The question refers to a circuit diagram, but the diagram is not present in the provided prompt. Since the value of current $i$ depends entirely on the circuit connections and component values, the answer cannot be derived uniquely without the figure.

Step 1: Identify the missing information

To calculate current in a circuit, we need the circuit diagram showing:

1. The source voltage(s)
2. The resistance values
3. The arrangement of resistors/batteries
4. The location of switch $S$
5. The branch where current $i$ is asked

None of these are available in the text.

Step 2: Can we infer the answer from the options alone?

No. The options are:

• A: $3\,\text{A}$
• B: $5\,\text{A}$
• C: $4\,\text{A}$
• D: $2\,\text{A}$

Without the actual circuit, there is no valid physics-based method to determine which one is correct.

Step 3: Comparison with stored answer

The stored correct answer is B = $5\,\text{A}$. However, because the circuit diagram is missing, I cannot independently verify this result.

So, I do not have enough information to derive the answer rigorously.