Final answer:
Batteries are represented as having some internal resistance to explain why voltage output decreases as current load increases. This internal resistance causes a voltage drop that becomes more significant as batteries become depleted or heavily loaded.
Step-by-step explanation:
To characterize the behavior of batteries when the load on a battery gets larger and the voltage output gets smaller, we represent batteries as having some internal resistance. The correct representation of this behavior is by treating batteries as if they have some small internal resistance (option 1). As the current load increases, the voltage output does not increase; rather, it decreases because of the voltage drop across the internal resistance.
The internal resistance (r) affects how much current a battery can supply to its load (Rload). When a battery is depleted or under a heavy load, r increases, which can significantly reduce the current if r becomes a large fraction of Rload. This reduction is because the terminal voltage of the battery is equal to EMF minus the voltage lost across the internal resistance (I · r).
Furthermore, the behavior of internal resistance can be complex, as it may also depend on factors like the magnitude and direction of current, temperature, and the history of the battery. These variations can especially be seen with rechargeable batteries like nickel-cadmium cells, where internal resistance changes with the number of depletion cycles.