Question

The temperature coefficient of a wire is ${0.00125}^0{C}^{-1}$. at 300 K its resistances is $1\Omega$. the resistance of the wire will be $2\Omega$ at

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

Answer 1

The correct option is D 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 $T-273=854.6$

$⟹$ $T=273+854.6=1127.6K$