With a real battery, show that the power supplied to a resistive load cannot exceed V^2/(2*Ri).
A battery has internal resistance Ri and terminal voltage V, showing that the power supplied to a resistive load cannot exceed V^2/(2*Ri).
The power dissipated at the load is at its maximum when the load resistance
is matched with the source's own internal resistance. Thus, a voltage source must have a low
internal resistance compared to your load resistance. If this is not true, then the voltage
across your load would depend on the resistance of the load, and this is not ideal because we
want the voltage source to dictate the voltage across the load.