Q²); PF=P/|S|=cosφ.
Why the Other Options Are Wrong
Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 1. Option C is incorrect because it omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 3.
Exam Shortcut / Approach
Draw the power triangle before choosing a power-factor relation.
Common Mistake
Do not confuse P/Q with power factor.
Quick Revision
Complex Power and Power Factor is linked with Complex Power, AC Fundamentals and Basic Electrical Engineering. Draw the power triangle before choosing a power-factor relation.
કોમ્પ્લેક્સ પાવર સંબંધિત નીચેના વિધાનો ધ્યાનમાં લો:
1. આભાસી પાવર (Apparent power) કોમ્પ્લેક્સ પાવરનું માન છે.
2. રિએક્ટિવ પાવર ઋણ હોઈ શકે છે.
3. પાવર ફેક્ટર વાસ્તવિક પાવર અને રિએક્ટિવ પાવરના ગુણોત્તર તરીકે વ્યાખ્યાયિત છે.
ઉપરોક્તમાંથી કયું/કયા વિધાન સાચું/સાચા છે?
જવાબ અને પગલાવાર ઉકેલ
સાઇનુસોઇડલ સ્થાયી સ્થિતિમાં S=P+jQ. પાવર ફેક્ટર P/|S| છે અને સાઇનુસોઇડલ વોલ્ટેજ-કરંટ માટે cosφ બરાબર છે. મુખ્ય સંબંધ: |S|=√(P²+Q²); PF=P/|S|=cosφ.
પરીક્ષા મુદ્દો: પહેલાં પાવર ત્રિકોણ દોરો. સામાન્ય ભૂલ: P/Q ને પાવર ફેક્ટર ન ગણો.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Apparent power is the magnitude of complex power.
Its magnitude |S| is apparent power in VA - Statement 2 - Correct.
Reactive power can be negative.
Inductive loads conventionally have positive Q and capacitive loads negative Q. - Statement 3 - Incorrect.
Power factor is defined as ratio of real power to reactive power.
The correct principle is: Power factor is the ratio P/|S| and equals cosφ for sinusoidal voltage and current.
Core Concept
In sinusoidal steady state, complex power combines real and reactive power as S=P+jQ. Its magnitude |S| is apparent power in VA, while P is measured in W and Q in var. Inductive loads conventionally have positive Q and capacitive loads negative Q. Power factor is the ratio P/|S| and equals cosφ for sinusoidal voltage and current.
Formula / Key Relationship
S=P+jQ; |S|=√(P²+Q²); PF=P/|S|=cosφ.
Why the Other Options Are Wrong
Option B is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 1. Option C is incorrect because it omits correct statement(s) 2. Option D is incorrect because it includes incorrect statement(s) 3.
Exam Shortcut / Approach
Draw the power triangle before choosing a power-factor relation.
Common Mistake
Do not confuse P/Q with power factor.
Quick Revision
Complex Power and Power Factor is linked with Complex Power, AC Fundamentals and Basic Electrical Engineering. Draw the power triangle before choosing a power-factor relation.
More AC Fundamentals questions