GATE EE 2023 Set 1 — Question 44

Let the bottom wire be the reference node (ground, 0V). The circuit has three main nodes: Node A (between the 4A source and $D_1$), Node B (between $D_1$ and the 2A source), and Node C (between the 2A source and $D_3$). From the diagram, Node B is connected to the cathode of $D_2$, which is at a fixed potential of 20V due to the ideal voltage source. Thus, $V_B = 20V$.Case 1: Switch $S$ is ON.
Node $C$ is connected to ground, so $V_C = 0V$. Diode $D_3$ has its anode at 0V and cathode at 40V, so it is reverse biased ($D_3$ is OFF). The 2A current source pulls 2A from Node $B$ to Node $C$. At Node $A$, 4A enters from the current source. If $D_1$ conducts all 4A, then $I_{D1} = 4A$ and $I_{D2} = 0$. In this state, $V_A = V_B = 20V$. Since $I_{D2} = 0$ and $V_A = 20V$, $D_2$ is at the threshold and is considered OFF. At Node $B$, 4A enters from $D_1$, 2A leaves to the 2A source, and the remaining 2A flows into the 20V source. This is a consistent state where $D_1$ conducts while $D_2$ and $D_3$ are reverse biased. Thus, statement (B) is true.Case 2: Switch $S$ is OFF.
The 2A current from the source must flow through $D_3$ to the 40V source, so $D_3$ conducts and $V_C = 40V$. At Node $B$ (20V), 2A leaves to the current source. If $D_1$ is reverse biased, $I_{D1} = 0$. Then all 4A from the 4A source must flow through $D_2$, so $D_2$ conducts and $V_A = 20V$. At Node $A$, $V_A = 20V$ and at Node $B$, $V_B = 20V$. $D_1$ is at the threshold with zero current and is considered OFF. The 2A required by the current source at Node $B$ is supplied by the 20V source. This is a consistent state where $D_1$ is reverse biased while $D_2$ and $D_3$ conduct. Thus, statement (C) is true.Therefore, statements (B) and (C) are true.