Resistivity and conductionEdexcel A-Level Physics: Subtopic test

1. 1
   A cable manufacturer draws copper into uniform wire of diameter 0.50 mm. The resistivity of copper at room temperature is 1.7 × 10⁻⁸ Ω m. A length of 2.0 m of this wire is used as a test sample.

   (a)

   What is the cross-sectional area of the wire?

   [1 mark]

   • A7.9 × 10⁻⁷ m²
   • B1.6 × 10⁻³ m²
   • C2.0 × 10⁻⁷ m²
   • D6.3 × 10⁻⁸ m²

   (b)

   What is the resistance of the 2.0 m sample?

   [1 mark]

   • A0.17 Ω
   • B0.043 Ω
   • C0.54 Ω
   • D1.7 × 10⁻⁷ Ω

   (c)

   A second wire of the same copper has twice the diameter and twice the length of the sample. Calculate its resistance.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A copper wire of cross-sectional area 1.0 × 10⁻⁶ m² carries a steady current of 3.0 A. Copper has 8.5 × 10²⁸ conduction electrons per cubic metre.

   (a)

   What is the mean drift velocity of the conduction electrons in the wire?

   [1 mark]

   • A4.5 × 10³ m s⁻¹
   • B2.2 × 10⁻¹⁰ m s⁻¹
   • C7.4 × 10⁻⁵ m s⁻¹
   • D2.2 × 10⁻⁴ m s⁻¹

   (b)

   The current in the same wire is increased to 6.0 A. What happens to the mean drift velocity of the electrons?

   [1 mark]

   • AIt stays the same
   • BIt doubles
   • CIt quadruples
   • DIt halves

   (c)

   The drift velocity is very small, yet a lamp connected to this wire lights almost immediately when the switch is closed. Explain why.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a core practical a student determines the resistivity of nichrome wire. She measures the diameter of the wire with a micrometer, then connects different lengths l of the wire into a circuit and measures the p.d. across each length and the current in it. She plots resistance R against length l, and the gradient of her best-fit line is 13.4 Ω m⁻¹. Her mean diameter for the wire is 0.32 mm.

   (a)

   Calculate the resistivity of nichrome from the student's results.

   [3 marks]

   (b)

   Describe two precautions the student should take to obtain accurate results, giving a reason for each.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A materials scientist is selecting materials for electrical products. She compares copper (resistivity about 1.7 × 10⁻⁸ Ω m), nichrome alloy (about 1.1 × 10⁻⁶ Ω m), pure silicon (about 10³ Ω m) and glass (about 10¹² Ω m), all at room temperature.

   (a)

   Explain, using I = nqvA, why the resistivities of copper, silicon and glass differ so greatly.

   [6 marks]

   (b)

   A 1.0 kW heating element is to be made for the 230 V mains supply from wire of diameter 0.50 mm. Evaluate whether copper or nichrome is the more suitable material for the wire.

   [6 marks]

   Total for question 4: 12 marks

End of questions