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GATE 2015 EE – Question 29

Electric Circuits · Network Theorems: Thevenin, Norton, Superposition and Maximum Power Transfer theorem · 1 mark · Numerical answer

For the given circuit, the Thevenin equivalent is to be determined. The Thevenin voltage, $V_{Th}$ (in Volt), seen from terminal AB is ________.

A 2 V source feeds a $1\ \Omega$ series resistor and a $1\ \Omega$ resistor to ground carrying current $i$. A dependent voltage source $20i$ and a $2\ \Omega$ resistor lead to terminals A and B.

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Correct answer: 3.3 to 3.4

Explanation

Let the middle node voltage be $V$, with the $1\ \Omega$ resistor to ground carrying $i = V$. The terminals A and B are across the $2\ \Omega$ resistor, whose current also flows through the dependent source $20i$, so $V_{AB} = V + 20i = 21V$ and the $2\ \Omega$ branch carries $\frac{21V}{2}$. KCL at the node gives $\frac{2 - V}{1} = V + \frac{21V}{2}$, so $2 = 12.5V$ and $V = 0.16$ V. Then $V_{Th} = 21 \times 0.16 = 3.36$ V.