Resistivity, thermistors and superconductivityAQA A-Level Physics: Subtopic test

1. 1
   A heating element is made from a nichrome wire of length 1.50 m and diameter 0.40 mm. The resistivity of nichrome at the operating temperature is 1.1 × 10⁻⁶ Ω m.

   (a)

   What is the resistance of the wire?

   [1 mark]

   • A3.3 Ω
   • B13 Ω
   • C10 Ω
   • D52 Ω

   (b)

   A second wire is made from the same material, with the same length, but with twice the diameter. How does its resistance compare with the first wire?

   [1 mark]

   • AIt is one quarter as large
   • BIt is half as large
   • CIt is twice as large
   • DIt is the same, because the resistivity is unchanged

   (c)

   The designer wants an element of resistance 20 Ω using the same wire. Calculate the length of wire required.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   An incubator uses a negative temperature coefficient (ntc) thermistor as its temperature sensor. The resistance of the thermistor is 4.7 kΩ at 20 °C and 1.2 kΩ at 50 °C. A constant pd of 5.0 V is applied across the thermistor.

   (a)

   What is the ratio of the current in the thermistor at 50 °C to the current at 20 °C?

   [1 mark]

   • A0.26
   • B1.0
   • C2.5
   • D3.9

   (b)

   Which statement best explains why the resistance of an ntc thermistor decreases as its temperature rises?

   [1 mark]

   • AThe lattice ions vibrate with larger amplitude and collide more often with the electrons
   • BThe thermistor contracts in length, which reduces its resistance
   • CMore charge carriers are released as the temperature rises, so the number of charge carriers per unit volume increases
   • DThe pd across the thermistor increases

   (c)

   The designer considers using a metal wire instead of the thermistor as the sensor. State how the resistance of a metal wire changes as its temperature rises, and explain why.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A power company is testing a 1.0 km cable made from a superconducting material with a critical temperature of 92 K. The cable is cooled by liquid nitrogen at 77 K and carries a constant current of 2.0 × 10³ A. For comparison, a copper cable of the same length would have a cross-sectional area of 5.0 × 10⁻⁴ m² and a resistivity of 1.7 × 10⁻⁸ Ω m.

   (a)

   State what is meant by the critical temperature of a superconductor, and explain why cooling the cable with liquid nitrogen reduces the energy lost during transmission.

   [3 marks]

   (b)

   Calculate the energy that would be transferred to thermal energy in the copper cable in one second, and state the corresponding energy for the superconducting cable.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A student determines the resistivity of a constantan wire. She measures the diameter of the wire with a micrometer at several places and obtains a mean of 0.28 mm with an uncertainty of ± 0.01 mm. She varies the length L of wire in the circuit from 0.200 m to 1.000 m, and for each length she measures the pd across the wire with a voltmeter and the current with an ammeter to calculate the resistance R. A graph of R against L is a straight line through the origin with a gradient of 7.9 Ω m⁻¹, which has a percentage uncertainty of 2.0%.

   (a)

   Use the graph to determine the resistivity of constantan, and calculate the percentage uncertainty in your value.

   [6 marks]

   (b)

   Describe how the student should carry out the experiment to obtain reliable values of the resistivity, including how she should reduce the error caused by the heating effect of the current.

   [6 marks]

   Total for question 4: 12 marks

End of questions