1. The problem statement, all variables and given/known data A certain electric hotplate, designed to operate on a 250 V supply, has two coils of nichrome wire of resistivity 9.8 * 10-7 Ω m. Each coil consists of 16 m of wire of cross-sectional area 0.20 mm2. (a) For one of the coils calculate (i) its resistance, (ii) the power dissipation when 250 V supply is connected across the coil, assuming its resistance does not change with temperature. (b) Show, by means of diagrams, how these coils may be arranged so that the hotplate may be made to operate at three different powers. In each case, calculate the power rating. (c) The hotplate is connected to the 250 V supply by means of cable of total resistance 3.0 Ω. (i) Calculate the power loss in the connecting cable when the hotplate is being used on its middle power rating. (ii) Comment qualitatively on any change in power loss in the cable when the hotplate is operating at each of its other power ratings. (d) Different connecting cables are available for use with the hotplate. The maximum safe current which can be used in any one of the cables is 1 A or 3 A or 6 A or 12 A. State which is the most appropriate cable to use and briefly explain one possible danger of using cable with a lower maximum safe current. Answers: (a) (i) 78 Ω, (ii) 8 * 102 W, (c) (i) 28 W. 2. The attempt at a solution (a) (i) ρ = (A R) / L → R = (ρ L) / A = (9.8 * 10 -7 * 16) / (2 * 10-7) = 78.4 Ω. (a) (ii) P = V2 / R = 2502 / 78.4 = 797 W. (b) Not even sure where to start. Am I required to make a circuit? What are coils in a circuit? Resistors? What is a hotplate in a circuit? A cell? (c) (i) As I understand we'll have RTotal = RCoil + RCable = 78 Ω + 3 Ω = 81 Ω. Then P = 2502 / 81 = 771.6 W. Difference between 800 W and 771.6 W is 28.4 W. (c) (ii) Not sure on this question either. So we need to say whether there will be any power losses in the cable when the hotplate is operating at what? What does "each of its other power ratings" actually mean? (d) Maybe the higher is the maximum safe current the better it is? So in case more current starts going through the circuit the cables will not overheat and start buring? Just a guess, also not sure on this part. Any suggestions please?