चित्र Q38 में दिखाए गए परिपथ पर विचार कीजिए और निम्नलिखित कथन पढ़िए।
कथन 1: संधारित्र से धारा केवल स्रोत रूपांतरण (source transformation) से, अध्यारोपण प्रमेय के बिना, प्राप्त की जा सकती है।
कथन 2: संधारित्र से धारा अध्यारोपण प्रमेय (superposition theorem) से प्राप्त की जा सकती है।
निम्नलिखित में से सही विकल्प चुनिए:
उत्तर और चरणबद्ध हल
C — कथन 2 सही, कथन 1 गलत। नेटवर्क रैखिक है, इसलिए प्रत्येक साइनसॉइडल स्रोत की अपनी आवृत्ति पर अलग विश्लेषण कर धाराएँ जोड़ी जा सकती हैं। दोनों स्रोत अलग आवृत्तियों पर हैं, इसलिए एक ही फेज़र-डोमेन स्रोत रूपांतरण से पूरा हल नहीं निकलता।
विस्तृत हल (मूल भाषा में)
Statement-wise Analysis
Statement 1: False
Statement 2: True
Concept and Reasoning
The network is linear, so superposition can be used by analyzing the response to each sinusoidal source at its own frequency and then adding the time-domain currents. Because the two sources operate at different frequencies and the reactive impedances are frequency-dependent, a single phasor-domain source transformation cannot combine the complete problem without separate frequency analysis. Thus statement 1 is false and statement 2 is true.
Calculation / Key Relation
iC(t)=iC,ω=2(t)+iC,ω=10(t)
Exam Takeaway
Different frequencies → solve separately, then superpose in time.
Common Mistake
Do not add phasors belonging to different frequencies.
Quick Trick
Different frequencies → solve separately, then superpose in time.
Consider the following circuit shown in Fig. Q38 and read the following statements.
Statement 1:The current through the capacitor can be obtained by using only source transformation without the use of superposition theorem.
Statement 2:The current through the capacitor can be obtained by using superposition theorem. Fig. Q38Choose the correct option from the following:
Answer & step-by-step solution
The network is linear, so superposition can be used by analyzing the response to each sinusoidal source at its own frequency and then adding the time-domain currents. Because the two sources operate at different frequencies and the reactive impedances are frequency-dependent, a single phasor-domain source transformation cannot combine the complete problem without separate frequency analysis. Thus statement 1 is false and statement 2 is true.
Statement-wise Analysis
Statement 1: False
Statement 2: True
Concept and Reasoning
The network is linear, so superposition can be used by analyzing the response to each sinusoidal source at its own frequency and then adding the time-domain currents. Because the two sources operate at different frequencies and the reactive impedances are frequency-dependent, a single phasor-domain source transformation cannot combine the complete problem without separate frequency analysis. Thus statement 1 is false and statement 2 is true.
Calculation / Key Relation
iC(t)=iC,ω=2(t)+iC,ω=10(t)
Exam Takeaway
Different frequencies → solve separately, then superpose in time.
Common Mistake
Do not add phasors belonging to different frequencies.
Quick Trick
Different frequencies → solve separately, then superpose in time.
આકૃતિ Q38માં દર્શાવેલો પરિપથ ધ્યાનમાં લો અને નીચેનાં વિધાનો વાંચો.
વિધાન 1: સંધારકમાંથી પ્રવાહ ફક્ત સ્રોત રૂપાંતરણ (source transformation)થી, સંપાતીકરણ પ્રમેય વિના, મેળવી શકાય છે.
વિધાન 2: સંધારકમાંથી પ્રવાહ સંપાતીકરણ પ્રમેય (superposition theorem)થી મેળવી શકાય છે.
નીચેનામાંથી સાચો વિકલ્પ પસંદ કરો:
જવાબ અને પગલાવાર ઉકેલ
C — વિધાન 2 સાચું, વિધાન 1 ખોટું. નેટવર્ક રેખીય છે, તેથી દરેક સાઇનસોઇડલ સ્રોતનું તેની પોતાની આવૃત્તિ પર અલગ વિશ્લેષણ કરીને પ્રવાહો ઉમેરી શકાય છે. બંને સ્રોત અલગ આવૃત્તિ પર છે, તેથી એક જ ફેઝર-ડોમેન સ્રોત રૂપાંતરણથી સંપૂર્ણ ઉકેલ મળતો નથી.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Analysis
Statement 1: False
Statement 2: True
Concept and Reasoning
The network is linear, so superposition can be used by analyzing the response to each sinusoidal source at its own frequency and then adding the time-domain currents. Because the two sources operate at different frequencies and the reactive impedances are frequency-dependent, a single phasor-domain source transformation cannot combine the complete problem without separate frequency analysis. Thus statement 1 is false and statement 2 is true.
Calculation / Key Relation
iC(t)=iC,ω=2(t)+iC,ω=10(t)
Exam Takeaway
Different frequencies → solve separately, then superpose in time.
Common Mistake
Do not add phasors belonging to different frequencies.
Quick Trick
Different frequencies → solve separately, then superpose in time.
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