The correct answer is option 'A' - the maximum current is obtained when the internal resistance of a battery is equal to the external resistance.

Explanation:
When a battery is connected to an external circuit, it creates an electric potential difference (voltage) between its terminals. This potential difference drives the flow of electric current through the circuit. However, the battery itself has an internal resistance that affects the flow of current.

Internal Resistance:
The internal resistance of a battery is the resistance offered by the electrolyte and other components inside the battery. It is denoted by the symbol 'r'. This resistance limits the amount of current that can flow through the battery.

External Resistance:
The external resistance is the resistance offered by the components connected to the battery in the external circuit. It is denoted by the symbol 'R'.

Effect of Internal Resistance on Current:
When a battery is connected to an external circuit, the current flowing through the circuit depends on the total resistance in the circuit, which includes both the internal resistance (r) of the battery and the external resistance (R) connected to it.

If the internal resistance (r) is greater than the external resistance (R), the total resistance in the circuit increases. According to Ohm's law (V = IR), if the resistance increases, the current decreases. Therefore, the maximum current is not obtained in this case.

If the internal resistance (r) is less than the external resistance (R), the total resistance in the circuit decreases. As per Ohm's law, if the resistance decreases, the current increases. However, the battery's internal resistance itself limits the maximum current that can flow through the circuit. Therefore, the maximum current is not obtained in this case either.

Maximum Current:
The maximum current is obtained when the internal resistance (r) is equal to the external resistance (R). In this case, the total resistance in the circuit is minimized, allowing the maximum amount of current to flow. This is known as the condition of maximum power transfer. The formula for calculating the maximum current is I = V / (2r), where V is the voltage across the terminals of the battery.

Conclusion:
To achieve the maximum current from a battery, the internal resistance should be equal to the external resistance. This condition minimizes the overall resistance in the circuit, allowing the maximum amount of current to flow.