Question

The resistance of a wire at roan temperature ${30}^{o}C$ is found' to be $10\Omega$ Now to increase the resistance by $10\Omega$, the temperature of the wire must. be [The temperature coefficient of resistance of die material of the wire is 0.002

• A. ${36}^{o}C$
• B. ${86}^{o}C$
• C. ${560}^{o}C$
• D. ${33}^{o}C$

Answer 1

The correct option is C ${560}^{o}C$

$R=R_0\left(1+\alpha \theta \right)$

$10=R_0\left(1+\alpha {30}^0\right)$

$10+10=R_0\left(1+\alpha \theta \right)$

$\frac{10}{20}=\frac{1+0.002\times 30}{1+0.002\times \theta }$

$\Rightarrow 1+0.002\theta =2+0.12$

$\Rightarrow 0.002\theta =1+0.12$

$\theta =\frac{1.12}{0.002}$

$\theta ={560}^{0}C$

Hence,

option $\left(C\right)$ is correct answer.