GPSC revised the final answer to option C. For Z-parameters, Z12 = V1/I2 with I1 = 0. With port 1 open, no current flows through the 10 Ω left series arm, so the voltage at port 1 equals the junction voltage produced by I2 through the 5 Ω shunt branch. Hence Z12 = 5 Ω.
Formula / Key Relation
V₁ = Z₁₁I₁ + Z₁₂I₂
Set I₁ = 0:
Z₁₂ = V₁/I₂ = 5 Ω
Detailed Explanation
Concept & ReasoningThe Z-parameter definition is crucial. For a two-port network,V1 = Z11 I1 + Z12 I2 and V2 = Z21 I1 + Z22 I2.To determine Z12, set I1 = 0, which means port 1 is open-circuited. Because the left 10 Ω branch terminates at an open port, it carries zero current and therefore has zero voltage drop. Current I2 entering port 2 flows through the 20 Ω series resistor to the central node and then through the 5 Ω shunt resistor to the common return. The central-node voltage is 5I2, and the open-circuit port-1 voltage is the same node…
Concept & Reasoning
The Z-parameter definition is crucial. For a two-port network, V1 = Z11 I1 + Z12 I2 and V2 = Z21 I1 + Z22 I2. To determine Z12, set I1 = 0, which means port 1 is open-circuited. Because the left 10 Ω branch terminates at an open port, it carries zero current and therefore has zero voltage drop. Current I2 entering port 2 flows through the 20 Ω series resistor to the central node and then through the 5 Ω shunt resistor to the common return. The central-node voltage is 5I2, and the open-circuit port-1 voltage is the same node voltage. Therefore V1/I2 = 5 Ω. This is why the final GPSC key changed the provisional choice.
How to Solve It in the Exam
For Z12: open port 1 (I1=0), inject current at port 2, then find V1/I2.
Important Exam Point
Apply the Z-parameter test condition before combining resistors.
Editorial / Answer-Key Note
The official GPSC final answer key revised the provisional outcome for this question from B to C.
Related Revision Path
This question sits in the revision path Network Theory → Two-Port Networks → Z Parameters .
Quick Trick
For Z12: open port 1 (I1=0), inject current at port 2, then find V1/I2.
Common Mistake
The 10 Ω and 20 Ω series resistors are not both in the transfer path under the I1=0 condition.
Exam Tip
Apply the Z-parameter test condition before combining resistors.
SEO + Knowledge GraphRelated PYQs & Exam ContextExam path, knowledge path and deeper practice links.
Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 124Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 124Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 124Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 124Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 124Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 124Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 124Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 124Assistant Engineer (Electrical), Class-2, Road and Building Department2025Q. 124
