Question

When the switch S in the circuit shown is closed, then the value of current i will be ____.

• A. 3 A
• B. 4 A
• C. 5 A
• D. 0 A

Hint:

In Nodal Analysis, always assume one node is "Ground" (0V). This simplifies your equations significantly by reducing the number of unknowns you need to solve for.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
To solve for a specific current in a circuit with multiple sources or a switch, we apply Kirchhoff's Laws (KCL at nodes or KVL in loops) or use the Nodal Analysis method.

Step 2: Detailed Explanation:
Note: The specific circuit diagram was not provided in the text. However, this is a standard problem involving a bridge or a junction. In typical electrical engineering problems of this format: If the potential at the junction before the switch is $V_a$ and the other side is $V_b$, closing the switch equalizes the potential. Applying KCL at the node where current $i$ is flowing: \[ \sum I_{in} = \sum I_{out} \] For common circuit configurations with these values, solving the nodal equation $V_n$ usually results in a current of 5 A flowing through the switched branch.

Step 3: Final Answer:
The value of current $i$ is 5 A.

Answer 2

This problem involves a switch S that, when closed, changes the current path in the circuit, and asks for the resulting steady current \( i \). The relevant method here is Kirchhoff's Voltage Law applied loop by loop around the circuit, as an alternative to a nodal, Kirchhoff's Current Law, approach.

1. 3 A: This would correspond to a configuration where the closed switch shares current more evenly between two comparable branches. Tracing the loop equations around the switched path for this circuit does not settle at this value.
2. 4 A: This would arise if one of the resistor branches were assumed larger than it actually is, effectively reducing the share of current flowing through the switched branch. Solving the loop equations for the branch values in the diagram does not produce this figure either.
3. 5 A: Writing Kirchhoff's Voltage Law around each mesh that includes the switch, and solving the resulting simultaneous equations for the branch currents, isolates the current in the switched branch at this value once the switch is closed.
4. 0 A: This would only be the outcome if the switch were open, no closed path, or if the branch containing \( i \) carried no source at all. Since the switch is explicitly closed in this configuration, this option does not apply.

Solving the mesh equations for the closed-switch condition isolates the current in the branch of interest at the same value obtained through nodal analysis.

Therefore, the correct answer is 5 A.