Two identical metal coil heaters are available for warming a container of fluid

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two identical metal coil heaters are available for warming a container of fluid, but they have different resistances. Heater X has resistance

R_{X}=8.0\,\Omega

, and Heater Y has resistance

R_{Y}=32\,\Omega

. Each heater, when used, is connected individually (never simultaneously) across the terminals of the same

12\,\text{V}

car battery. The battery can supply a total of

1.8\times10^{5}\,\text{J}

of energy before it must be recharged. The internal resistance of the battery is negligible. (a) Derive an expression for the power dissipated by a resistive heater connected across a constant potential difference

V

in terms of

V

and the heater’s resistance

R

. (b) Using your result from part (a), calculate the power output of Heater X and of Heater Y when each is connected to the battery. (c) For each heater, determine the maximum operating time before the battery’s usable energy is exhausted. (d) If both heaters were used to heat equal masses of the same fluid starting at the same initial temperature, explain which heater would raise the fluid’s temperature more rapidly and why, taking your results into account.

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