एक इंडक्शन मोटर 50 Hz सप्लाई आवृत्ति पर 5% स्लिप पर चलती है।
1. रोटर आवृत्ति लगभग 2.5 Hz है।
2. सिंक्रोनस गति पर रोटर करंट आवृत्ति शून्य हो जाती है।
3. स्थिर अवस्था (standstill) में रोटर आवृत्ति सप्लाई आवृत्ति के बराबर होती है।
4. रोटर आवृत्ति स्लिप से स्वतंत्र है।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
रोटर करंट आवृत्ति स्लिप के समानुपाती है: fr=s f=0.05×50=2.5 Hz। सिंक्रोनस गति पर s=0, fr=0; स्थिर अवस्था में s=1, fr=f। मुख्य संबंध: s=(N_s−N)/N_s; f_r=s f_s।
परीक्षा फोकस: स्थिर अवस्था: s=1; सिंक्रोनस गति: s=0। सामान्य गलती: रोटर आवृत्ति स्लिप से स्वतंत्र नहीं है।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Rotor frequency is approximately 2.5 Hz.
Rotor frequency fr=s f=0.05×50=2.5 Hz. - Statement 2 - Correct.
Rotor current frequency becomes zero at synchronous speed.
Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. - Statement 3 - Correct.
Rotor frequency equals supply frequency at standstill.
Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. - Statement 4 - Incorrect.
Rotor frequency is independent of slip.
The correct principle is: Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero.
Core Concept
Slip measures the difference between synchronous speed and rotor speed. Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. These relations are fundamental to induction-motor torque and rotor-circuit behavior.
Formula / Key Relationship
s=(N_s−N)/N_s; f_r=s f_s.
Step-by-Step Check
Rotor frequency fr=s f=0.05×50=2.5 Hz. At synchronous speed s=0, fr=0; at standstill s=1, fr=f.
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
Standstill: s=1; synchronous speed: s=0.
Common Mistake
Rotor frequency is not independent of slip.
Quick Revision
Rotor Frequency versus Slip is linked with Slip and Rotor Frequency, Induction Motors and Electrical Machines. Standstill: s=1; synchronous speed: s=0.
An induction motor operates at a slip of 5% with a supply frequency of 50 Hz.
1. Rotor frequency is approximately 2.5 Hz.
2. Rotor current frequency becomes zero at synchronous speed.
3. Rotor frequency equals supply frequency at standstill.
4. Rotor frequency is independent of slip.
Which of the above statements is/are correct?
Answer & step-by-step solution
Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. Rotor frequency fr=s f=0.05×50=2.5 Hz. At synchronous speed s=0, fr=0; at standstill s=1, fr=f. Key relation: s=(N_s−N)/N_s; f_r=s f_s.
Exam focus: Standstill: s=1; synchronous speed: s=0. Common trap: Rotor frequency is not independent of slip.
Statement-wise Verification
- Statement 1 - Correct.
Rotor frequency is approximately 2.5 Hz.
Rotor frequency fr=s f=0.05×50=2.5 Hz. - Statement 2 - Correct.
Rotor current frequency becomes zero at synchronous speed.
Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. - Statement 3 - Correct.
Rotor frequency equals supply frequency at standstill.
Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. - Statement 4 - Incorrect.
Rotor frequency is independent of slip.
The correct principle is: Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero.
Core Concept
Slip measures the difference between synchronous speed and rotor speed. Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. These relations are fundamental to induction-motor torque and rotor-circuit behavior.
Formula / Key Relationship
s=(N_s−N)/N_s; f_r=s f_s.
Step-by-Step Check
Rotor frequency fr=s f=0.05×50=2.5 Hz. At synchronous speed s=0, fr=0; at standstill s=1, fr=f.
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
Standstill: s=1; synchronous speed: s=0.
Common Mistake
Rotor frequency is not independent of slip.
Quick Revision
Rotor Frequency versus Slip is linked with Slip and Rotor Frequency, Induction Motors and Electrical Machines. Standstill: s=1; synchronous speed: s=0.
એક ઇન્ડક્શન મોટર 50 Hz સપ્લાય આવૃત્તિ પર 5% સ્લિપ પર ચાલે છે.
1. રોટર આવૃત્તિ આશરે 2.5 Hz છે.
2. સિંક્રોનસ ઝડપે રોટર કરંટ આવૃત્તિ શૂન્ય થાય છે.
3. સ્થિર સ્થિતિ (standstill) માં રોટર આવૃત્તિ સપ્લાય આવૃત્તિ બરાબર હોય છે.
4. રોટર આવૃત્તિ સ્લિપથી સ્વતંત્ર છે.
ઉપરોક્તમાંથી કયું/કયા વિધાન સાચું/સાચા છે?
જવાબ અને પગલાવાર ઉકેલ
રોટર કરંટ આવૃત્તિ સ્લિપના સમપ્રમાણમાં છે: fr=s f=0.05×50=2.5 Hz. સિંક્રોનસ ઝડપે s=0, fr=0; સ્થિર સ્થિતિમાં s=1, fr=f. મુખ્ય સંબંધ: s=(N_s−N)/N_s; f_r=s f_s.
પરીક્ષા મુદ્દો: સ્થિર સ્થિતિ: s=1; સિંક્રોનસ ઝડપ: s=0. સામાન્ય ભૂલ: રોટર આવૃત્તિ સ્લિપથી સ્વતંત્ર નથી.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Rotor frequency is approximately 2.5 Hz.
Rotor frequency fr=s f=0.05×50=2.5 Hz. - Statement 2 - Correct.
Rotor current frequency becomes zero at synchronous speed.
Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. - Statement 3 - Correct.
Rotor frequency equals supply frequency at standstill.
Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. - Statement 4 - Incorrect.
Rotor frequency is independent of slip.
The correct principle is: Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero.
Core Concept
Slip measures the difference between synchronous speed and rotor speed. Rotor-current frequency is proportional to slip: at standstill it equals supply frequency, and at synchronous speed it becomes zero. These relations are fundamental to induction-motor torque and rotor-circuit behavior.
Formula / Key Relationship
s=(N_s−N)/N_s; f_r=s f_s.
Step-by-Step Check
Rotor frequency fr=s f=0.05×50=2.5 Hz. At synchronous speed s=0, fr=0; at standstill s=1, fr=f.
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
Standstill: s=1; synchronous speed: s=0.
Common Mistake
Rotor frequency is not independent of slip.
Quick Revision
Rotor Frequency versus Slip is linked with Slip and Rotor Frequency, Induction Motors and Electrical Machines. Standstill: s=1; synchronous speed: s=0.
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