Question

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

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

Answer 1

The correct option is D. 1127 K.

Given Initial resistance at 300K is 1Ω.

Let temperature be T when final resistance becomes 2Ω

Applying Relation between Temperature and Resistance

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

$2\Omega =1\Omega (1+0.00125(T_2-27\left)\right)$

$T_2-27=\frac{1}{0.00125}$

$T=800+27={827}^{o}C$

$T=827+273=1100K$

$\frac{{\rho }_1}{{\rho }_2}=\frac{(1+\alpha t_1)}{(1+\alpha t_2)}=\frac{1}{2}\Rightarrow \frac{(1+0.00125\times 27)}{(1+0.00125\times t)}$

$\Rightarrow t={854}^{\circ }C\Rightarrow T=1127K$