Current, resistance and potential difference

Figure 1 shows two lamps in series in a circuit.

The resistance of each lamp is 12 Ω.

Calculate the total resistance of the lamps in the circuit.

total resistance of lamps =_........

The current in a lamp in Figure 1 is 0.50 A.

The resistance of the lamp is 12 Ω.

Calculate the voltage across this lamp.

Use the equation

V = I × R

The voltage across a different lamp is 4.5 V.

The current in this lamp is 0.40 A.

Calculate the energy transferred to the lamp in 5 minutes.

Use the equation

E = I × V × t

energy transferred =_........

Figure 2 shows a circuit with a switch, two ammeters and two resistors in series with a cell.

Which of these statements is true for the circuit in Figure 2?

The resistance of the circuit is increased by adding one resistor to the circuit.

State how increasing the resistance changes the current in the circuit.

A student connects a resistor across the terminals of a 9 V battery.

There is a current of 6 mA in the resistor.

Calculate the resistance of the resistor.

Describe how an additional component could be used to vary the current in the resistor.

A voltmeter has four different scales.

Which one of these scales would be most suitable to measure a voltage of 0.85 V?

*(c) The table in Figure 14 gives some information about series and parallel circuits.

Describe how a student can use ammeters and voltmeters to investigate the information given in Figure 14.

Your answer should include

• circuit diagrams showing how the currents and voltages can be measured

• a comparison of the results that would be expected

Space for circuit diagrams

Answer lines for this question are on page 27.

Some students investigate resistors in parallel.

The students set up a circuit containing four identical resistors.

The circuit used is shown in Figure 11.

Figure 11

The students measure the current from the power supply and the voltage (p.d.) across the resistors.

On Figure 11, draw a voltmeter connected to measure the voltage (p.d.) across the resistors.

T he students remove one resistor and measure the current and voltage again with only 3 resistors in the circuit.

T hey repeat the measurements of current and voltage with only 2 resistors in the circuit and then with only 1 resistor in the circuit.

Figure 12 is a table of their results.

Using data from the table in Figure 12, predict the current from the power supply when there are 4 resistors in the circuit.

current =_........ mA

Using data from the table in Figure 12, calculate the resistance of only 1 resistor.

resistance =_........ Ω

Using data from the table in Figure 12, explain what happens to the total resistance of the circuit as the number of resistors in parallel decreases.

An electric fire is connected to a 230 V mains supply.

A current of 9.0 A is supplied to the fire.

Calculate the power supplied to the fire.

Use the equation

power = current voltage

power =_........ W

Figure 1 is a circuit diagram.

The current at P is

Some students investigate resistors in parallel.

The students set up a circuit containing four identical resistors.

The circuit used is shown in Figure 2.

Figure 2

The students measure the current from the power supply and the voltage (p.d.) across the resistors.

On Figure 2, draw a voltmeter connected to measure the voltage (p.d.) across the resistors.

T he students remove one resistor and measure the current and voltage again with only 3 resistors in the circuit.

T hey repeat the measurements of current and voltage with only 2 resistors in the circuit and then with only 1 resistor in the circuit.

Figure 3 is a table of their results.

Using data from the table in Figure 3, predict the current from the power supply when there are 4 resistors in the circuit.

current =_........ mA

Using data from the table in Figure 3, calculate the resistance of only 1 resistor.

resistance =_........ Ω

Using data from the table in Figure 3, explain what happens to the total resistance of the circuit as the number of resistors in parallel decreases.

A student investigates how current varies with potential difference across a filament lamp.

The student uses a power supply, a variable resistor, the filament lamp and two meters.

Part of the circuit diagram is shown in Figure 10.

Complete the circuit diagram needed for this investigation.

Figure 10

Another student repeats the investigation in part (a) using a data logger.

The data logger records observations using sensors instead of meters. The sensors are connected to a computer to collect and display the observations.

The data logger collects 555 pairs of data in 2 minutes.

The results are shown in Figure 11.

Suggest one advantage of using a data logger instead of meters in this investigation.

Describe how current varies with potential difference in the graph in Figure 11.

