Question

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

• A. 1127 K
• B. 727 K
• C. 454 K
• D. 900 K

Answer 1

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

$⟹$ $T=273+854.6=1127.6K$