Question

A brass disc and a carbon disc of same radius are assembled alternatively to make a cylindrical conductor. The resistance of the cylinder is independent of the temperature. The ratio of thickness of the brass disc to that of the carbon disc is $\underset{–}{}$ .$\alpha$ is temperature coefficient of resistance & Neglect linear expansion

• A. $\frac{{\alpha }_C{\rho }_C}{{\alpha }_B{\rho }_B}$
• B. $\frac{{\alpha }_C{\rho }_B}{{\alpha }_B{\rho }_C}$
• C. $\frac{{\alpha }_B{\rho }_C}{{\alpha }_C{\rho }_B}$
• D. $\frac{{\alpha }_B{\rho }_B}{{\alpha }_C{\rho }_C}$

Answer 1

The correct option is A $\frac{{\alpha }_C{\rho }_C}{{\alpha }_B{\rho }_B}$

Given the resistance is independent of temperature .
Hence ,

$\frac{{\rho }_B{l}_B}{A}\left({\alpha }_B\Delta T\right)=\frac{{\rho }_C{l}_C}{A}\left({\alpha }_C\Delta T\right)$

$\therefore \frac{l_B}{l_C}=\frac{{\rho }_C{\alpha }_C}{{\rho }_B{\alpha }_B}$