GATE EE 2017 Set 1 — Question 43
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Electric Circuits → Network Theorems → Maximum Power Transfer
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Question
In the circuit shown below, the maximum power transferred to the resistor R is ________ W.
Correct answer
3 to 3.1
Solution
Maximum power reaches when equals the Thevenin resistance at its terminals, and then1. Thevenin resistance (R removed, sources deactivated):
The and sources become short circuits and the source an open circuit. The shorted source ties the two middle nodes together (and short-circuits the resistor), so the terminals of see the left in parallel with the right :2. Thevenin voltage (R removed):
Take the bottom rail as reference. Let be the node at the top of and the node at the top of the right-hand . The source fixesThe resistor is connected across the same two nodes, so it is internal to the supernode. KCL for the supernode :Substituting :So in magnitude.3. Maximum power:Answer: (obtained with )
The and sources become short circuits and the source an open circuit. The shorted source ties the two middle nodes together (and short-circuits the resistor), so the terminals of see the left in parallel with the right :2. Thevenin voltage (R removed):
Take the bottom rail as reference. Let be the node at the top of and the node at the top of the right-hand . The source fixesThe resistor is connected across the same two nodes, so it is internal to the supernode. KCL for the supernode :Substituting :So in magnitude.3. Maximum power:Answer: (obtained with )
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