A department store sells two compact electric space heaters, Heater A and Heater B. Each heater contains a single resistive element made of the same material, and the two elements have identical resistance at room temperature. Heater A is plugged directly into a standard 120 V wall outlet. Heater B is powered through an adjustable transformer so that a constant current equal in magnitude to the current in Heater A flows through its element, even though the voltage across Heater B’s element differs from 120 V.
Assume that the resistance of each element remains constant while operating and that all electrical energy converted by an element appears as thermal energy within that element.
(a) Describe qualitatively how the rate at which each heater converts electrical energy into thermal energy depends on the electrical quantities across the element.
(b) Without performing any numerical calculation, indicate which heater releases thermal energy at a greater rate. Justify your answer in terms of the electrical conditions specified for the two heaters.
(c) Suppose the resistance of each element is 24 Ω. Support your explanation in part (b) by calculating the rate of energy conversion for Heater A and for Heater B.
(d) If Heater A operates for 15 min, compare the total thermal energy released by each heater during that time interval. Provide reasoning that connects your answer to parts (b) and (c).