Resistivity - UNSOLVED PRACTICE SET

Q7. Define resistivity. How is it related to resistance, length, and area? Write the formula and state its SI unit. 

Q8. The resistivity of copper is 1.7 × 10⁻⁸ Ω·m and that of nichrome is 1.0 × 10⁻⁶ Ω·m.
(a) Which is a better conductor?
(b) What does the difference in resistivity tell us about how these materials are used?

Q9. Explain why resistivity is called an intrinsic property of a material. Does the resistivity of a material change if you change the shape of the conductor made from it?

Q10. How does the resistivity of a metal change with temperature? How is this different for semiconductors? Give one example of each.

Q11. Calculate the resistivity of a material from the following data: A wire 4 m long, cross-sectional area 2 × 10⁻⁶ m², resistance 40 Ω. Show full working.

Q12. Compare the resistivity of conductors, semiconductors, and insulators. Give one example of each and its approximate resistivity value.

Q13. Explain the concept of resistivity in detail. Your answer must cover:
(a) the definition of resistivity as ρ = RA/L,
(b) why resistivity is independent of the shape and size of the conductor,
(c) the SI unit Ω·m and physical meaning,
(d) a comparison of resistivity ranges for conductors (10⁻⁸), semiconductors (10⁻²), and insulators (10¹²), and
(e) two examples of how resistivity values determine the choice of material in electrical applications in India.

Q14. A wire manufacturer in Pune needs to produce wires for two applications:
(i) electrical wiring in homes (low resistance needed), and
(ii) heating elements in toasters (high, stable resistance needed).
(a) Which material would you choose for each application? Justify using resistivity values.
(b) Copper: ρ = 1.7×10⁻⁸ Ω·m, Nichrome: ρ = 1.0×10⁻⁶ Ω·m. Calculate the resistance of 10 m of each material with cross-section 1 mm² (= 10⁻⁶ m²).
(c) How much greater is nichrome's resistance than copper's for the same dimensions?
(d) Why does nichrome not melt in a toaster but copper would?
(e) What other property besides resistivity must a heating element material have?

Q15. Explain the temperature dependence of resistivity for different classes of materials.
(a) For pure metals: describe how resistivity increases approximately linearly with temperature using the formula ρ_T = ρ₀(1 + αT).
(b) For alloys like nichrome: why does resistivity change very little with temperature? 

(c) For semiconductors like silicon: why does resistivity decrease with temperature?
(d) What is the practical importance of low temperature coefficient of resistance in heating elements?
(e) What is a Positive Temperature Coefficient (PTC) thermistor and give one Indian household application.

Q16. A nichrome wire (ρ = 1.0 × 10⁻⁶ Ω·m) has length 3 m and cross-sectional area 1.5 × 10⁻⁶ m².
(a) Calculate its resistance.
(b) If the same length of copper wire (ρ = 1.7 × 10⁻⁸ Ω·m) with the same area is used, calculate its resistance.
(c) What is the ratio of nichrome's resistance to copper's? 

(d) If both are connected to 9 V, calculate the current through each.

Q17. A student measures the resistance of four wires and records:   
Wire 1: R = 5 Ω, L = 0.5 m, A = 2 × 10⁻⁶ m²   

Wire 2: R = 10 Ω, L = 1 m, A = 2 × 10⁻⁶ m²   
Wire 3: R = 20 Ω, L = 1 m, A = 1 × 10⁻⁶ m²   
Wire 4: R = 5 Ω, L = 1 m, A = 4 × 10⁻⁶ m²
(a) Calculate the resistivity of each wire.
(b) Which two wires are made of the same material? How do you know?
(c) What material might Wire 1 be? (Compare with known values.)

Q18. The filament of a tungsten bulb (ρ = 5.6 × 10⁻⁸ Ω·m) has a resistance of 240 Ω at operating temperature. The filament diameter is 0.04 mm (radius = 0.02 mm = 2 × 10⁻⁵ m).
(a) Calculate the cross-sectional area.
(b) Calculate the length of the filament.
(c) A 60 W bulb operates at 240 V — verify the resistance using R = V²/P.
(d) The filament is coiled to fit in the bulb — what advantage does this shape have?