अधिकतम शक्ति स्थानांतरण (Maximum Power Transfer) के संबंध में निम्नलिखित कथनों पर विचार कीजिए:
1. DC परिपथों में अधिकतम शक्ति स्थानांतरण तब होता है जब लोड प्रतिरोध स्रोत प्रतिरोध के बराबर हो।
2. AC परिपथों में अधिकतम शक्ति स्थानांतरण तब होता है जब लोड प्रतिबाधा स्रोत प्रतिबाधा का सम्मिश्र संयुग्मी (complex conjugate) हो।
3. अधिकतम शक्ति स्थानांतरण स्थिति में प्रणाली की दक्षता 50 प्रतिशत होती है।
4. अधिकतम शक्ति स्थानांतरण स्थिति परिपथ में न्यूनतम हानि सुनिश्चित करती है।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
B — केवल 1, 2 और 3। DC: R_L = R_th; AC: Z_L = Z_th*। इस बिंदु पर आधी शक्ति आंतरिक रूप से व्यय होती है, इसलिए दक्षता 50% है — अतः यह न्यूनतम हानि की स्थिति नहीं है।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Maximum power transfer occurs when load resistance equals source resistance in DC circuits.
In a DC resistive Thevenin equivalent, maximum load power occurs at RL=Rth. - Statement 2 - Correct.
In AC circuits, maximum power transfer occurs when load impedance is complex conjugate of source impedance.
In AC, ZL must equal the complex conjugate of source/Thevenin impedance. - Statement 3 - Correct.
At maximum power transfer condition, efficiency of the system becomes 50 percent.
At the resistive maximum-power point, half of the source power is dissipated internally, so efficiency is 50%. - Statement 4 - Incorrect.
Maximum power transfer condition ensures minimum losses in the circuit.
At the resistive maximum-power condition half the source power is lost internally, so it is not a minimum-loss operating point
Core Concept
Maximum power transfer is a matching condition, not an efficiency condition. In a DC resistive Thevenin equivalent, maximum load power occurs at RL=Rth. In AC, ZL must equal the complex conjugate of source/Thevenin impedance. At the resistive maximum-power point, half of the source power is dissipated internally, so efficiency is 50%.
Formula / Key Relationship
DC: R_L=R_th. AC: Z_L=Z_th*.
Why the Other Options Are Wrong
Option A is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1. Option D is incorrect because it includes incorrect statement(s) 4.
Exam Shortcut / Approach
Maximum power and maximum efficiency are different design objectives.
Common Mistake
Do not claim the maximum-power condition minimizes circuit losses.
Quick Revision
Maximum Power Transfer Condition is linked with Maximum Power Transfer, Network Theorems and Network Theory. Maximum power and maximum efficiency are different design objectives.
Consider the following statements regarding Maximum Power Transfer:
1. Maximum power transfer occurs when load resistance equals source resistance in DC circuits.
2. In AC circuits, maximum power transfer occurs when load impedance is complex conjugate of source impedance.
3. At maximum power transfer condition, efficiency of the system becomes 50 percent.
4. Maximum power transfer condition ensures minimum losses in the circuit.
Which of the above statements is/are correct?
Answer & step-by-step solution
In AC, ZL must equal the complex conjugate of source/Thevenin impedance. At the resistive maximum-power point, half of the source power is dissipated internally, so efficiency is 50%. Key relation: DC: R_L=R_th. AC: Z_L=Z_th*.
Exam focus: Maximum power and maximum efficiency are different design objectives. Common trap: Do not claim the maximum-power condition minimizes circuit losses.
Statement-wise Verification
- Statement 1 - Correct.
Maximum power transfer occurs when load resistance equals source resistance in DC circuits.
In a DC resistive Thevenin equivalent, maximum load power occurs at RL=Rth. - Statement 2 - Correct.
In AC circuits, maximum power transfer occurs when load impedance is complex conjugate of source impedance.
In AC, ZL must equal the complex conjugate of source/Thevenin impedance. - Statement 3 - Correct.
At maximum power transfer condition, efficiency of the system becomes 50 percent.
At the resistive maximum-power point, half of the source power is dissipated internally, so efficiency is 50%. - Statement 4 - Incorrect.
