Question

The temperature coefficient of resistance for a wire is $0.00125^{\circ} C ^{-1}$. At $300\, K$ its resistance is $1 \Omega$. The temperature at which the resistance becomes $2 \Omega$ is

• A. 450 K
• B. 1127 K
• C. 454 K
• D. 900 K

Answer 1

Answer: (B)

Here, $R_{27}=1 \Omega,\,\,\alpha=0.00125^{\circ} C ^{-1}$
$R_{T}=2 \Omega, T=?,\,\,\, R_{T}=R_{0}(1+\alpha T)$
where $R_{T}, R_{0}$ is the resistance at $0^{\circ} C$ and $T^{\circ} C$ respectively.
$1=R_{0}(1+0.00125 \times 27)$...(i)
$2=R_{0}(1+0.00125 \times T)$...(ii)
Divide (ii) by (i), we get
$\frac{2}{1}=\frac{R_{0}(1+0.00125 \times T)}{R_{0}(1+0.00125 \times 27)}$
$2+ 0.0675=1+0.00125 T$
$\Rightarrow T=\frac{1.0675}{0.00125}=854^{\circ} C$
$\Rightarrow T=1127\, K$