Question

A rod of certain metal is 1 m long and 0.6 cm in diameter. It’s resistance is $3\times {10}^{-3}\Omega$. A disc of the same metal is 1 mm thick and 2 cm in diameter, what is the resistance between it’s circular faces.

• A. $1.35\times {10}^{-6}\Omega$
• B. $2.7\times {10}^{-7}\Omega$
• C. $4.05\times {10}^{-6}\Omega$
• D. $8.1\times {10}^{-6}\Omega$

Answer 1

The correct option is B $2.7\times {10}^{-7}\Omega$

By using $R=\rho \frac{l}{A};\frac{R_{disc}}{R_{rod}}=\frac{l_{disc}}{l_{rod}}\times \frac{A_{rod}}{A_{disc}}\Rightarrow \frac{R_{disc}}{3\times {10}^{-3}}=\frac{{10}^{-3}}{1}\times \frac{\pi (0.3\times {10}^{-2}{)}^2}{\pi ({10}^{-2}{)}^2}\Rightarrow R_{disc}=2.7\times {10}^{-7}\Omega$