According to the slope of the image, the internal resistance r =1.2Ω is obtained.
The total power consumed by the battery in A and B states is pa=EIa and pb=EIb, respectively.
Therefore, the difference between the total power consumed by the battery in the two states of A and B is △ P =1.5× (0.5-0.25) = 0.375 W..
According to the analysis of mathematical knowledge, when the external resistance is equal to the internal resistance of the power supply, that is, R external =r, the output power of the power supply is the maximum.
But the measuring range cannot reach r =r,
The maximum output power of the power supply is PM = UI = 0.9× 0.5 = 0.45 W..
So the answer is: 0.375; 0.45