Use data from the graph in Figure 11 to show how the resistance changes with potential difference for the filament lamp.

Which of these equations is correct?

The unit of work is the joule.

Starting with the meaning of work, we may obtain an equivalent unit of work as Nm.

Using work F d

unit of work unit of force unit of distance Nm

The unit of potential difference is the volt.

Explain how, starting with the meaning of potential difference, we may obtain an equivalent unit of potential difference.

The voltage (potential difference) across a length of wire is 1.5 V.

A charge of 0.042 C flows through the wire.

Calculate the energy transferred.

Use the equation

E =_........ J

Figure 12 shows some of the apparatus that students use to determine the resistance of a piece of iron wire.

Add connecting wires, a voltmeter and an ammeter to complete the circuit in Figure 12 so that the students can determine the resistance of the piece of iron wire.

The students extend the investigation to determine how the resistance of the iron wire changes with its length.

Give the name of one additional piece of apparatus the students would need.

Figure 13 shows a graph of the results.

Draw a straight line of best fit on Figure 13.

Use Figure 13 to estimate the resistance of a 100 cm length of the iron wire.

resistance =_........ Ω

The variable resistor shown in Figure 12 is used to prevent the iron wire from becoming too hot.

Explain how the variable resistor is used to prevent the iron wire from becoming too hot.

The potential difference (voltage) across another piece of wire is 1.56 V.

The current in the wire is 0.45 A.

Calculate the resistance of this piece of wire.

Use the equation

resistance =_........ Ω

Figure 1 shows some of the apparatus that students use to determine the resistance of a piece of iron wire.

Add connecting wires, a voltmeter and an ammeter to complete the circuit in Figure 1 so that the students can determine the resistance of the piece of iron wire.

The students extend the investigation to determine how the resistance of the iron wire changes with its length.

Give the name of one additional piece of apparatus the students would need.

Figure 2 shows a graph of the results.

Draw a straight line of best fit on Figure 2.

Use Figure 2 to estimate the resistance of a 100 cm length of the iron wire.

resistance =_........ Ω

The variable resistor shown in Figure 1 is used to prevent the iron wire from becoming too hot.

Explain how the variable resistor is used to prevent the iron wire from becoming too hot.

The potential difference (voltage) across another piece of wire is 1.56 V.

The current in the wire is 0.45 A.

Calculate the resistance of this piece of wire.

Use the equation

resistance =_........ Ω

Figure 9 shows a lamp connected to a d.c. power supply.

The power supply provides a potential difference (voltage) of 4.5 V.

The current in the lamp is 0.30 A.

Calculate the resistance of the lamp.

Use the equation

resistance =_........ Ω

Calculate the power supplied to the lamp.

power =_........ W

Another identical lamp is added to the circuit, as shown in Figure 10.

The power supply provides the same potential difference as it provided in the circuit in Figure 9.

State and explain the difference between the brightness of the lamp in Figure 9 and the brightness of a lamp in Figure 10.

A student is given a low voltage power supply and 1 m of resistance wire.

The student uses these and other pieces of equipment to measure the resistance of just 50 cm of the resistance wire.

Draw a diagram of the circuit that the student should use.

Your circuit diagram should identify the pieces of equipment that the student uses.

Describe the difference between direct current (d.c.) and alternating current (a.c.) in electrical circuits.

Figure 1 shows a lamp connected to a d.c. power supply.

The power supply provides a potential difference (voltage) of 4.5 V.

The current in the lamp is 0.30 A.

Calculate the resistance of the lamp.

Use the equation

resistance =_........ Ω

Calculate the power supplied to the lamp.

power =_........ W

Another identical lamp is added to the circuit, as shown in Figure 2.

The power supply provides the same potential difference as it provided in the circuit in Figure 1.

State and explain the difference between the brightness of the lamp in Figure 1 and the brightness of a lamp in Figure 2.

A student is given a low voltage power supply and 1 m of resistance wire.

The student uses these and other pieces of equipment to measure the resistance of just 50 cm of the resistance wire.

Draw a diagram of the circuit that the student should use.

Your circuit diagram should identify the pieces of equipment that the student uses.

