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GATE 2021 EE – Question 14

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

For the network shown, the equivalent Thevenin voltage and Thevenin impedance as seen across terminals 'ab' is

Diagram for GATE 2021 EE question 14
  1. 10 V in series with $12\ \Omega$
  2. 65 V in series with $15\ \Omega$
  3. 50 V in series with $2\ \Omega$
  4. 35 V in series with $2\ \Omega$

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Correct answer: (B) 65 V in series with $15\ \Omega$

Explanation

With terminals open, no current flows in the $2\ \Omega$ resistor, so the $5$ A source flows through the $10\ \Omega$ resistor: $i_1=5$ A and the node voltage is $50$ V. The dependent source $3i_1=15$ V adds to it, so $V_{th}=65$ V. With the terminals shorted, $5=\frac{V_n}{10}+\frac{V_n+3V_n/10}{2}=0.75V_n$, so $V_n=6.67$ V and $I_{sc}=\frac{1.3\times6.67}{2}=4.33$ A. Hence $R_{th}=\frac{65}{4.33}=15\ \Omega$.