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GATE 2020 EC – Question 19

Networks, Signals and Systems · Circuit Analysis · 1 mark · Multiple choice

In the circuit shown below, the Thevenin voltage $V_{TH}$ is

Diagram for GATE 2020 EC question 19
  1. 2.4 V
  2. 2.8 V
  3. 3.6 V
  4. 4.5 V

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Correct answer: (C) 3.6 V

Explanation

No current flows in the $4\ \Omega$ resistor (open terminals), so $V_{TH}$ is the voltage across the right-hand $2\ \Omega$ resistor, $V_B$. Let $I$ flow from node A to node B through the 2 V source and $2\ \Omega$. At A: $1=V_A+I$. At B: $I+2=\frac{V_B}{2}$. The branch gives $V_B=V_A+2-2I$. Solving, $I=-0.2$ A, $V_A=1.2$ V and $V_B=3.6$ V.