A resistor has a resistance of 30 Ω at 20°C. If the temperature coefficient of resistivity is 4.5 × 10⁻³ °C⁻¹, what is its resistance at 200°C? A) 24 Ω B) 27 Ω C) 48 Ω D) 54 Ω E) 57 Ω

Question

Quizplus · Accepted Answer

We can use the formula:

R2 = R1[1 + α(T2 - T1)]

where R1 is the resistance at the initial temperature T1, R2 is the resistance at the final temperature T2, and α is the temperature coefficient of resistivity.

Plugging in the values given:

R1 = 30 Ω
α = 4.5 × 10^-3 / °C
T1 = 20°C
T2 = 200°C

R2 = 30 Ω [1 + (4.5 × 10^-3 / °C) (200°C - 20°C)]
R2 = 30 Ω [1 + 0.81]
R2 = 30 Ω (1.81)
R2 = 54.3 Ω

So the resistance at 200°C is approximately 54 Ω (closest to D).

A Resistor Has a Resistance of 30 Ω at 20°C