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GATE 2026 IN – Question 39

Electrical Circuits and Machines · Transients and two-port networks · 2 marks · Multiple choice

A two-port network has z-parameters $z_{11}=z_{22}=10\ \Omega$ and $z_{12}=z_{21}=5\ \Omega$. The value of $R_L$ such that maximum power is transferred to $R_L$ is ________ Ω.

Diagram for GATE 2026 IN question 39
  1. 5.67
  2. 8.33
  3. 10.33
  4. 25.67

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Correct answer: (B) 8.33

Explanation

Deactivate the independent 5 V source, leaving its series resistance $R_s=5\ \Omega$ connected to port 1. With port currents defined into the network, $v_1=z_{11}i_1+z_{12}i_2=-R_si_1$, so $i_1=-z_{12}i_2/(z_{11}+R_s)$.

Then $v_2/i_2=z_{22}-z_{21}z_{12}/(z_{11}+R_s)=10-25/15=8.333\ \Omega$. Maximum power transfer to a resistive load requires $R_L=R_{out}$, giving **8.33 Ω (B)**.