Potential dividers

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 potential divider circuit is shown below.

The battery has electromotive force (e.m.f.) 9.0 V and negligible internal resistance. At room temperature the potential difference (p.d.) across the thermistor is 4.5 V. The temperature of the thermistor is increased and its resistance decreases by 20% from its previous value.

What is the p.d. across the thermistor now?

A 3.6 V

B 4.0 V

C 5.0 V

D 5.4 V

Your answer

A circuit with a thermistor is shown below.

The resistance of the resistor is R and the resistance of the thermistor is 2.5 R. The potential difference (p.d.) across the thermistor is 5.0 V.

What is the total p.d. across both components?

A 2.0 V

B 7.0 V

C 12.5 V

D 17.5 V

Your answer

A light-emitting diode (LED) emits red light when it is positively biased and has a potential difference (p.d.) greater than about 1.8 V.

The energy of a photon of red light is about 1.8 eV.

Calculate the wavelength of this red light.

The LED is connected into a circuit, as shown below.

The battery has electromotive force (e.m.f.) 4.5 V and negligible internal resistance. The resistor R has resistance 150 . Assume the p.d. across the LED is 1.8 V.

The diagram below shows a circuit designed by a student.

The LED is very close to, and facing the light dependent resistor (LDR). The circuit is taken into a dark room.

The student thought that the LED would switch on. Instead, the LED was found to repeatedly switch on and off.

Explain this behaviour of the LED in this potential divider circuit.

Suggest a possible refinement so that the LED switches on permanently when taken into the dark room.

A potential divider circuit is shown below.

The resistance of the variable resistor is R. The potential difference across the variable resistor is V.

Which graph shows the correct variation with R of V ?

Your answer

17* A metal circular plate is rotated at a constant frequency by an electric motor. The plate has a small hole close to its rim. Fig. 17.1 shows an arrangement used by a student to determine the frequency of the rotating

A light-dependent resistor (LDR) and a fixed resistor of resistance 1.2 k are connected in series to a battery. The battery has e.m.f. 4.5 V and has negligible internal resistance. The potential difference V across the resistor is monitored using a data-logger.

Fig. 17.2 shows the variation of V with time t.

Use your knowledge and understanding of potential divider circuits to explain the shape of the graph shown in Fig. 17.2. Include in your answer the maximum and minimum values of the resistance of the LDR. Describe how the student can determine the frequency of the rotating plate.

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