Current, resistance and potential difference

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.

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

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.