A carbon resistor has a resistance of 18 Ω at a temperature of 20°C. What is its resistance at a temperature of 120°C? (The temperature coefficient of resistivity for carbon is -5.0 × 10^-⁴ /C°.)

Question

Quizplus · Accepted Answer

The resistance of a carbon resistor changes with temperature according to the following equation:$$R_t = R_0 [1 + \alpha (t - t_0)]$$where:* $$R_t$$ is the resistance at temperature t* $$R_0$$ is the resistance at temperature $$t_0$$* $$\alpha$$ is the temperature coefficient of resistivityIn this problem, we are given that $$R_0 = 18 \Omega$$, $$t_0 = 20°C$$, $$t = 120°C$$, and $$\alpha = -5.0 × 10^{-4} /C°$$. Plugging these values into the equation, we get:$$R_t = 18 \Omega [1 + (-5.0 × 10^{-4} /C°) (120°C - 20°C)]$$$$R_t = 18 \Omega [1 + (-5.0 × 10^{-4} /C°) (100°C)]$$$$R_t = 18 \Omega [1 - 0.05]$$$$R_t = 17.1 \Omega$$Therefore, the resistance of the carbon resistor at a temperature of 120°C is 17.1 Ω, which is closest to choice B) 17 Ω.

A Carbon Resistor Has a Resistance of 18 Ω at a Temperature