GATE 2024 EC – Question 62
In the network shown below, maximum power is to be transferred to the load $R_L$.
The value of $R_L$ (in Ω) is ________.
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Show answer and explanation
Correct answer: 2.49 to 2.51
Explanation
Maximum power transfer needs $R_L=R_{th}$. Short the 50 V source and apply a test voltage $V_t$ at the load terminals. Path 1 (3 Ω then 2 Ω to ground) carries $V_t/5$, so the node between them is at $0.4V_t$ and $V_x=V_t-0.4V_t=0.6V_t$. Path 2 is the dependent source (− left, + right) in series with 2 Ω; the source raises its right terminal to $V_x=0.6V_t$, so the current is $(V_t-0.6V_t)/2=0.2V_t$. Total current $=0.2V_t+0.2V_t=0.4V_t$, so $R_{th}=V_t/(0.4V_t)=2.5\ \Omega$.