GATE 2017 EC (EC2) – Question 42
Consider the circuit shown, including the dependent voltage source of value $3i_0$. The Thevenin equivalent resistance (in Ω) across P–Q is ________.
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Correct answer: -1.01 to -0.99
Explanation
Deactivate only the independent 10 V source, replacing it by a short. Keep the dependent source active. Apply test voltage $v=V_P-V_Q$ across the port.
The right 1 Ω resistor carries $i_0=v$. With the left node grounded, the dependent source sets $V_P=3i_0=3v$, so $V_Q=2v$.
At Q, current arriving from the right resistor is v, while $2v$ flows through the bottom 1 Ω resistor toward ground. Thus the test-source return current is $I=v-2v=-v$.
Consequently $R_{Th}=v/I=$ **−1 Ω**. A negative resistance is possible because the circuit contains an active dependent source.