Question

The resistance of a wire at ${20}^{\circ }C$ is $20\Omega$ and at ${500}^{\circ }C$ is $60\Omega$. At which temperature resistance will be $25\Omega$

• A. ${50}^{\circ }C$
• B. ${60}^{\circ }C$
• C. ${70}^{\circ }C$
• D. ${80}^{\circ }C$

Answer 1

The correct option is D ${80}^{\circ }C$

By using $\frac{R_1}{R_2}=\frac{(1+\alpha t_1)}{(1+\alpha t_2)}\Rightarrow \frac{20}{60}=\frac{1+20\alpha }{1+500\alpha }\Rightarrow \alpha =\frac{1}{220}$
Again by using the same formula for $20\Omega$ and $25\Omega \Rightarrow \frac{20}{25}=\frac{(1+\frac{1}{220}\times 20)}{(1+\frac{1}{220}\times t)}\Rightarrow t={80}^{\circ }C$