Resistivity and Conductivity - UNSOLVED PRACTICE SET

Q7. Define resistivity and conductivity. Write their SI units.

Q8. Why is resistivity called an intrinsic property of a material? How does it differ from resistance?

Q9. The resistivity of copper is 1.7 × 10⁻⁸ Ω m and that of nichrome is 1.1 × 10⁻⁶ Ω m. Which material is better for (a) electrical wiring, and (b) heating elements? Explain.

Q10. A wire of material A has resistivity ρ_A and a wire of material B has resistivity ρ_B = 2ρ_A. Both have the same dimensions. Compare their resistances and conductivities.

Q11. Why do metals have low resistivity while insulators have very high resistivity? Explain in terms of free electrons.

Q12. Calculate the resistance of a nichrome wire of length 2 m and cross-sectional area 0.5 mm². The resistivity of nichrome is 1.1 × 10⁻⁶ Ω m.

Q13. Derive the relation R = ρl/A connecting resistance with resistivity. Explain why resistivity is independent of the dimensions of the conductor but depends on the material and temperature.

Q14. Compare the electrical properties of conductors, insulators, and semiconductors in terms of resistivity, conductivity, and temperature dependence. Give two examples of each.

Q15. A wire of length 3 m and cross-sectional area 2 mm² has a resistance of 0.255 Ω.

(a) Calculate the resistivity of the material.

(b) Identify the material using standard resistivity values.

(c) Calculate the conductivity of the material.

(d) If the wire is stretched to increase its length by 50%, what is the new resistance?

Q16. In a school science fair, students compare the electrical properties of different materials. They have wires of copper, aluminium, nichrome, and constantan, each of length 2 m and diameter 0.4 mm.

(a) Calculate the resistance of each wire.

(b) Rank the wires in order of increasing resistance.

(c) Which wire would get hottest if the same current flows through all of them? Explain.

(d) If a student needs a wire with resistance exactly 5 Ω, which material and what length should be chosen? (Assume same diameter)

[Given: ρ_copper = 1.7 × 10⁻⁸ Ω m, ρ_aluminium = 2.8 × 10⁻⁸ Ω m, ρ_nichrome = 1.1 × 10⁻⁶ Ω m, ρ_constantan = 4.9 × 10⁻⁷ Ω m]

Q17. A conducting wire has length l = 10 m, radius r = 0.5 mm, and carries a current I = 2 A when connected to a 5 V battery.

(a) Calculate the resistance of the wire.

(b) Calculate the resistivity of the material.

(c) Calculate the current density and the electric field inside the wire.

(d) If the wire is replaced by another wire of the same material but with radius 1 mm and length 5 m, what current will flow for the same 5 V?

(e) Compare the drift velocities in the two wires.

[Given: n = 8.5 × 10²⁸ m⁻³, e = 1.6 × 10⁻¹⁹ C]

Q18. The resistivity of a material varies with temperature according to the relation ρ = ρ₀(1 + αT), where α is the temperature coefficient of resistivity.

(a) For a material with ρ₀ = 2 × 10⁻⁸ Ω m and α = 4 × 10⁻³ /°C, calculate the resistivity at 50°C.

(b) A wire of this material has length 5 m and diameter 1 mm at 20°C. Calculate its resistance at 20°C and at 80°C.

(c) If this wire is used in a precision instrument where resistance must not change by more than 1%, what is the maximum allowable temperature change?

(d) Explain why materials with low α are preferred for making standard resistors.