A wire has a resistance of 3.0 Ω at 30 °C and a resistance of 4.5 Ω at 100 °C. The temperature coefficient of resistance of the wire is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $0.0071\, °C^{-1}$
Given:
$R_1 = 3.0 \, \Omega$ at $T_1 = 30^\circ \text{C}$
$R_2 = 4.5 \, \Omega$ at $T_2 = 100^\circ \text{C}$
Relation: $R_2 = R_1 [1 + \alpha (T_2 - T_1)]$
Substitute values:
$4.5 = 3.0 [1 + \alpha (100 - 30)]$
$4.5 = 3.0 [1 + 70 \alpha]$
$\frac{4.5}{3.0} = 1 + 70 \alpha$
$1.5 = 1 + 70 \alpha$
$70 \alpha = 0.5$
$\alpha = \frac{0.5}{70} = \frac{1}{140}$
$\alpha = 0.00714 \, /^\circ \text{C}$
Final Answer: Temperature coefficient of resistance $\alpha = 0.00714 \, /^\circ \text{C}$