Figure 1 shows an electrical circuit.

Draw a circuit diagram of the electrical circuit in Figure 1 in the space below.

When the current in a lamp is 0.15 A, the resistance of the lamp is 40 Ω.

Calculate the voltage across the lamp.

Use the equation

V = I × R

voltage =_........ V

Figure 2 shows an ammeter that can read up to 5 A.

State the value of the current shown on the ammeter in Figure 2.

current =_........ A

Figure 10 shows two different types of the same circuit component.

What is the name of this circuit component?

Which row in the table describes the way that ammeters and voltmeters should be connected with a component in a circuit?

Figure 11 shows the results from an experiment where the potential difference (voltage) across a filament lamp was varied.

The current and voltage were measured.

Describe the relationship between the current and the voltage as shown in the graph in Figure 11.

Use the values of the voltage and current at point P and at point Q on the graph in Figure 11 to complete the table in Figure 12.

Calculate the resistance of the filament lamp when the voltage is 4.5 V and the current is 51 mA.

Use the equation

resistance =_........ Ω

Explain why the resistance of the filament lamp changes as the voltage across it increases.

Figure 1 shows the results from an experiment where the potential difference (voltage) across a filament lamp was varied.

The current and voltage were measured.

Describe the relationship between the current and the voltage as shown in the graph in Figure 1.

Use the values of the voltage and current at point P and at point Q on the graph in Figure 1 to complete the table in Figure 2.

Calculate the resistance of the filament lamp when the voltage is 4.5 V and the current is 51 mA.

Use the equation

resistance =_........ Ω

Explain why the resistance of the filament lamp changes as the voltage across it increases.

A technician investigates different electrical devices that are used in a car.

The technician connects a device to the 12 V car battery.

The technician measures the current in the circuit and the potential difference (voltage) across the device.

Figure 8 shows the car battery and the device that is being tested.

Draw on Figure 8 to show how the circuit should be completed so that the current in the circuit and voltage across the device can be measured.

The technician tests a headlamp.

The current in the headlamp is 4.8 A when connected to the 12 V battery.

Calculate the power supplied to the headlamp.

power =_........ W

The technician tests an interior light.

The current in the interior light is 600 mA when connected to the 12 V battery.

Calculate the energy transferred to the interior light in 7 minutes.

Use an equation selected from the list of equations at the end of the paper.

energy transferred =_........ J

The technician connects four devices to the car battery.

Each device is connected to its own switch and its own fuse.

Figure 9 shows how the four devices, fuses and switches are connected.

The current in each device is shown next to the device.

Calculate the current in the wires to the battery when all the devices are switched on.

current =_........ A

State how the overall resistance of the circuit changes when any one of the devices is switched off.

There is a current of 2.3 A in the radio when the radio is working correctly.

Which of these should the technician choose to protect the radio circuit?

Explain why the wires to the battery in a car are thicker than the wires that connect each device to its switch and its fuse.

A student investigates resistors connected in series in an electrical circuit.

The student has

The student does not know the value of the resistor marked X.

The student decides to measure the potential difference (voltage) across resistor X.

Figure 8 shows the circuit that the student connected.

The circuit is connected incorrectly.

Describe how the student should correct the mistake.

The student corrects the mistake.

The voltage across resistor X is 2.1 V.

The circuit is connected to a 3 V battery.

State the value of the voltage across the 22 Ω resistor.

voltage across 22Ω resistor =_........ V

The current in resistor X is 0.041 A.

The voltage across resistor X is 2.1 V.

Show that the resistance of resistor X must be about 50 ohms.

Use the equation

Calculate the power in resistor X when the voltage across X is 2.1 V and the current in resistor X is 0.041 A.

power =_........ W

Calculate the overall resistance of the 22 ohm resistor and resistor X.

overall resistance =_........ Ω

The current in the circuit is 0.041 A.

The voltage across the battery is 3.0 V.

Calculate the energy transferred in 2 minutes.

Use the equation

energy =_........ J

A student investigates resistors connected in parallel using a number of resistors. Each resistor has the same resistance.

Figure 10 shows a circuit diagram with one resistor, R.

