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 23 gives some information about series and parallel circuits.

Describe how a student can use ammeters and voltmeters to investigate the information given in Figure 23.

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 37.

Figure 20 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 21.

Figure 21

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

On Figure 21, 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 22 is a table of their results.

Using data from the table in Figure 22, predict the current from the power supply when there are 4 resistors in the circuit.

current =_........

Using data from the table in Figure 22, calculate the resistance of only 1 resistor.

resistance =_........

Using data from the table in Figure 22, 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 =_........

Figure 4 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 5.

Figure 5

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

On Figure 5, 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 6 is a table of their results.

Using data from the table in Figure 6, predict the current from the power supply when there are 4 resistors in the circuit.

current =_........

Using data from the table in Figure 6, calculate the resistance of only 1 resistor.

resistance =_........

Using data from the table in Figure 6, 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 19.

Complete the circuit diagram needed for this investigation.

Figure 19

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 20.

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 20.

Use data from the graph in Figure 20 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

Figure 20 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 20 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 21 shows a graph of the results.

Draw a straight line of best fit on Figure 21.

Use Figure 21 to estimate the resistance of a 100 cm length of the iron wire.

The variable resistor shown in Figure 20 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

Figure 3 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 3 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 4 shows a graph of the results.

Draw a straight line of best fit on Figure 4.

Use Figure 4 to estimate the resistance of a 100 cm length of the iron wire.

The variable resistor shown in Figure 3 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

An electric car is travelling at a speed of 16.0 m/s.

The total mass of the car is 1200 kg.

Calculate the kinetic energy, in kJ, of the car.

kinetic energy =_........

On a journey, the car transfers energy from the battery at an average rate of 17.5 kW.

The battery in the car transfers a total of 126 MJ of energy before it becomes discharged.

Calculate the time taken for the battery to become discharged on this journey.

Give your answer in hours.

time taken =_........ hours

Figure 20 shows an electrical device connected to the wheels of an electric car.

dynamo when the car decelerates.

Explain how using the device can help to increase the time that the car can be driven before the battery becomes discharged.

The battery can be recharged at a charging point.

The charging point provides an average current of 15.0 A to the battery, at a potential difference (voltage) of 400 V.

It is claimed that 126 MJ of energy can be transferred to the battery in less than 6 hours.

Comment on this claim.

Use this equation to support your answer

Calculate the total charge that moves into the battery while it is being recharged.

Use the equation

Figure 19 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

Calculate the power supplied to the lamp.

Another identical lamp is added to the circuit, as shown in Figure 20.

The power supply provides the same potential difference as it provided in the circuit in Figure 19.

State and explain the difference between the brightness of the lamp in Figure 19 and the brightness of a lamp in Figure 20.

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 3 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

Calculate the power supplied to the lamp.

Another identical lamp is added to the circuit, as shown in Figure 4.

The power supply provides the same potential difference as it provided in the circuit in Figure 3.

State and explain the difference between the brightness of the lamp in Figure 3 and the brightness of a lamp in Figure 4.

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

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.

Figure 17 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 18 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 18.

Use the values of the voltage and current at point P and at point Q on the graph in Figure 18 to complete the table in Figure 19.

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

Use the equation

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

Figure 4 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 4.

Use the values of the voltage and current at point P and at point Q on the graph in Figure 4 to complete the table in Figure 5.

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

Use the equation

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

A student investigates moments of forces.

Figure 14 shows the apparatus used.

The pivot is under the centre of the rod.

A magnet is fixed to one end of the rod.

A piece of modelling clay is fixed to the other end of the rod.

The system is in equilibrium.

State the relationship between the moment of the weight of the magnet and the moment of the weight of the piece of modelling clay about the pivot.

The student fixes a coil to the bench under the magnet as shown in Figure 15.

The coil of wire is connected to a d.c. power supply so that there is a current in the coil.

To bring the system back into equilibrium, the student hangs a 0.050 N weight on the rod, 8.4 cm away from the pivot, as shown in Figure 15.

Calculate the size of the force between the magnet and the coil.

Describe how the student could develop the investigation to determine if the size of the force between the magnet and the coil is directly proportional to the size of the current in the coil.

The student reverses the direction of the current in the coil. Describe how the student can bring the system back into equilibrium without making any changes to the magnet.

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 17 shows the car battery and the device that is being tested.

Draw on Figure 17 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.

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.

The technician connects four devices to the car battery.

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

Figure 18 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.

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 15 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.

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.

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

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

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

Figure 19 shows a circuit diagram with one resistor, R.

Add to Figure 19:

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 20 shows the results of the student’s investigation.

State the resistance of a single resistor.

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

Use information from Figure 20 to support your answer.

A different circuit is then set up with two resistors as shown in Figure 21.

Calculate the potential difference across the 15 Ω resistor.

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

Use the equation

power produced_........

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 17.

One value of resistance is missing from the table in Figure 17.

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 17 in your answer.

*(c) Figure 18 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 5.

One value of resistance is missing from the table in Figure 5.

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 5 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 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.

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

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

Explain why the resistor becomes warm.

Figure 16 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.