Question

The temperature coefficient of resistance of a wire is $0.00125$ per degree celcius. At $300K$ its resistance is $1$ ohm. The resistance of the wire will be $2$ ohm at following temperature :-

• A. $1100K$
• B. $400K$
• C. $600K$
• D. $1400K$

Answer 1

The correct option is A $1100K$

$\text{Step 1: Applying Relation between Temperature and Resistance}$

$R=R_0(1+\alpha (T_2-T_1\left)\right)$

Given Initial resistance at $300K$ is $1\Omega$.

Let temperature be T when final resistance becomes $2\Omega$

$\Rightarrow 2\Omega =1\Omega (1+0.00125(T-300K\left)\right)$

$\Rightarrow 1=\frac{5}{4}\times {10}^{-3}(T-300K)$

$\therefore T=1100K$

Hence correct Option is A