Add to Figure 10:

a voltmeter to find the potential difference across resistor R

another resistor in parallel with resistor R.

State the measurements that the student must take to find the overall resistance of the resistors in parallel.

The student investigates how the overall resistance of the circuit changes when additional resistors are added in parallel to R.

Each resistor has the same resistance.

Figure 11 shows the results of the student’s investigation.

State the resistance of a single resistor.

resistance =_........ Ω

Comment on the relationship between the overall resistance of the circuit and the number of resistors in parallel.

Use information from Figure 11 to support your answer.

A different circuit is then set up with two resistors as shown in Figure 12.

Calculate the potential difference across the 15 Ω resistor.

potential difference =_........ V

Calculate the total power dissipated when there is a current of 0.20 A in the two resistors.

Use the equation

power produced_........ W

Which of these symbols is used to represent a thermistor in an electrical circuit?

A student investigates how the current in a lamp changes with the potential difference across the lamp.

The student uses the results to calculate the resistance of the lamp.

The results are shown in the table in Figure 9.

One value of resistance is missing from the table in Figure 9.

Calculate the value of resistance that is missing from the table.

missing resistance =_........ Ω

The student writes this conclusion:

‘The resistance of the lamp is directly proportional to the potential difference.’

Comment on the student’s conclusion. Use information from Figure 9 in your answer.

*(c) Figure 10 shows a battery connected to a filament lamp.

Explain, in terms of the movement of charged particles, how energy is transferred from the battery, through the lamp, to the surroundings.

Which of these symbols is used to represent a thermistor in an electrical circuit?

A student investigates how the current in a lamp changes with the potential difference across the lamp.

The student uses the results to calculate the resistance of the lamp.

The results are shown in the table in Figure 2.

One value of resistance is missing from the table in Figure 2.

Calculate the value of resistance that is missing from the table.

missing resistance =_........ Ω

The student writes this conclusion:

‘The resistance of the lamp is directly proportional to the potential difference.’

Comment on the student’s conclusion. Use information from Figure 2 in your answer.

The student used a power supply that had fixed output voltage settings. Each of these outputs was a whole number of volts.

Describe how the student could add a component to the circuit that would provide a continuously variable voltage across the lamp.

A student has a bar magnet, a piece of iron the same size as the magnet, and some paper clips.

Describe how the student could use these items to demonstrate temporary induced magnetism.

A student sets up the apparatus shown in Figure 4.

When the current in the solenoid is switched on, the solenoid attracts the iron nail.

Describe how the student could use this apparatus to investigate how the size of the current in the solenoid affects the force of attraction between the solenoid and the iron nail.

The spring constant of a different spring is 24 N/m.

The spring is extended from its unstretched length by 12 cm.

Calculate the energy transferred in extending the spring by 12 cm.

Use an equation selected from the list of equations at the end of this paper.

energy transferred =_........ J

A resistor is connected to a power supply.

The potential difference across the resistor is 6.0 V.

Which of these corresponds to a potential difference of 6.0 V?

The resistor remains connected for a period of time.

The current in the resistor is 200 mA.

A total charge of 42 C flows through the resistor.

Calculate, in minutes, the time taken for this amount of charge to flow through the resistor.

time =_........ minutes

Calculate the total energy transferred by the 6.0 V power supply when a charge of 42 C flows through the resistor.

energy =_........ J

The resistor becomes warm while there is a current in it.

Explain why the resistor becomes warm.

Figure 7 shows a cardboard tube with a wire coming out from each end.

There are two 10 ohm resistors inside the cardboard tube.

A potential difference of 6.0 V is connected between P and Q.

There is a current of 1.2 A in the wires.

Deduce how the resistors have been arranged inside the cardboard tube.

Figure 8 shows identical filament lamps connected together to a 12 V power supply.

Calculate the potential difference across each lamp.

potential difference =_........ V

The power output of each lamp is 0.75 W

Calculate the resistance of each lamp.

resistance =_........ Ω

*(b) Explain, with the aid of a circuit diagram, the method a student could use to investigate how the resistance of a single lamp changes with the potential difference across the lamp.