(a)
12 \( \Omega \)
Resistance is calculated using the equation \( R = \frac{V}{I} \). Substituting the given values: \( R = \frac{4.8\text{ V}}{0.40\text{ A}} = 12\ \Omega \).
(b)
Lamp L becomes brighter (brightness increases).
Closing switch S places resistor R in parallel with the wire, significantly reducing the total resistance of that branch. This decreases the overall circuit resistance, increasing the total current from the battery and the potential difference across lamp L, thus causing a higher current through the lamp.
