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

$0.0071\, °C^{-1}$

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 $\alpha = 0.00714 \, /^\circ \text{C}$