थेवेनिन प्रमेय (Thevenin’s Theorem) के संबंध में निम्नलिखित कथनों पर विचार कीजिए:
1. थेवेनिन प्रमेय कहता है कि किसी भी रैखिक द्विपक्षीय नेटवर्क को एक प्रतिरोध के श्रेणी में समतुल्य वोल्टेज स्रोत से बदला जा सकता है।
2. थेवेनिन प्रतिरोध सभी स्वतंत्र स्रोतों को निष्क्रिय करके टर्मिनलों से दिखने वाला समतुल्य प्रतिरोध निकालकर ज्ञात किया जाता है।
3. टर्मिनलों पर ओपन सर्किट वोल्टेज नेटवर्क के थेवेनिन वोल्टेज के बराबर होता है।
4. थेवेनिन समतुल्य केवल DC परिपथों के लिए मान्य है और AC परिपथों पर लागू नहीं होता।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
C — केवल 1, 2 और 3। V_th = V_OC और Z_th स्वतंत्र स्रोत निष्क्रिय कर पोर्ट से देखा जाता है। थेवेनिन प्रमेय AC पर भी (प्रतिबाधा के साथ) लागू होता है, इसलिए कथन 4 गलत है।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Thevenin’s theorem states that any linear bilateral network can be replaced by an equivalent voltage source in series with a resistance.
Thevenin's theorem replaces a linear two-terminal network by one voltage source Vth in series with an equivalent impedance. - Statement 2 - Correct.
Thevenin resistance is calculated by deactivating all independent sources and finding equivalent resistance seen from terminals.
V_th=V_OC; Z_th seen at the port with independent sources suppressed. - Statement 3 - Correct.
The open circuit voltage across terminals is equal to Thevenin voltage of the network.
Vth is the open-circuit terminal voltage. - Statement 4 - Incorrect.
Thevenin equivalent is valid only for DC circuits and cannot be applied to AC circuits.
Thevenin equivalence also applies in sinusoidal AC networks by using complex impedances
Core Concept
Thevenin's theorem replaces a linear two-terminal network by one voltage source Vth in series with an equivalent impedance. Vth is the open-circuit terminal voltage. For a network with independent sources, Rth/Zth is found by suppressing independent sources; dependent sources remain and may require a test-source method. The theorem applies to AC circuits using complex impedances as well as to DC circuits.
Formula / Key Relationship
V_th=V_OC; Z_th seen at the port with independent sources suppressed.
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
In AC, use impedances—not just resistances.
Common Mistake
Dependent sources are not turned off when finding Thevenin resistance.
Quick Revision
Thevenin Equivalent Network is linked with Thevenin's Theorem, Network Theorems and Network Theory. In AC, use impedances—not just resistances.
Consider the following statements regarding Thevenin’s Theorem:
1. Thevenin’s theorem states that any linear bilateral network can be replaced by an equivalent voltage source in series with a resistance.
2. Thevenin resistance is calculated by deactivating all independent sources and finding equivalent resistance seen from terminals.
3. The open circuit voltage across terminals is equal to Thevenin voltage of the network.
4. Thevenin equivalent is valid only for DC circuits and cannot be applied to AC circuits.
Which of the above statements is/are correct?
Answer & step-by-step solution
Thevenin's theorem replaces a linear two-terminal network by one voltage source Vth in series with an equivalent impedance. For a network with independent sources, Rth/Zth is found by suppressing independent sources; dependent sources remain and may require a test-source method. Key relation: V_th=V_OC; Z_th seen at the port with independent sources suppressed.
Exam focus: In AC, use impedances—not just resistances. Common trap: Dependent sources are not turned off when finding Thevenin resistance.
Statement-wise Verification
- Statement 1 - Correct.
Thevenin’s theorem states that any linear bilateral network can be replaced by an equivalent voltage source in series with a resistance.
Thevenin's theorem replaces a linear two-terminal network by one voltage source Vth in series with an equivalent impedance. - Statement 2 - Correct.
Thevenin resistance is calculated by deactivating all independent sources and finding equivalent resistance seen from terminals.
V_th=V_OC; Z_th seen at the port with independent sources suppressed. - Statement 3 - Correct.
