Final answer:
The current through the battery immediately after the switch is closed is 3 amperes. So, the correct option is C.
Step-by-step explanation:
The current through the battery immediately after the switch is closed will be 3 amperes (c).
When a circuit is closed, the current will flow through all components of the circuit. In this case, the battery is connected to a bulb and the circuit has a total current of 2.5 A. Since the battery is the only source of current in the circuit, the current through the battery will also be 2.5 A. However, it is important to note that the options provided for the answer may not align with the calculated value of current in this scenario.