Question

The temperature coefficient of resistance of a wire is $0.00125/K$. At $300\,K$ its resistance is 1 $\Omega$ .The resistance of the wire will be 2 $\Omega$ at

• A. 1154 K
• B. 1100 K
• C. 1400 K
• D. 1127 K

Answer 1

The Correct Option is C

The resistance $R_{t}$ of a metal conductor at temperature $t^{\circ} C$ is given by $R_{t}=R_{0}\left(1+\alpha t+\beta t^{2}\right)$ where $\alpha$ and $\beta$ are temperature coefficients of resistance. $R_{0}$ is the resistance of conductor at $0^{\circ} C$. Their values vary from metal to metal. If the temperature $t^{\circ} C$ is not sufficiently large which is so in the most practical cases, the above relation may be expressed as $R_{t} =R_{0}(1+\alpha t)....$(i) Given, $\alpha =0.00125 / K$ $R_{300}=1 \Omega$ From E (i), we have $ 1 =R_{0}(1+0.00125 \times 300) $...(ii) and, $2 =R_{0}(1+0.00125 \times T) $...(iii) $ \therefore \frac{2}{1} =\frac{1+0.00125 \times T}{1+0.00125 \times 300} $ or $2.75 =1+0.00125 \times T$ or $T=\frac{1.75}{0.00125}$ $=1400\, K$