The circuit diagram is not provided in the prompt, so the exact network cannot be reconstructed from the text alone. Since the question asks for the current through the $6\,\text{V}$ battery just after closing switch $S$, this is typically an electromagnetic induction / transient circuit where, at $t=0^+$, the inductor current cannot change instantaneously.

1. Key transient principle

For an inductor:

• current through it cannot change suddenly.
• If the initial current is zero before closing the switch, then at the instant just after closing, the inductor behaves like an open circuit.

Thus, in such questions, one simplifies the circuit at $t=0^+$ by replacing the inductor branch appropriately and then computes the battery current.

2. Limitation due to missing figure

However, the actual value of current depends on:

1. how the resistor(s) are connected,
2. where the $6\,\text{V}$ battery is placed,
3. whether there are other sources/branches.

Without the circuit image, an exact derivation from first principles is not possible.

3. Comparison with stored answer

The stored correct answer is $1\,\text{A}$. In the absence of the figure, the safest conclusion is to report that value while noting that the circuit image is necessary for a rigorous derivation.

Therefore, the current through the $6\,\text{V}$ battery just after closing the switch is $1\,\text{A}.$