Question

The resistance of a wire at temperature ${30}^{\circ }C$ is found to be $10\Omega$ . Now to increase the resistance by $10\%,$ the temperature of the wire must be $($ The temperature coefficient of resistance of the material of the wire is $0.002{{}^{\circ }C}^{-1}$ and reference temperature is $0^{\circ }C)$.

• A. ${36}^{\circ }C$
• B. ${83}^{\circ }C$
• C. ${33}^{\circ }C$
• D. ${35}^{\circ }$C

Answer 1

Answer: (B)

$\frac{R_2}{R_1}=\frac{(1+\alpha t_2)}{(1+\alpha t_1)}$
Here $R_1=10\Omega ,R_2=10+10\times \frac{1}{10}=11\Omega ,\alpha =0.002{/}^{o}C,t_1={30}^{o}C$
thus, $t_2=\frac{1}{\alpha }\left[\frac{R_2}{R_1}\right(1+\alpha t_1)-1]=\frac{1}{0.002}\left[\frac{11}{10}\right(1+0.002\times 30)-1]={83}^{o}C$