A synchronous generator has 8 poles and rotates at 750 rpm.
1. Generated frequency is 50 Hz.
2. If speed increases to 1500 rpm, frequency becomes 100 Hz.
3. Frequency depends on speed and number of poles.
4. Frequency is independent of rotor speed.
Which of the above statements is/are correct?
Answer & step-by-step solution
A generator with more poles produces the same frequency at a lower mechanical speed; for fixed pole count, frequency is directly proportional to speed. f=PN/120. With P=8 and N=750 rpm, f=50 Hz; at 1500 rpm, f=100 Hz. Key relation: f=PN/120; N_s=120f/P.
Exam focus: Use rpm in the 120-factor formula. Common trap: Frequency is not independent of rotor speed in a synchronous generator.
Statement-wise Verification
- Statement 1 - Correct.
Generated frequency is 50 Hz.
With P=8 and N=750 rpm, f=50 Hz - Statement 2 - Correct.
If speed increases to 1500 rpm, frequency becomes 100 Hz.
At 1500 rpm, f=100 Hz. - Statement 3 - Correct.
Frequency depends on speed and number of poles.
A generator with more poles produces the same frequency at a lower mechanical speed - Statement 4 - Incorrect.
Frequency is independent of rotor speed.
The correct principle is: For fixed pole count, frequency is directly proportional to speed.
Core Concept
Electrical frequency, mechanical speed and pole count of a synchronous machine are locked by the synchronous-speed relation. A generator with more poles produces the same frequency at a lower mechanical speed; for fixed pole count, frequency is directly proportional to speed.
Formula / Key Relationship
f=PN/120; N_s=120f/P.
Step-by-Step Check
f=PN/120. With P=8 and N=750 rpm, f=50 Hz; at 1500 rpm, f=100 Hz.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 1. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option D is incorrect because it includes incorrect statement(s) 4.
Exam Shortcut / Approach
Use rpm in the 120-factor formula.
Common Mistake
Frequency is not independent of rotor speed in a synchronous generator.
Quick Revision
Frequency-Speed-Pole Relation is linked with Synchronous Generator, Synchronous Machines and Electrical Machines. Use rpm in the 120-factor formula.
एक सिंक्रोनस जनरेटर में 8 पोल हैं और यह 750 rpm पर घूमता है।
1. उत्पन्न आवृत्ति 50 Hz है।
2. गति 1500 rpm करने पर आवृत्ति 100 Hz हो जाती है।
3. आवृत्ति गति और पोलों की संख्या पर निर्भर करती है।
4. आवृत्ति रोटर गति से स्वतंत्र है।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
f=PN/120। P=8 और N=750 rpm पर f=50 Hz; 1500 rpm पर f=100 Hz। स्थिर पोल संख्या पर आवृत्ति गति के सीधे समानुपाती है। मुख्य संबंध: f=PN/120; N_s=120f/P।
परीक्षा फोकस: 120 वाले सूत्र में rpm लें। सामान्य गलती: सिंक्रोनस जनरेटर में आवृत्ति रोटर गति से स्वतंत्र नहीं है।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Generated frequency is 50 Hz.
With P=8 and N=750 rpm, f=50 Hz - Statement 2 - Correct.
If speed increases to 1500 rpm, frequency becomes 100 Hz.
At 1500 rpm, f=100 Hz. - Statement 3 - Correct.
Frequency depends on speed and number of poles.
A generator with more poles produces the same frequency at a lower mechanical speed - Statement 4 - Incorrect.
Frequency is independent of rotor speed.
The correct principle is: For fixed pole count, frequency is directly proportional to speed.
Core Concept
Electrical frequency, mechanical speed and pole count of a synchronous machine are locked by the synchronous-speed relation. A generator with more poles produces the same frequency at a lower mechanical speed; for fixed pole count, frequency is directly proportional to speed.
Formula / Key Relationship
f=PN/120; N_s=120f/P.
Step-by-Step Check
f=PN/120. With P=8 and N=750 rpm, f=50 Hz; at 1500 rpm, f=100 Hz.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 1. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option D is incorrect because it includes incorrect statement(s) 4.
Exam Shortcut / Approach
Use rpm in the 120-factor formula.
Common Mistake
Frequency is not independent of rotor speed in a synchronous generator.
Quick Revision
Frequency-Speed-Pole Relation is linked with Synchronous Generator, Synchronous Machines and Electrical Machines. Use rpm in the 120-factor formula.
એક સિંક્રોનસ જનરેટરમાં 8 પોલ છે અને તે 750 rpm પર ફરે છે.
1. ઉત્પન્ન આવૃત્તિ 50 Hz છે.
2. ઝડપ 1500 rpm કરતાં આવૃત્તિ 100 Hz થાય છે.
3. આવૃત્તિ ઝડપ અને પોલની સંખ્યા પર આધાર રાખે છે.
4. આવૃત્તિ રોટર ઝડપથી સ્વતંત્ર છે.
ઉપરોક્તમાંથી કયું/કયા વિધાન સાચું/સાચા છે?
જવાબ અને પગલાવાર ઉકેલ
f=PN/120. P=8 અને N=750 rpm પર f=50 Hz; 1500 rpm પર f=100 Hz. અચળ પોલ સંખ્યા પર આવૃત્તિ ઝડપના સીધા સમપ્રમાણમાં છે. મુખ્ય સંબંધ: f=PN/120; N_s=120f/P.
પરીક્ષા મુદ્દો: 120 વાળા સૂત્રમાં rpm લો. સામાન્ય ભૂલ: સિંક્રોનસ જનરેટરમાં આવૃત્તિ રોટર ઝડપથી સ્વતંત્ર નથી.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Generated frequency is 50 Hz.
With P=8 and N=750 rpm, f=50 Hz - Statement 2 - Correct.
If speed increases to 1500 rpm, frequency becomes 100 Hz.
At 1500 rpm, f=100 Hz. - Statement 3 - Correct.
Frequency depends on speed and number of poles.
A generator with more poles produces the same frequency at a lower mechanical speed - Statement 4 - Incorrect.
Frequency is independent of rotor speed.
The correct principle is: For fixed pole count, frequency is directly proportional to speed.
Core Concept
Electrical frequency, mechanical speed and pole count of a synchronous machine are locked by the synchronous-speed relation. A generator with more poles produces the same frequency at a lower mechanical speed; for fixed pole count, frequency is directly proportional to speed.
Formula / Key Relationship
f=PN/120; N_s=120f/P.
Step-by-Step Check
f=PN/120. With P=8 and N=750 rpm, f=50 Hz; at 1500 rpm, f=100 Hz.
Why the Other Options Are Wrong
Option A is incorrect because it omits correct statement(s) 1. Option B is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option D is incorrect because it includes incorrect statement(s) 4.
Exam Shortcut / Approach
Use rpm in the 120-factor formula.
Common Mistake
Frequency is not independent of rotor speed in a synchronous generator.
Quick Revision
Frequency-Speed-Pole Relation is linked with Synchronous Generator, Synchronous Machines and Electrical Machines. Use rpm in the 120-factor formula.
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