A step-down delta-star transformer, with per-phase turns ration of 5, is fed from a 3-phase, 1100 V, 50 Hz source. The secondary of this transformer through a 3-pulse type rectifier feeds a R load of 10 Ω. Find the maximum value of the load current (phase).
Answer & step-by-step solution
The primary is delta-connected, so its phase voltage is 1100 V. With a per-phase turns ratio of 5, the star-secondary phase voltage is 1100/5 = 220 V rms. The three-pulse rectifier's maximum load voltage is the phase-voltage peak, so I_max = √2×220/10 = √2×22 A.
Concept & Reasoning
Because the primary is delta, V1,phase = V1,line = 1100 V. The per-phase turns ratio N1/N2=5 gives V2,phase=220 V rms. A three-pulse midpoint rectifier connected to the star secondary uses the phase-to-neutral secondary voltages, whose peak is √2V2,phase. For a 10 Ω resistive load, the maximum instantaneous load current is therefore √2×22 A. This calculation is a good example of why line/phase voltage must be resolved before applying transformer ratio and rectifier relations.
How to Solve It in the Exam
Convert line/phase voltage before applying turns ratio.
Important Exam Point
Always write the delta/star line-to-phase relationships; this avoids √3 errors.
Quick Trick
Convert line/phase voltage before applying turns ratio.
Common Mistake
Using line voltage directly on the star-connected secondary without checking the phase relation.
प्रति-फेज़ टर्न अनुपात 5 वाला एक स्टेप-डाउन डेल्टा-स्टार ट्रांसफार्मर 3-फेज़, 1100 V, 50 Hz स्रोत से पोषित है। इस ट्रांसफार्मर की सेकेंडरी 3-पल्स प्रकार के रेक्टिफायर द्वारा 10 Ω के R लोड को पोषित करती है। लोड धारा (फेज़) का अधिकतम मान ज्ञात कीजिए।
उत्तर और चरणबद्ध हल
A — √2 × 22 A। डेल्टा प्राइमरी का फेज़ वोल्टेज 1100 V है; टर्न अनुपात 5 से स्टार सेकेंडरी फेज़ वोल्टेज = 220 V rms। 3-पल्स रेक्टिफायर का अधिकतम लोड वोल्टेज फेज़-वोल्टेज शिखर है, अतः I_max = √2×220/10 = √2×22 A।
विस्तृत हल (मूल भाषा में)
Concept & Reasoning
Because the primary is delta, V1,phase = V1,line = 1100 V. The per-phase turns ratio N1/N2=5 gives V2,phase=220 V rms. A three-pulse midpoint rectifier connected to the star secondary uses the phase-to-neutral secondary voltages, whose peak is √2V2,phase. For a 10 Ω resistive load, the maximum instantaneous load current is therefore √2×22 A. This calculation is a good example of why line/phase voltage must be resolved before applying transformer ratio and rectifier relations.
How to Solve It in the Exam
Convert line/phase voltage before applying turns ratio.
Important Exam Point
Always write the delta/star line-to-phase relationships; this avoids √3 errors.
Quick Trick
Convert line/phase voltage before applying turns ratio.
Common Mistake
Using line voltage directly on the star-connected secondary without checking the phase relation.
પ્રતિ-ફેઝ ટર્ન ગુણોત્તર 5 વાળો એક સ્ટેપ-ડાઉન ડેલ્ટા-સ્ટાર ટ્રાન્સફોર્મર 3-ફેઝ, 1100 V, 50 Hz સ્રોતથી પોષિત છે. આ ટ્રાન્સફોર્મરની સેકન્ડરી 3-પલ્સ પ્રકારના રેક્ટિફાયર દ્વારા 10 Ω ના R લોડને પોષે છે. લોડ પ્રવાહ (ફેઝ)નું મહત્તમ મૂલ્ય શોધો.
જવાબ અને પગલાવાર ઉકેલ
A — √2 × 22 A. ડેલ્ટા પ્રાઇમરીનું ફેઝ વોલ્ટેજ 1100 V છે; ટર્ન ગુણોત્તર 5 થી સ્ટાર સેકન્ડરી ફેઝ વોલ્ટેજ = 220 V rms. 3-પલ્સ રેક્ટિફાયરનું મહત્તમ લોડ વોલ્ટેજ ફેઝ-વોલ્ટેજનું શિખર છે, તેથી I_max = √2×220/10 = √2×22 A.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Concept & Reasoning
Because the primary is delta, V1,phase = V1,line = 1100 V. The per-phase turns ratio N1/N2=5 gives V2,phase=220 V rms. A three-pulse midpoint rectifier connected to the star secondary uses the phase-to-neutral secondary voltages, whose peak is √2V2,phase. For a 10 Ω resistive load, the maximum instantaneous load current is therefore √2×22 A. This calculation is a good example of why line/phase voltage must be resolved before applying transformer ratio and rectifier relations.
How to Solve It in the Exam
Convert line/phase voltage before applying turns ratio.
Important Exam Point
Always write the delta/star line-to-phase relationships; this avoids √3 errors.
Quick Trick
Convert line/phase voltage before applying turns ratio.
Common Mistake
Using line voltage directly on the star-connected secondary without checking the phase relation.
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