एक द्वि-पोर्ट नेटवर्क के Z-पैरामीटर परिभाषित हैं। तब
1. ये ओपन-सर्किट स्थितियों में परिभाषित होते हैं।
2. Z11 इनपुट प्रतिबाधा दर्शाता है।
3. Z12 ट्रांसफर प्रतिबाधा दर्शाता है।
4. इन्हें नेटवर्क अंतर्संयोजन (interconnections) में उपयोग किया जा सकता है।
उपरोक्त में से कौन-सा/से कथन सही है/हैं?
उत्तर और चरणबद्ध हल
A — उपरोक्त सभी। V1 = Z11I1 + Z12I2, V2 = Z21I1 + Z22I2; Z11 = (V1/I1)|I2=0 (इनपुट), Z12 = (V1/I2)|I1=0 (ट्रांसफर)। श्रेणी-संयोजित द्वि-पोर्ट में Z-पैरामीटर सीधे जुड़ते हैं। याद रखें: Z → ओपन सर्किट, Y → शॉर्ट सर्किट।
विस्तृत हल (मूल भाषा में)
Statement-wise Verification
- Statement 1 - Correct.
Defined under open-circuit conditions.
Z-parameters are determined using open-circuit conditions because the defining current at the other port is set to zero. - Statement 2 - Correct.
Z11 represents input impedance.
Z11 = V1/I1 with I2=0, so it is the driving-point/input impedance at port 1 under output open circuit. - Statement 3 - Correct.
Z12 represents transfer impedance.
Z12 = V1/I2 with I1=0 is a transfer impedance (reverse transfer impedance in the usual port convention). - Statement 4 - Correct.
Can be used in network interconnections.
Two-port parameter sets are used to analyze interconnected networks; Z-parameters are especially convenient for series-type interconnections and general two-port modeling.
Core Concept
For a linear two-port, terminal voltages are expressed in terms of terminal currents. Each Z coefficient has units of ohms. Open-circuiting a port forces its current to zero and isolates the required coefficient. Do not confuse the separate ideas of reciprocity and symmetry: reciprocity requires Z12=Z21, whereas symmetry requires Z11=Z22.
Formula / Key Relationship
V1 = Z11 I1 + Z12 I2; V2 = Z21 I1 + Z22 I2. Z11=(V1/I1)|I2=0, Z12=(V1/I2)|I1=0.
Step-by-Step Check
Independent check of the defining equations makes statements 1–3 direct identities. Statement 4 is a valid application of two-port parameters. Hence all four are correct and option A is the only complete choice.
Why the Other Options Are Wrong
Option B is incorrect because it omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1, 4. Option D is incorrect because it omits correct statement(s) 4.
Answer-Key Verification Note
The uploaded provisional key marks C . After independent technical verification, the defensible answer is A . This discrepancy is stated explicitly rather than silently copying the provisional key.
Exam Shortcut / Approach
Memorize the condition “Z → open circuit (I=0)” and “Y → short circuit (V=0)”.
Common Mistake
Do not label Z12=Z21 as symmetry; that equality is the reciprocity condition.
Quick Revision
Impedance Parameters is linked with Z-Parameters, Two-Port Networks and Network Theory. Memorize the condition “Z → open circuit (I=0)” and “Y → short circuit (V=0)”.
A two-port network has defined Z-parameters. Then
1. Defined under open-circuit conditions.
2. Z11 represents input impedance.
3. Z12 represents transfer impedance.
4. Can be used in network interconnections.
Which of the above statements is/are correct?
Answer & step-by-step solution
For a linear two-port, terminal voltages are expressed in terms of terminal currents. Open-circuiting a port forces its current to zero and isolates the required coefficient. Key relation: V1 = Z11 I1 + Z12 I2; V2 = Z21 I1 + Z22 I2. Z11=(V1/I1)|I2=0, Z12=(V1/I2)|I1=0.
Exam focus: Memorize the condition “Z → open circuit (I=0)” and “Y → short circuit (V=0)”. Common trap: Do not label Z12=Z21 as symmetry; that equality is the reciprocity condition.
Statement-wise Verification
- Statement 1 - Correct.
Defined under open-circuit conditions.
Z-parameters are determined using open-circuit conditions because the defining current at the other port is set to zero. - Statement 2 - Correct.
Z11 represents input impedance.
Z11 = V1/I1 with I2=0, so it is the driving-point/input impedance at port 1 under output open circuit. - Statement 3 - Correct.
Z12 represents transfer impedance.
Z12 = V1/I2 with I1=0 is a transfer impedance (reverse transfer impedance in the usual port convention). - Statement 4 - Correct.
Can be used in network interconnections.
Two-port parameter sets are used to analyze interconnected networks; Z-parameters are especially convenient for series-type interconnections and general two-port modeling.
