Find the resistance of a hollow cylindrical conductor of length 1.0 m and inner and outer radii 1.0 mm and 2.0 mm respectively. The resistivity of…

Question

Find the resistance of a hollow cylindrical conductor of length 1.0 m and inner and outer radii 1.0 mm and 2.0 mm respectively. The resistivity of the material is 2.0 × 10⁻⁸ Ω-m.

Answer 1

Find the resistance of a hollow cylindrical conductor of length 1.0 m and inner and outer radii 1.0 mm and 2.0 mm respectively. The resistivity of the material is 2.0 × 10⁻⁸ Ω-m.

2.1 × 10⁻³ Ω ✓
1.1 × 10⁻³ Ω
3.2 × 10⁻³ Ω
1.2 × 10⁻³ Ω

Explanation

Use R = ρL/A. The conducting area is the ring between the two radii: A = π(R² − r²) = π[(2.0 × 10⁻³)² − (1.0 × 10⁻³)²] = π × 3 × 10⁻⁶ = 9.42 × 10⁻⁶ m².

R = (2.0 × 10⁻⁸ × 1.0) ÷ 9.42 × 10⁻⁶ ≈ 2.1 × 10⁻³ Ω.

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