A

Step 1: Understand the concept of maximum current in a circuit with internal and external resistance. The total voltage ( extit{V}) from the battery is applied across both internal resistance ( extit{r}) and external resistance ( extit{R}).
Step 2: According to Ohm's Law, the current ( extit{I}) flowing through the circuit can be expressed as:
$$ I = \frac{V}{R + r} $$
Step 3: To maximize the current, we need to minimize the denominator (\(R + r\)).
Step 4: We consider the conditions where internal resistance equals external resistance. If \(r = R\), then:
$$ I = \frac{V}{R + R} = \frac{V}{2R} $$
This condition provides maximum current compared to when either resistance is significantly larger than the other.
Conclusion: Therefore, maximum current is provided by the battery when internal resistance is equal to external resistance.
Hence, the correct answer is Option A.