Question

The temperature coefficient of resistance of a wire is $0.00125/{}^{\circ }C$. Its resistance is $1\Omega$ at $300K$. Its resistance will be $2\Omega$ at:

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

Answer 1

The correct option is A $1127K$

Given : $\alpha =0.00125{/}^{o}C$

Using $R_T=R_{273}(1+\alpha (T-273\left)\right)$

For $T=300$, $R_{300}=1\Omega$

$\therefore$ $R_{300}=R_{273}(1+\alpha (300-273\left)\right)$

OR $1=R_{273}(1+0.00125(300-273\left)\right)$ $⟹R_{273}=0.967\Omega$

Let at temperature be $T$ when $R_T=2\Omega$

$\therefore$ $R_T=R_{273}(1+\alpha (T-273\left)\right)$

OR $2=0.967(1+0.00125(T-273\left)\right)$

OR $T-273=854.6$

$⟹$ $T=273+854.6=1127.6K$