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Resistance & Resistivity (OCR A Level Physics)

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Resistance & Resistivity

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Resistance & Resistivity

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1a1 mark

State one S.I. base quantity other than length, mass and time.

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1b8 marks

Fig. 17 shows two resistors X and Y connected in series.

q17b-paper-2-june-2017-ocr-a-level-physics

Fig. 17

The resistors are wires. Both wires have the same length L and diameter d. The material of X has resistivity ρ and the material of Y has resistivity 2ρ.

i) Show that the total resistance R of the wires is given by the equation

R equals fraction numerator 12 rho L over denominator πd squared end fraction

[2]

ii) A student uses the equation in (i) to determine R.

The table below shows the data recorded by the student in her lab book.

Quantity

  Value

ρ

 4.7 × 10−7 Ω m

L

 9.5 ± 0.1 cm

d

 0.270 ± 0.003 mm

 

1. Name the likely instruments used by the student to measure L and d.

L: ........................................................................................

d: ........................................................................................

[1]

 2. Use the data in the table and the equation in (i) to determine R and the absolute uncertainty. Write your answer to the correct number of significant figures.

R = ...................... ± ...................... Ω [4]

3. The instrument used to measure d has a zero-error. The measured d is much larger than the actual value.

Discuss how the actual value of R compares with the value calculated above.

[1]

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2a6 marks

This question is about a resistance wire made of nichrome.

It is suggested that the resistance R of a length of nichrome wire varies with temperature θ in °C according to the equation

R = R0 (1 + kθ)

where R0 is the resistance of the wire at 0 °C and k is a constant for the wire.

Fig. 1.1 shows a diagram of the arrangement of apparatus in an experiment to test the relationship between R and θ and to determine the value of k.

q1a-paper-3-june-2018-ocr-a-level-physics

Fig. 1.1

The resistance wire is coiled and placed in a water bath.

Describe how you would carry out the experiment, analyse the data to verify the relationship between R and θ and determine a value for k.

In your description, state any precautions that you would take to improve the accuracy and precision of the measurements.

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2b7 marks

A student is investigating a 230 V, 1.0 kW heating element. The heating element is shown in Fig. 1.2.

q1b-paper-3-june-2018-ocr-a-level-physics

Fig. 1.2

A length of nichrome wire is wound in a spiral groove along 18 cm of a ceramic cylinder of diameter 1.4 cm. The distance between the centres of adjacent turns of the wire is 1.5 mm.

The numbers labelling the reels of loose wire on the laboratory shelf are the imperial standard wire gauge (swg). The student wishes to find out which reel holds the same wire as that wound on the heating element of Fig. 1.2.

The book of data gives the following information:

resistivity of nichrome at operating temperature = 1.1 × 10−6 Ω m

swg

24

26

28

30

32

diameter of wire / 10−3 m

0.56

0.46

0.38

0.32

0.27

cross-sectional area/10−6 m2

0.25

0.16

0.11

0.08

0.06

 i) Show that the resistance of the nichrome wire wound on the ceramic cylinder is 53 Ω.

[2]

ii) Show that the length of wire wound on the heating element is 5.3 m.

[2]

iii) Use the information given in (i) and (ii) to determine the swg number of the wire used as the heating element.

swg number = ............................................ [3]

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1a2 marks

State Kirchhoff’s second law and the physical quantity that is conserved according to this law.

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1b2 marks

The S.I. base units for the ohm (Ω) are kg m2 s–3A–2.

Use the equation R space equals space fraction numerator rho L over denominator A end fraction to determine the S.I. base units for resistivity rho.

base units for rho .......................................... 

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1c8 marks

Fig. 18.1 shows a circuit used by a student to determine the resistivity of the material of a wire.

q18c-paper-2-june-2019-ocr-a-level-physics

Fig. 18.1

The wire is uniform and has diameter 0.38 mm. The cell has electromotive force (e.m.f.) E and internal resistance r. The length of the wire between X and Y is L.

The student varies the length L and measures the current I in the circuit for each length.

Fig. 18.2 shows the data points plotted by the student.

q18c-2-paper-2-june-2019-ocr-a-level-physics

Fig. 18.2

i) On Fig. 18.2 draw the straight line of best fit. Determine the gradient of this line.

gradient = ............................... A–1m–1  [2]

ii) Show that the gradient of the line is fraction numerator rho over denominator A E end fraction space, where rho is the resistivity of the material of the wire, A is the area of cross-section of the wire and E is the e.m.f. of the cell.

[2]

iii) The e.m.f. E of the cell is 1.5 V. The diameter of the wire is 0.38 mm.

Use your answer to (i) and the equation given in (ii) to determine rho.

rho = .................................................. Ωm  [2]

iv) Fig. 18.3 illustrates how the student had incorrectly measured all the lengths L of the wire.

q18c-iv-paper-2-june-2019-ocr-a-level-physics

Fig. 18.3

According to the student, re-plotting the data points using the actual lengths of the wire will not affect the value of the resistivity obtained in (iii).

Explain why the student is correct.

[2]

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