Resistivity and conductionEdexcel International A Level Physics: Subtopic test

1. 1
   A technician has a 2.0 m length of constantan wire of diameter 0.50 mm. The resistivity of constantan is 4.9 × 10⁻⁷ Ω m.

   (a)

   What is the resistance of the wire?

   [1 mark]

   • A1.2 Ω
   • B5.0 Ω
   • C3.9 Ω
   • D20 Ω

   (b)

   A second wire is made of the same material and has the same length, but its diameter is twice as large. What is its resistance?

   [1 mark]

   • A2.5 Ω
   • B10 Ω
   • C1.25 Ω
   • D20 Ω

   (c)

   The technician needs a resistance of 12 Ω from the 0.50 mm diameter constantan wire. Calculate the length of wire required.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A copper wire of cross-sectional area 1.5 mm² carries a current of 3.0 A. It is connected in series with a strip of doped silicon, a semiconductor, of the same cross-sectional area, in which the number density of conduction electrons is much smaller than in copper. For copper, the number density of conduction electrons is 8.5 × 10²⁸ m⁻³. The elementary charge is 1.60 × 10⁻¹⁹ C.

   (a)

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

   [1 mark]

   • A1.5 × 10⁻⁴ m s⁻¹
   • B1.5 × 10⁻¹⁰ m s⁻¹
   • C1.5 × 10⁻⁷ m s⁻¹
   • D6.8 × 10³ m s⁻¹

   (b)

   How does the mean drift velocity of the conduction electrons in the silicon compare with that in the copper?

   [1 mark]

   • ASmaller, because silicon has a higher resistivity
   • BThe same, because the current and area are the same
   • CZero, because a semiconductor does not conduct
   • DMuch greater, because there are far fewer charge carriers to carry the same current

   (c)

   Use I = nqvA to explain why an insulator has a much greater resistivity than copper.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student determines the resistivity of a nichrome wire as part of a core practical. She measures the diameter of the wire at several points and finds a mean of 0.32 mm. She then measures the resistance R of different lengths l of the wire and plots a graph of R against l. The graph is a straight line through the origin with gradient 14.0 Ω m⁻¹.

   (a)

   Describe how the student should measure the diameter of the wire accurately.

   [3 marks]

   (b)

   Use the graph gradient and the mean diameter to determine the resistivity of nichrome.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A uniform resistance wire of length 1.00 m and resistance 5.0 Ω is connected across a 2.0 V cell of negligible internal resistance. A sliding contact connected to a voltmeter of very high resistance measures the potential difference between one end of the wire and the contact.

   (a)

   Explain how the potential at the contact varies with its distance from one end of the wire, calculating the current in the wire and the potential difference at a distance of 0.35 m.

   [6 marks]

   (b)

   The wire is replaced by one of the same material and length but with half the diameter. Evaluate, with calculations, whether this is a better wire for the investigation. Consider the current, the p.d. at 0.35 m, the power dissipated and the drift velocity of the electrons.

   [6 marks]

   Total for question 4: 12 marks

End of questions