GATE EC 2017 Set 2 — Question 32
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Network Theory → Circuit Fundamentals & Theorems → Thevenin & Norton Theorems
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Question
Consider the circuit shown in the figure.
The circuit has nodes A, B, P and Q, connected as follows: a 10 V independent source with its + terminal at A and − terminal at B; a resistor between A and B; a resistor between A and P; a current-controlled voltage source of value between A and P with its + terminal at P (so ); a resistor between P and Q carrying current from P to Q; and a resistor between B and Q.The Thevenin equivalent resistance (in ) across P-Q is __________.
Correct answer
-1.01 to -0.99
Solution
Deactivate the 10 V source (short it), so nodes A and B merge; the A–B resistor is shorted out. Take Q as ground and apply a test voltage at P, drawing test current into P.
- flows through the P–Q resistor: .
- Dependent source: .
- A and P form a supernode (the A–P resistor lies inside it and carries a current internal to the supernode). The currents leaving the supernode to ground are through the P–Q resistor () and the B–Q resistor ().
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