Final answer:
When a heater coil is halved, its resistance is also reduced by half and the heat generated is reduced by a factor of four, assuming constant voltage.
Step-by-step explanation:
When a heater coil is cut into two equal parts, and only one part is now used in the heater, the amount of heat generated will be reduced. To understand this, we need to consider the electrical resistance of the heater coil and how it changes when the coil is cut. The resistance (R) of a wire (the coil, in this case) depends on its length (l), cross-sectional area (A), and the resistivity (ρ) of the material, according to the formula R = ρl/A. When you cut the heater coil in half, you are halving the length, which essentially halves the resistance. Since power (P) is directly proportional to the square of the current (I) and the resistance (R), as per the formula P = I2R, reducing the resistance to half will also reduce the heat generated by a factor of four (since P is proportional to R), assuming that the voltage remains constant.