A physics laboratory stores handheld heaters powered by a chemical battery of emf 3.00 V and unknown internal resistance r0 at room temperature (20∘C). When a heater with resistance 4.50 Ω is connected at this temperature, the current through the circuit is measured to be 0.550 A.
During a field experiment in a cold environment (−10∘C), the same battery–heater combination is used. At this lower temperature, the current is observed to have decreased to 0.450 A. Assume the heater’s resistance remains constant and that the emf of the battery does not change with temperature.
(1) Determine the internal resistance r0 of the battery at 20∘C. Show all algebraic work.
(2) Calculate the internal resistance rcold of the battery at −10∘C based on the measured current.
(3) Derive a general expression for the fractional change in terminal voltage of a battery when its internal resistance changes from r0 to rcold while driving a fixed external resistance RL.
(4) Using numerical values from parts (a) and (b), compute the fractional change in terminal voltage for this heater. Interpret what this result implies about the heater’s power output in the cold environment.
(5) Engineers propose connecting a second identical battery in parallel with the first to mitigate the performance loss at low temperature. Qualitatively discuss whether this configuration would reduce, increase, or leave unchanged (i) the current through each battery and (ii) the total power dissipated in the heaters, assuming both batteries have the same internal resistance rcold. Support your reasoning with appropriate equations or proportional arguments.