Question 45: The resistance of platinum wire at 0^{\circ} \mathrm{C} is 2 \Omega and 6.8 \Omega at 80^{\circ} \mathrm{C}. The temperature coefficient of resistance of the wire is :
(1) 3 \times 10^{-2}{ }^{\circ} \mathrm{C}^{-1}
(2) 3 \times 10^{-1}{ }^{\circ} \mathrm{C}^{-1}
(3) 3 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}
(4) 3 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}
Answer: Option (1)
Explanation:
The resistance of a conductor at temperature T is given by
R_T = R_0 \left(1 + \alpha T \right),
where R_0 is the resistance at 0^{\circ} \mathrm{C} and \alpha
is the temperature coefficient of resistance.
Given R_0 = 2 \Omega and R_{80} = 6.8 \Omega.
Substituting the values,
6.8 = 2 \left(1 + 80\alpha \right).
Dividing both sides by 2,
3.4 = 1 + 80\alpha.
80\alpha = 2.4.
\alpha = \frac{2.4}{80} = 0.03.
Thus,
\alpha = 3 \times 10^{-2} { }^{\circ} \mathrm{C}^{-1}.
Hence, the correct answer is Option (1).