A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is n × 10⁻³ Ω. If the resistivity of the material is 2.4 × 10⁻⁸ Ωm. The value of n i s ______ .
Physics · Current electricity · electric current ,current density and resistance
JEE Mains 2023 24 jan morning shift

Question

A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is n × 10⁻³ Ω. If the resistivity of the material is 2.4 × 10⁻⁸ Ωm. The value of n i s ______ .

Physics · Current electricity · electric current ,current density and resistance

JEE Mains 2023 24 jan morning shift

G1 Physics · Accepted Answer

Inner radius a = 2 mm and outer radius b = 4 mm. Cross-sectional area A = π(b² - a²) = π(16 - 4)×10⁻⁶ m². Thus R = ρl/A = (2.4×10⁻⁸×3.14)/(3.14×12×10⁻⁶) = 2×10⁻³ Ω. Hence n = 2.