Resistivity

Thermistors are circuit components whose resistance varies with temperature.

There are two major types; negative temperature coefficient (NTC) thermistors, whose resistance decreases with increasing temperature and positive temperature coefficient (PTC) thermistors, whose resistance increases with increasing temperature.

A student is investigating how the resistance of a thermistor varies with temperature by measuring current and voltage. The thermistor is placed in a water bath and the temperature of the water measured using a thermometer.

The diagram below shows how the student set up the experiment (water bath not shown). The circuit has been set up incorrectly.

Describe how the student should change the circuit.

The circuit was corrected and then used to collect data.

The table shows data collected from the investigation.

Temperature / C	Current / mA	Voltage / V
30	0.75	3.00
40	1.10	3.00
50	1.51	3.00
60	2.10	3.00
70	2.80	3.00
80	3.66	3.00
90	4.76	3.00

The axes below show a plot of current against temperature. The first four points from the table have been plotted. Plot the remaining points.

Draw a suitable line of best fit through the data points.

Describe, using the graph and calculations using data from the table, how the resistance of the thermistor varies for increasing temperature. Hence determine whether the thermistor the student used was an NTC or a PTC thermistor.

The thermistor is used in a temperature‑sensing circuit for a heating system to warm milk for a baby.

The student considers two possible designs for the circuit which are shown below.

In each circuit, the voltage V_out across the thermistor is connected to the heating system for warming the milk.

Discuss which circuit may be suitable for the heating system by considering the response of the circuit to changes in temperature.

A student uses the circuit below to investigate the resistivity of a wire.

The cell has e.m.f. and internal resistance r. The wire has resistivity and diameter d.

The student takes five measurements of the diameter of the wire, which are shown in the table below.

Suggest how the student made these measurements.

The student calculates the value of the diameter as d = 0.455 ± 0.005 mm.

Explain how the student calculated the value of the diameter, and its uncertainty, from the data in the table above.

The student varies the length L of the wire in the circuit and records the current I using the ammeter.

The student plots a graph of against L. The data points, error bars, line of best fit and a line of worst fit are shown in the graph below.

The cell has e.m.f. = 1.45 ± 0.05 V

The wire has diameter d = 0.455 ± 0.005 mm

1 Calculate the gradient of the best fit line and use this to determine a value for the resistivity of the wire.

You are not required to determine an uncertainty.

2 Determine a value for the internal resistance r of the cell and its absolute uncertainty.

r =........ ±........

Compare the e.m.f. of the battery and the potential difference (p.d.) across the variable resistor in terms of energy transfers or changes.

State which physical quantity of the variable resistor is changed to alter its resistance.

A student connects up the circuit above to determine r.

The student varies R and measures the current I. The student plots a graph of against R.

1 Use the graph to determine the power dissipated in the variable resistor when

2 The e.m.f. E of the battery is 5.0 V.

Determine r from the intercept of the line with the vertical axis.

The circuit diagram of an electrical circuit is shown below.

The positive terminals of the batteries are connected together. One battery has electromotive force (e.m.f.) 4.5 V and internal resistance 0.80 . The other battery has e.m.f. 2.4 V and internal resistance 0.50 . R is a coil of insulated wire of resistance 1.2 at room temperature.

The switch S is closed.

On the diagram, draw an arrow to show the direction of the conventional current.

Calculate the current I shown by the ammeter.

The current measured by the ammeter is smaller than that calculated in (ii). This is because the temperature of R increased due to heating by the current.

Without any changes to the circuit itself, state and explain what practically can be done to make the measured current the same as the calculated current..

The diagram below shows the arrangement of the 3 protons inside the nucleus of lithium-6

The separation between each proton is about 1.0 × 10⁻¹⁵ m.

Calculate the magnitude of the repulsive electric force F experienced by the proton P

Explain how protons stay within the nucleus of lithium-6.

A spherical metal dome shown below is charged to a potential of −12 kV.

The dome is supported by a cylindrical plastic rod. The radius of the dome is 0.19 m.

Show that the magnitude of the total charge Q on the dome is 2.5 × 10⁻⁷ C.

The dome discharges slowly through the plastic rod. It takes 78 hours for the dome to completely discharge.

1 Show that the mean current I in the plastic rod is about 9 × 10⁻¹³ A.

2 The average potential difference across the plastic rod during discharge is 6000 V. The rod has cross-sectional area 1.1 × 10⁻⁴ m² and length 0.38 m.

Calculate the resistivity of the plastic.

=........ m

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

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

gradient =........ A^–1 m^–1

Show that the gradient of the line is , where 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.

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 .

=........ m

Derive the S.I. base units for resistance.

Fig. 16.1 shows the I-V characteristics of two electrical components L and R.

The component L is a filament lamp and the component R is a resistor.

Show that the resistance of R is 40 .

This question is about a resistance wire made of nichrome.

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

Show that the resistance of the nichrome wire wound on the ceramic cylinder is 53

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

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

A circuit is shown below.

The battery has negligible internal resistance. The temperature of the NTC thermistor is decreased.

Which of the following statements is/are correct?

1 The current at X increases. 2 The current at Y remains the same. 3 The potential difference across the thermistor increases.

A 1, 2 and 3

B Only 2 and 3

C Only 3

D Only 2

Your answer

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

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

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
	4.7 10−7 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.

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.

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.