Core Concept
For a linear two-port, terminal voltages are expressed in terms of terminal currents. Each Z coefficient has units of ohms. Open-circuiting a port forces its current to zero and isolates the required coefficient. Do not confuse the separate ideas of reciprocity and symmetry: reciprocity requires Z12=Z21, whereas symmetry requires Z11=Z22.
Formula / Key Relationship
V1 = Z11 I1 + Z12 I2; V2 = Z21 I1 + Z22 I2. Z11=(V1/I1)|I2=0, Z12=(V1/I2)|I1=0.
Step-by-Step Check
Independent check of the defining equations makes statements 1–3 direct identities. Statement 4 is a valid application of two-port parameters. Hence all four are correct and option A is the only complete choice.
Why the Other Options Are Wrong
Option B is incorrect because it omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1, 4. Option D is incorrect because it omits correct statement(s) 4.
Answer-Key Verification Note
The uploaded provisional key marks C . After independent technical verification, the defensible answer is A . This discrepancy is stated explicitly rather than silently copying the provisional key.
Exam Shortcut / Approach
Memorize the condition “Z → open circuit (I=0)” and “Y → short circuit (V=0)”.
Common Mistake
Do not label Z12=Z21 as symmetry; that equality is the reciprocity condition.
Quick Revision
Impedance Parameters is linked with Z-Parameters, Two-Port Networks and Network Theory. Memorize the condition “Z → open circuit (I=0)” and “Y → short circuit (V=0)”.
એક દ્વિ-પોર્ટ નેટવર્કના Z-પેરામીટર વ્યાખ્યાયિત છે. તો
1. તે ઓપન-સર્કિટ સ્થિતિમાં વ્યાખ્યાયિત થાય છે.
2. Z11 ઇનપુટ અવબાધ દર્શાવે છે.
3. Z12 ટ્રાન્સફર અવબાધ દર્શાવે છે.
4. તેનો નેટવર્ક આંતરજોડાણ (interconnections)માં ઉપયોગ કરી શકાય છે.
ઉપરોક્તમાંથી કયું/કયાં વિધાન સાચું/સાચાં છે?
જવાબ અને પગલાવાર ઉકેલ
A — ઉપરોક્ત તમામ. V1 = Z11I1 + Z12I2, V2 = Z21I1 + Z22I2; Z11 = (V1/I1)|I2=0 (ઇનપુટ), Z12 = (V1/I2)|I1=0 (ટ્રાન્સફર). શ્રેણી-જોડાણવાળા દ્વિ-પોર્ટમાં Z-પેરામીટર સીધા ઉમેરાય છે. યાદ રાખો: Z → ઓપન સર્કિટ, Y → શોર્ટ સર્કિટ.
વિગતવાર ઉકેલ (મૂળ ભાષામાં)
Statement-wise Verification
- Statement 1 - Correct.
Defined under open-circuit conditions.
Z-parameters are determined using open-circuit conditions because the defining current at the other port is set to zero. - Statement 2 - Correct.
Z11 represents input impedance.
Z11 = V1/I1 with I2=0, so it is the driving-point/input impedance at port 1 under output open circuit. - Statement 3 - Correct.
Z12 represents transfer impedance.
Z12 = V1/I2 with I1=0 is a transfer impedance (reverse transfer impedance in the usual port convention). - Statement 4 - Correct.
Can be used in network interconnections.
Two-port parameter sets are used to analyze interconnected networks; Z-parameters are especially convenient for series-type interconnections and general two-port modeling.
Core Concept
For a linear two-port, terminal voltages are expressed in terms of terminal currents. Each Z coefficient has units of ohms. Open-circuiting a port forces its current to zero and isolates the required coefficient. Do not confuse the separate ideas of reciprocity and symmetry: reciprocity requires Z12=Z21, whereas symmetry requires Z11=Z22.
Formula / Key Relationship
V1 = Z11 I1 + Z12 I2; V2 = Z21 I1 + Z22 I2. Z11=(V1/I1)|I2=0, Z12=(V1/I2)|I1=0.
Step-by-Step Check
Independent check of the defining equations makes statements 1–3 direct identities. Statement 4 is a valid application of two-port parameters. Hence all four are correct and option A is the only complete choice.
Why the Other Options Are Wrong
Option B is incorrect because it omits correct statement(s) 2, 3. Option C is incorrect because it omits correct statement(s) 1, 4. Option D is incorrect because it omits correct statement(s) 4.
Answer-Key Verification Note
The uploaded provisional key marks C . After independent technical verification, the defensible answer is A . This discrepancy is stated explicitly rather than silently copying the provisional key.
Exam Shortcut / Approach
Memorize the condition “Z → open circuit (I=0)” and “Y → short circuit (V=0)”.
Common Mistake
Do not label Z12=Z21 as symmetry; that equality is the reciprocity condition.
Quick Revision
Impedance Parameters is linked with Z-Parameters, Two-Port Networks and Network Theory. Memorize the condition “Z → open circuit (I=0)” and “Y → short circuit (V=0)”.
More Two-Port Networks questions