Maximum power transfer condition ensures minimum losses in the circuit.
At the resistive maximum-power condition half the source power is lost internally, so it is not a minimum-loss operating point
Core Concept
Maximum power transfer is a matching condition, not an efficiency condition. In a DC resistive Thevenin equivalent, maximum load power occurs at RL=Rth. In AC, ZL must equal the complex conjugate of source/Thevenin impedance. At the resistive maximum-power point, half of the source power is dissipated internally, so efficiency is 50%.
Formula / Key Relationship
DC: R_L=R_th. AC: Z_L=Z_th*.
Why the Other Options Are Wrong
Option A is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1. Option D is incorrect because it includes incorrect statement(s) 4.
Exam Shortcut / Approach
Maximum power and maximum efficiency are different design objectives.
Common Mistake
Do not claim the maximum-power condition minimizes circuit losses.
Quick Revision
Maximum Power Transfer Condition is linked with Maximum Power Transfer, Network Theorems and Network Theory. Maximum power and maximum efficiency are different design objectives.
મહત્તમ પાવર સ્થાનાંતરણ (Maximum Power Transfer) અંગે નીચેનાં વિધાનો ધ્યાનમાં લો:
1. DC પરિપથોમાં મહત્તમ પાવર સ્થાનાંતરણ ત્યારે થાય છે જ્યારે લોડ અવરોધ સ્રોત અવરોધ જેટલો હોય.
2. AC પરિપથોમાં મહત્તમ પાવર સ્થાનાંતરણ ત્યારે થાય છે જ્યારે લોડ અવબાધ સ્રોત અવબાધનો સંકર અનુબદ્ધ (complex conjugate) હોય.
3. મહત્તમ પાવર સ્થાનાંતરણ સ્થિતિમાં પ્રણાલીની કાર્યક્ષમતા 50 ટકા હોય છે.
4. મહત્તમ પાવર સ્થાનાંતરણ સ્થિતિ પરિપથમાં લઘુતમ નુકસાન સુનિશ્ચિત કરે છે.
ઉપરોક્તમાંથી કયું/કયાં વિધાન સાચું/સાચાં છે?
જવાબ અને પગલાવાર ઉકેલ
B — ફક્ત 1, 2 અને 3. DC: R_L = R_th; AC: Z_L = Z_th*. આ બિંદુએ અડધો પાવર આંતરિક રીતે વ્યય થાય છે, તેથી કાર્યક્ષમતા 50% છે — એટલે તે લઘુતમ નુકસાનની સ્થિતિ નથી.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Maximum power transfer occurs when load resistance equals source resistance in DC circuits.
In a DC resistive Thevenin equivalent, maximum load power occurs at RL=Rth. - Statement 2 - Correct.
In AC circuits, maximum power transfer occurs when load impedance is complex conjugate of source impedance.
In AC, ZL must equal the complex conjugate of source/Thevenin impedance. - Statement 3 - Correct.
At maximum power transfer condition, efficiency of the system becomes 50 percent.
At the resistive maximum-power point, half of the source power is dissipated internally, so efficiency is 50%. - Statement 4 - Incorrect.
Maximum power transfer condition ensures minimum losses in the circuit.
At the resistive maximum-power condition half the source power is lost internally, so it is not a minimum-loss operating point
Core Concept
Maximum power transfer is a matching condition, not an efficiency condition. In a DC resistive Thevenin equivalent, maximum load power occurs at RL=Rth. In AC, ZL must equal the complex conjugate of source/Thevenin impedance. At the resistive maximum-power point, half of the source power is dissipated internally, so efficiency is 50%.
Formula / Key Relationship
DC: R_L=R_th. AC: Z_L=Z_th*.
Why the Other Options Are Wrong
Option A is incorrect because it includes incorrect statement(s) 4 and omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1. Option D is incorrect because it includes incorrect statement(s) 4.
Exam Shortcut / Approach
Maximum power and maximum efficiency are different design objectives.
Common Mistake
Do not claim the maximum-power condition minimizes circuit losses.
Quick Revision
Maximum Power Transfer Condition is linked with Maximum Power Transfer, Network Theorems and Network Theory. Maximum power and maximum efficiency are different design objectives.
More Network Theorems questions