GATE 2021 EC – Question 28
Consider the circuit shown in the figure.
The current $I$ flowing through the $7\ \Omega$ resistor between P and Q (rounded off to one decimal place) is ________ A.
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Show answer and explanation
Correct answer: 0.49 to 0.51
Explanation
The vertical wire joins the top and bottom nodes into a single node X (it hops over the $7\ \Omega$ branch). Between P and X the $3\ \Omega$ and $6\ \Omega$ are in parallel, $2\ \Omega$; between X and Q the two $2\ \Omega$ resistors are in parallel, $1\ \Omega$. The $5$ A source carries current from Q to X. With X as reference, KCL at P gives $\frac{V_P}{2}+\frac{V_P-V_Q}{7}=0$, so $V_P=\frac29V_Q$. KCL at Q gives $5+V_Q+\frac{V_Q-V_P}{7}=0$, so $5+\frac{10}{9}V_Q=0$, $V_Q=-4.5$ V and $V_P=-1$ V. Then $I=\frac{V_P-V_Q}{7}=\frac{3.5}{7}=0.5$ A.