Final answer:
Without the exact temperature coefficient of resistance for carbon, calculating the resistance change over the temperature range for carbon resistors is not possible. Carbon has a negative temperature coefficient, meaning its resistance decreases with increasing temperature. None of the provided options match this description, suggesting there may be an error in the question.
Step-by-step explanation:
To determine by what factor the resistance of pure carbon resistors increases over the temperature range from -10.0°C to 55.0°C, we need to use the temperature coefficient of resistance (α) for carbon. The resistance change can be calculated using the formula: R = R_0(1 + αΔT).
However, without the exact value for the temperature coefficient of resistance for carbon, we cannot calculate the exact factor. Given that carbon is a negative temperature coefficient (NTC) material, its resistance decreases with increasing temperature. From information that the resistance is 40.0% greater at 100.0°C than at 20.0°C, we know that, as a general trend, the resistance increases as the temperature decreases. Thus, over the range from -10°C to 55°C, the resistance would decrease because the temperature increases.
Given this, the answer to the question would be less than one, because as temperature increases, the resistance of carbon decreases. Therefore, none of the options given is suitable if taken at face value, indicating either the question is framed incorrectly or lacks adequate information to reach a conclusion.