To determine the condition required for a DC shunt generator to successfully charge a battery bank, we need to consider the relationship between the generator's terminal voltage and the battery voltage.

1. The primary condition for charging a battery using a DC shunt generator is that the terminal voltage of the generator must be higher than the battery voltage. This ensures that the current flows from the generator to the battery, as current naturally flows from a higher potential to a lower potential.
2. If the generator's terminal voltage is equal to the battery voltage, no current will flow, and the battery will not charge.
3. A higher generator terminal voltage provides the necessary voltage difference needed to overcome the battery's internal resistance and ensure effective charging. This condition aligns with the principle that, to charge a battery, the charging device must have a greater voltage than the battery being charged.
4. By analyzing the options given:
   • The armature resistance must be maximum: This is incorrect because high armature resistance could cause excessive voltage drop and reduce the efficiency of the charging process.
   • The generator terminal voltage must be equal to the battery voltage: This is incorrect as no charging will occur without a voltage difference.
   • The generator terminal voltage must be higher than the battery voltage: This is correct for effective charging.
   • The generator field resistance must be minimum: This might increase the field current but does not directly ensure charging; the focus should be on terminal voltage.

Therefore, the correct condition for a DC shunt generator to successfully charge a battery bank is that the generator terminal voltage must be higher than the battery voltage.