Resistance and Factors Affecting Resistance - UNSOLVED PRACTICE SET

Q7. State the four factors that affect the resistance of a conductor. Write the formula R = ρL/A and define each term.

Q8. A copper wire has resistance R. What will be the resistance if:
(a) its length is tripled?
(b) its cross-sectional area is doubled?
(c) both length is doubled and area is halved?

Q9. Why is nichrome wire used in electric heaters even though it has much higher resistivity than copper? Give two reasons.

Q10. Explain why the resistance of a metallic conductor increases with temperature. What is the opposite effect in semiconductors?

Q11. A student uses two wires:
Wire A (copper, 2 m long, 1 mm² area) and,
Wire B (iron, 1 m long, 1 mm² area). Without calculating, predict which wire has higher resistance and explain your reasoning.

Q12. Why are overhead power transmission lines made of thick aluminium cables rather than thin copper wires? Give two reasons related to resistance.

Q13. Explain in detail the four factors that affect the resistance of a conductor. For each factor:
(a) state the relationship (directly/inversely proportional),
(b) write the relevant formula term,
(c) give a real-life Indian example, and
(d) derive the combined formula R = ρL/A. Explain what resistivity ρ represents physically.

Q14. A BSNL technician is installing telephone cables across a 2 km distance in rural Maharashtra. He must choose between: Cable X: Copper, 2 mm diameter, 2 km long. Cable Y: Aluminium, 3 mm diameter, 2 km long. (ρ_Cu = 1.7×10⁻⁸ Ω·m, ρ_Al = 2.8×10⁻⁸ Ω·m.)
(a) Calculate the cross-sectional area of each cable (A = πd²/4).
(b) Calculate the resistance of each cable using R = ρL/A.
(c) Which cable has lower resistance?
(d) Even though aluminium has higher resistivity, it is widely used for long-distance power lines — why?
(e) What is the disadvantage of using aluminium over copper?

Q15. Explain how temperature affects resistance in metals and semiconductors differently.
(a) Describe the microscopic mechanism by which increasing temperature increases resistance in metals (increased lattice vibrations).
(b) Why does resistance decrease with temperature in semiconductors?
(c) What is a thermistor and how does it use the temperature-resistance relationship?
(d) Give one practical Indian use of a thermistor.
(e) What is superconductivity and at what temperature does it occur?

Q16. A copper wire of length 2 m has a cross-sectional area of 0.5 mm² (= 0.5 × 10⁻⁶ m²). (ρ_copper = 1.7 × 10⁻⁸ Ω·m)
(a) Calculate the resistance.
(b) The wire is stretched to twice its length (area halves to maintain volume). Find the new resistance.
(c) By what factor has resistance increased?
(d) What happens to current if 12 V is applied to the original vs stretched wire?

Q17. Three wires A, B, and C are made of the same material (ρ = 2 × 10⁻⁸ Ω·m):   
Wire A: length 1 m, area 1 mm²   
Wire B: length 2 m, area 1 mm²   
Wire C: length 1 m, area 2 mm²
(a) Calculate the resistance of each.
(b) Rank them from highest to lowest resistance.
(c) Which wire would get hottest if 5 V is applied to each? Explain.

Q18. A heating coil made of nichrome wire (ρ = 1.0 × 10⁻⁶ Ω·m) is designed to have resistance 10 Ω. The wire has a cross-sectional area of 0.5 mm² (= 0.5 × 10⁻⁶ m²).
(a) Calculate the required length of wire.
(b) If the coil is connected to 220 V, calculate the current.
(c) Calculate the power dissipated.
(d) Why is nichrome preferred over copper for this application?