Carbon has a negative temperature coefficient of resistance of -0.5 × 10^-3 (°C)−¹.What temperature increase would result in a resistance decrease of 1.0% for a carbon resistor? A)2.0°C B)20°C.. C)20°C. D)50°C E)100°C

Question

Quizplus · Accepted Answer

From the given data, we know that the temperature coefficient of resistance (α) of carbon is -0.5 × 10^-3 (°C)^-1. We also know that the resistance decreases by 1% when the temperature increases by a certain amount, which we will denote as ΔT.

We can use the formula for the temperature coefficient of resistance to relate the change in resistance to the change in temperature:

α = (ΔR/R) / ΔT

where R is the resistance at some initial temperature and ΔR/R is the fractional change in resistance.

Solving for ΔT, we get:

ΔT = (ΔR/R) / α

We are given that ΔR/R is -0.01 (since the resistance decreases by 1%). Plugging in the values for ΔR/R and α, we get:

ΔT = (-0.01) / (-0.5 × 10^-3) = 20°C

Therefore, a temperature increase of 20°C would result in a resistance decrease of 1% for a carbon resistor. Answer is B) 20°C.

Carbon Has a Negative Temperature Coefficient of Resistance of -0