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GATE 2017 EE – Question 53

Electric Circuits · Network Theorems: Thevenin, Norton, Superposition and Maximum Power Transfer theorem · 2 marks · Numerical answer

In the circuit shown below, the maximum power transferred to the resistor R is ________ W.

A 5 V source in series with a $5\ \Omega$ resistor feeds a node. The resistor R is connected from this node to ground. A $6$ V source (with its negative terminal on the left) connects this node to a second node, with a $3\ \Omega$ resistor in parallel with the source. The second node has a $5\ \Omega$ resistor to ground and a 2 A current source pulling current to ground.

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Correct answer: 3 to 3.1

Explanation

Remove R and find the Thevenin equivalent at its terminals. The 6 V source makes the second node 6 V above the first. Applying KCL to the combined node, the current from the 5 V source is $\frac{5 - V_1}{5}$, and the current leaving is $\frac{V_1 + 6}{5} + 2$. Setting them equal gives $5 - V_1 = V_1 + 6 + 10$, so $V_{oc} = V_1 = -5.5$ V. With the sources off, the resistance seen at R is the two $5\ \Omega$ resistors in parallel, $R_{th} = 2.5\ \Omega$. The maximum power is $\frac{V_{oc}^2}{4R_{th}} = \frac{30.25}{10} = 3.025$ W.