Potential dividers

A student is investigating circuits that include a filament bulb. The filament bulb is labelled ‘1.5 V, 0.50 W’.

Show that the resistance of the filament bulb when operating normally is about 5 Ω.

*(b) The student wishes to control the brightness of the filament bulb using a potentiometer. The student connects the circuit shown. The total resistance of the potentiometer is very much larger than the resistance of the filament bulb.

Explain how the brightness of the filament bulb changes as the potentiometer slider is moved from A to B.

The student connects the filament bulb in the circuit shown below. The capacitor is initially uncharged and has a capacitance of 1.2 F.

The resistance of the filament bulb is 5 Ω.

Explain how the brightness of the filament bulb will vary as the switch is closed.

A student connected a voltmeter to a potential divider, as shown in the circuit diagram.

The potential divider was adjusted by moving sliding contact S from position X to position Y.

Explain how the voltmeter reading V depends upon the position of S.

A filament bulb and ammeter were connected to the potential divider. The potential divider was used to vary V across the filament bulb. The ammeter gave the corresponding current I in the filament.

I varied with V, as shown in the graph below.

Explain the shape of the graph.

The temperature T of the filament varies with the potential difference V across the filament according to the expression

where a and b are constants.

Explain why a graph of logT against logV would give a straight line.

Data for T and V is shown in the table below.

Plot a graph of logT against logV on the grid opposite. Use the extra columns provided to show any processed data.

Determine a value for b using your graph.

The circuit shown provides an input to a transistor. A transistor is a type of electronic switch and in this circuit it can be assumed to have infinite resistance.

The resistance of the LDR varies with light level as shown below.

The transistor switches on when the potential difference across the input increases above 0.7 V. This should happen as the light level reaching the LDR increases above 30 lux.

Deduce whether this circuit responds as required.

Explain how the resistance of the LDR changes as the light level increases.

A potential divider circuit may contain a component known as a potentiometer. One type of potentiometer consists of a track with terminals X and Y at either end. There is a sliding contact that can move along the track connected to a terminal Z as shown.

The length of the track is 115 mm and the width is 5.0 mm.

The resistance of the track between terminal X and terminal Y is 12.0 kΩ.

Calculate the thickness t of the track.

resistivity of track material = 0.49 Ω m

The potentiometer is used to monitor the displacement of a moving tool on a machine in a production line. The tool is attached to the sliding contact. The potentiometer is connected to a resistor of resistance R and a potential difference is applied as shown. The tool moves through a maximum displacement of 60 mm from end X, producing a maximum potential difference of 5.0 V between Z and X.

Show that the potential difference between X and Y is about 10 V.

Calculate the value of R.

When the circuit is assembled, using the correctly calculated resistance value and a battery of e.m.f. 12 V, it is found that the maximum output from the potentiometer is slightly less than 5.0 V.

Explain why the maximum output is slightly less than predicted.

The tool on the machine should not travel with a speed any larger than 0.8 m s⁻¹.

The graph shows how the displacement varies with time for the downward stroke of the moving tool.

Deduce whether this speed is exceeded by the moving tool.

A student is planning to collect data to produce a current-potential difference graph for a filament lamp. Her teacher suggests two circuits that she could use.

Circuit 1 uses a potential divider and circuit 2 uses a variable resistor to vary the potential difference across the filament lamp.

*(a) Discuss the suitability of each circuit to collect the data.

The student sets up the following circuit with the filament lamp. The battery has negligible internal resistance.

The reading on the ammeter is 17.5 mA. Calculate the value of the potential difference (p.d.) across the filament lamp.

p.d. across filament lamp =_........

When a voltmeter with a resistance of 1.5 kΩ is connected as shown, the p.d. across the filament lamp decreases.

Explain why the p.d. across the filament lamp decreases.

A student carried out an experiment to calibrate a thermistor. She connected the thermistor in series with a resistor and a power supply as shown. Then she placed the thermistor in a beaker of hot water and used a thermometer to record the temperature θ of the water.

The student recorded θ and corresponding values of the reading V on the voltmeter as the water cooled.

Explain, making reference to charge carriers, why V increased as the water cooled.

Over a limited temperature range V varies with θ according to the expression

where b and V₀ are constants.

Explain why a graph of lnV against θ would give a straight line.

The student’s data is shown in the table below.

Plot a graph of lnV against θ on the grid opposite. Use the column provided to show any processed data.

Determine values for b and V₀.

A light dependent resistor (LDR) and a resistor are connected to a battery, as shown.

The intensity of light incident on the LDR increases.

Which row of the table describes the change in the resistance of the LDR and the change in the potential difference across the resistor?

A “metre bridge” is a circuit which can be used to measure an unknown resistance accurately. The metre bridge includes a metre length of nichrome wire.

Calculate the resistance of a 1.00 m length of the nichrome wire.

resistivity of nichrome = 1.12 10^–6 diameter of wire = 4.00 10^–4 m

This metre length of wire, labelled AB, is connected to a 1.50 V cell of negligible internal resistance and a switch as shown.

Explain how the potential along this wire varies with distance from A when the switch is closed.

Show that the potential difference between A and a point 75.0 cm along the wire from A is about 1.1 V.

A student set up the circuit shown and measured the current I through the filament lamp for a range of values of potential difference (p.d.) V.

The student’s data is shown in the table.

Criticise the student’s recording of the data.

The student drew a graph of how current varies with p.d. She drew a straight line on the graph and claimed that the data demonstrates that the filament lamp obeys Ohm’s law because the graph is linear.

Assess the validity of the student’s statement.

Using the circuit shown the student was unable to obtain data for p.d.s less than 2.5 V.

Draw a diagram of a circuit the student could have used to enable a full range of p.d.s from 0 to 12 V to be investigated.

A light‑dependent resistor (LDR) and resistor are connected in series with a 6V battery as shown. A voltmeter measures the potential difference across the LDR.

In daylight the voltmeter reads 3.0V.

Which reading is most likely if the circuit is now in total darkness?

A student investigates the motion of a friction‑free trolley down a ramp. On the top of the trolley there is a metal loop which makes contact with a length of thin resistance wire, AB, fixed above the ramp. The resistance wire has a uniform diameter.

The trolley accelerates down the ramp and the metal loop stays in contact with the wire along the full length of the ramp.

The student uses a protractor to measure the angle θ between the ramp and the horizontal

and records a value of 4° with an uncertainty of ±1°.

The two ends of the wire are connected to a 1.5 V cell. A data logger, set to measure potential difference, is connected to the metal loop and to the negative terminal of the cell.

Explain how the potential difference recorded by the data logger will vary as the loop moves along the length of the wire AB.

The graph shows the data obtained from the data logger.

Determine the velocity of the trolley at 1.5 s.

1.5 V represents a distance of 2.00 m.

The student calculated the velocity of the trolley at 2.0 s to be 1.5 m s^–1.

By considering the acceleration of the trolley, determine whether the student’s measurement of θ was within the uncertainty quoted.