Question

The temperature coefficient of a wire is ${0.00125}^0{C}^{-1}$. At 300 K its resistance is one ohm.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 D 1127 K

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 $T-273=854.6$

$⟹$ $T=273+854.6=1127.6K$