A wire has a resistance of 3 Ω at 20 °C and 5 Ω at 100 °C. The temperature coefficient of resistance of the wire is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $0.00833 °C^{-1}$
Resistance at $T_1 = 20^\circ \text{C}$: $R_1 = 3 \, \Omega$
Resistance at $T_2 = 100^\circ \text{C}$: $R_2 = 5 \, \Omega$
Temperature coefficient of resistance: $\alpha = \frac{R_2 - R_1}{R_1 (T_2 - T_1)}$
$\alpha = \frac{5 - 3}{3 \cdot (100 - 20)} = \frac{2}{3 \cdot 80} = \frac{2}{240} = 0.00833 \, \text{°C}^{-1}$
Answer: $\alpha \approx 8.33 \times 10^{-3} \, \text{°C}^{-1}$