A coil of nichrome wire has a resistance of 10Ω at room temperature. When an electric current of 2A is passed through it for 5 minutes, its temperature rises uniformly so that its resistance reaches 11Ω by the end of the interval.
(i) Assuming that the resistance increases linearly with temperature and taking the average resistance during the interval as the mean of the initial and final values, calculate the heat produced in the coil during the 5-minute period.
(ii) If a student, neglecting the change in resistance, had assumed the resistance to remain constant at 10Ω, how much heat would he or she have calculated?
(iii) Determine the percentage error introduced by neglecting the rise in resistance. Comment briefly on whether this simplification is acceptable in ordinary household calculations.