Q138 / 160 · TS EAMCET 2017 · Physics
A wire has resistance of $3.1 \Omega$ at $30^{\circ} \mathrm{C}$ and $4.5 \Omega$ at $100^{\circ} \mathrm{C}$. The temperature coefficient of resistance of the wire is
- Correct answerA$0.008^{\circ} \mathrm{C}^{-1}$
- B$0.0024^{\circ} \mathrm{C}^{-1}$
- C$0.0032^{\circ} \mathrm{C}^{-1}$
- D$0.0064^{\circ} \mathrm{C}^{-1}$
Solution
Given,
$$
\begin{aligned}
& t_1=30^{\circ} \mathrm{C} \\
& R_1=3.1 \Omega \\
& t_2=100^{\circ} \mathrm{C} \\
& R_2=4.5 \Omega
\end{aligned}
$$
We know that,
Temperature coefficient of resistance,
$$
\begin{aligned}
\alpha & =\frac{R_2-R_1}{R_1 t_2-R_2 t_1}=\frac{4.5-3.1}{(3.1)(100)-(4.5 \times 30)} \\
& =\frac{1.4}{310-135}=\frac{1.4}{175}=0.008^{\circ} \mathrm{C}^{-1}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.