Question

A rod of certain metal is 1 m long and 0.6 cm in diameter. It’s resistance is 3 × 10^–3Ω. 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 × 10^–6Ω
• B. 2.7 × 10^–7Ω
• C. 4.05 × 10^–6Ω
• D. 8.1 × 10^–6Ω

Answer 1

Answer: (B)

2.7 × 10^–7Ω

Answer 2

By using $R = \rho.\frac{l}{A};\frac{R_{\text{disc}}}{R_{\text{rod}}} = \frac{l_{\text{disc}}}{l_{\text{rod}}} \times \frac{A_{\text{rod}}}{A_{\text{disc}}}$

⇒ $\frac{R_{\text{disc}}}{3 \times 10^{- 3}} = \frac{10^{- 3}}{1} \times \frac{\pi(0.3 \times 10^{- 2})^{2}}{\pi(10^{- 2})^{2}}$

⇒ R_disc = 2.7 × 10^–7Ω.