The correct answer is: D. they have identical internal resistance.
When two batteries are connected in parallel, the current will flow through the battery with the lower internal resistance. This can cause the battery with the lower internal resistance to overheat and be damaged. To prevent this, it is important to ensure that the batteries have identical internal resistance.
Option A is incorrect because the batteries can have different emfs as long as they have identical internal resistance. The emf of a battery is the voltage that it produces. The internal resistance of a battery is the resistance to the flow of current through the battery.
Option B is incorrect because the batteries can have different makes as long as they have identical internal resistance. The make of a battery is the brand of the battery. The internal resistance of a battery is the resistance to the flow of current through the battery.
Option C is incorrect because the batteries can have different ampere-hour capacities as long as they have identical internal resistance. The ampere-hour capacity of a battery is the amount of current that the battery can produce for a given period of time. The internal resistance of a battery is the resistance to the flow of current through the battery.