Question

The temperature coefficient of resistance of a wire is 0.00125 per ${}^{\circ }C$. At 300K its resistance is 1$\Omega$. The resistance of wire will be 2$\Omega$ at

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

Answer 1

The correct option is D 1127K

Resistance of wire varies with temperature as R =$R_0(1+\alpha T_c)$ where $\alpha$ is temperature coefficient of resistance
$\Rightarrow$ $\frac{R_{27}}{R_{T_c}}=\frac{R_0(1+27\alpha )}{R_0(1+\alpha T_c)}=\frac{1}{2}$ $\Rightarrow$ $T_c$= $\frac{1+54\alpha }{\alpha }$= $\frac{1+54\times 0.00125}{0.00125}$= ${854}^{\circ }C$
$\therefore$ $T_K$ = $(854+273)=1127K$ = 1127 K.