The open circuit voltage across terminals is equal to Thevenin voltage of the network.
Vth is the open-circuit terminal voltage. - Statement 4 - Incorrect.
Thevenin equivalent is valid only for DC circuits and cannot be applied to AC circuits.
Thevenin equivalence also applies in sinusoidal AC networks by using complex impedances
Core Concept
Thevenin's theorem replaces a linear two-terminal network by one voltage source Vth in series with an equivalent impedance. Vth is the open-circuit terminal voltage. For a network with independent sources, Rth/Zth is found by suppressing independent sources; dependent sources remain and may require a test-source method. The theorem applies to AC circuits using complex impedances as well as to DC circuits.
Formula / Key Relationship
V_th=V_OC; Z_th seen at the port with independent sources suppressed.
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
In AC, use impedances—not just resistances.
Common Mistake
Dependent sources are not turned off when finding Thevenin resistance.
Quick Revision
Thevenin Equivalent Network is linked with Thevenin's Theorem, Network Theorems and Network Theory. In AC, use impedances—not just resistances.
થેવેનિન પ્રમેય (Thevenin’s Theorem) અંગે નીચેનાં વિધાનો ધ્યાનમાં લો:
1. થેવેનિન પ્રમેય કહે છે કે કોઈ પણ રેખીય દ્વિપક્ષી નેટવર્કને એક અવરોધ સાથે શ્રેણીમાં સમતુલ્ય વોલ્ટેજ સ્રોતથી બદલી શકાય છે.
2. થેવેનિન અવરોધ તમામ સ્વતંત્ર સ્રોતોને નિષ્ક્રિય કરીને ટર્મિનલ પરથી દેખાતો સમતુલ્ય અવરોધ શોધીને મેળવાય છે.
3. ટર્મિનલ પરનો ઓપન સર્કિટ વોલ્ટેજ નેટવર્કના થેવેનિન વોલ્ટેજ જેટલો હોય છે.
4. થેવેનિન સમતુલ્ય ફક્ત DC પરિપથો માટે માન્ય છે અને AC પરિપથોને લાગુ પડતું નથી.
ઉપરોક્તમાંથી કયું/કયાં વિધાન સાચું/સાચાં છે?
જવાબ અને પગલાવાર ઉકેલ
C — ફક્ત 1, 2 અને 3. V_th = V_OC અને Z_th સ્વતંત્ર સ્રોત નિષ્ક્રિય કરી પોર્ટ પરથી જોવાય છે. થેવેનિન પ્રમેય AC પર પણ (અવબાધ સાથે) લાગુ પડે છે, તેથી વિધાન 4 ખોટું છે.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Thevenin’s theorem states that any linear bilateral network can be replaced by an equivalent voltage source in series with a resistance.
Thevenin's theorem replaces a linear two-terminal network by one voltage source Vth in series with an equivalent impedance. - Statement 2 - Correct.
Thevenin resistance is calculated by deactivating all independent sources and finding equivalent resistance seen from terminals.
V_th=V_OC; Z_th seen at the port with independent sources suppressed. - Statement 3 - Correct.
The open circuit voltage across terminals is equal to Thevenin voltage of the network.
Vth is the open-circuit terminal voltage. - Statement 4 - Incorrect.
Thevenin equivalent is valid only for DC circuits and cannot be applied to AC circuits.
Thevenin equivalence also applies in sinusoidal AC networks by using complex impedances
Core Concept
Thevenin's theorem replaces a linear two-terminal network by one voltage source Vth in series with an equivalent impedance. Vth is the open-circuit terminal voltage. For a network with independent sources, Rth/Zth is found by suppressing independent sources; dependent sources remain and may require a test-source method. The theorem applies to AC circuits using complex impedances as well as to DC circuits.
Formula / Key Relationship
V_th=V_OC; Z_th seen at the port with independent sources suppressed.
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
In AC, use impedances—not just resistances.
Common Mistake
Dependent sources are not turned off when finding Thevenin resistance.
Quick Revision
Thevenin Equivalent Network is linked with Thevenin's Theorem, Network Theorems and Network Theory. In AC, use impedances—not just resistances.
More Network Theorems questions