Question

The temperature coefficient of resistance for a wire is $0.00125^{\circ }{C}^{-1}$. At $300K$ 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
$\frac{2}{1}=\frac{R_0(1+0.00125\times T)}{R_0(1+0.00125\times 27)}$
$2+0.0675=1+0.00125T$
$\Rightarrow T=\frac{1.0675}{0.00125}=854^{\circ }C$
$\Rightarrow T=1127K$