GATE 2023 EC – Question 32
In the circuit shown below, the current $i$ flowing through the 200 Ω resistor is ________ mA (rounded off to two decimal places).
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Correct answer: 1.35 to 1.37
Explanation
Work in kΩ, mA and V. The source and both 2 kΩ resistors hang from the left node $X$, and the top-right node is $C$. KCL at $X$: the 1 mA source injects 1 mA; currents leaving are $V_X/2$ (shunt 2 kΩ), $(V_X-2)/2$ (2 V source branch), 1 mA (top source) and $V_X-V_C$ (1 kΩ). So $1=V_X-1+1+V_X-V_C$, i.e. $2V_X-V_C=1$. KCL at $C$: $1+(V_X-V_C)=5V_C$, so $V_X=6V_C-1$. Solving, $V_C=3/11$ V. Then $i=V_C/0.2\text{ k}\Omega=15/11\approx1.36$ mA.