Key Stage 4 science · Physics – Electricity

GCSE circuits: current, resistance, charge and series circuits

This GCSE physics topic turns the circuits of earlier years into measurement and calculation. Students draw circuit diagrams, measure current and potential difference to find resistance, explore how current depends on voltage for different components using graphs, calculate the charge flowing as current multiplied by time, and work out the equivalent resistance of resistors connected in series.

Current, resistance, charge and circuits, explained

Three quantities describe a circuit. Current is the rate of flow of electric charge, measured in amperes (amps), and it is measured with an ammeter connected in series, so that the current passes through it. Potential difference, often called voltage, is the energy transferred per unit of charge between two points, measured in volts, and a voltmeter is connected in parallel across the component. Resistance, measured in ohms, shows how hard it is for current to flow through a component. Students are expected to draw circuit diagrams with the correct symbols for cells, switches, lamps, resistors, meters, diodes, thermistors and light-dependent resistors.

Resistance is found by dividing the potential difference across a component by the current through it. In the standard investigation, students connect a component in series with a variable resistor and ammeter, put a voltmeter across the component, and record pairs of readings, then plot current against potential difference. For a fixed resistor at constant temperature, the graph is a straight line through the origin, so current is directly proportional to voltage. This is Ohm’s law, and components that obey it are called ohmic.

Not every component is ohmic. As current flows through a filament lamp, the filament heats up and its resistance increases, so the graph curves and flattens. A diode lets current pass in one direction only. A thermistor’s resistance falls as it gets warmer, and a light-dependent resistor’s falls as the light gets brighter, which is why they are used in temperature and light sensors. Students must be able to describe these graphs and explain the shape.

Charge is measured in coulombs, and the charge that flows is the current multiplied by the time. A current of 2 amperes for 10 seconds moves 20 coulombs. In a series circuit, the components are connected in a single loop. The current is the same everywhere in the loop, the potential difference of the supply is shared between the components, and the total resistance is the sum of the individual resistances, because the current has to pass through each one in turn. Parallel circuits, where the current splits, follow different rules and are usually met in the same unit, so ask the school how far the course goes.

Words your child will hear

Current: The rate of flow of electric charge. Measured in amperes (A) with an ammeter in series.
Potential difference: The energy transferred per unit of charge between two points. Measured in volts (V), with a voltmeter in parallel.
Resistance: How much a component opposes current. Potential difference ÷ current, in ohms (Ω).
Charge: The quantity that flows in a circuit. Measured in coulombs (C): current × time.
Series circuit: A circuit with a single loop, so the same current passes through every component.
Ohmic conductor: A component, such as a fixed resistor at constant temperature, whose current is proportional to its potential difference.
Variable resistor: A resistor whose resistance can be changed, used to alter the current.

What the National Curriculum says

The programme of study for Key Stage 4 says:

Students should be taught about measuring resistance using p.d. and current measurements
Students should be taught about exploring current, resistance and voltage relationships for different circuit elements, including their graphical representations
Students should be taught about the quantity of charge flowing as the product of current and time
Students should be taught about drawing circuit diagrams; exploring equivalent resistance for resistors in series

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

A student measures a resistor and finds that the voltmeter reads 4.5 V when the ammeter reads 0.15 A. She then connects it in series with a second resistor of 60 Ω and a 9.0 V battery. Find the first resistor’s resistance, the total resistance, the current, the potential difference across each resistor and the charge that flows in 2 minutes.

Resistance = potential difference ÷ current, for the first resistor.
```
R = V ÷ I
  = 4.5 ÷ 0.15
  = 30 Ω
```
In series, resistances add.
```
R(total) = 30 + 60
         = 90 Ω
```
Rearrange the same equation to find the current, using the battery voltage and the total resistance.
```
I = V ÷ R
  = 9.0 ÷ 90
  = 0.10 A
```
The current is the same through both resistors. The potential difference across each is current × resistance. Check that they add up to the battery voltage.
```
30 Ω: 0.10 × 30 = 3.0 V
60 Ω: 0.10 × 60 = 6.0 V
3.0 + 6.0 = 9.0 V
```
Charge = current × time. Convert the time to seconds first: 2 minutes is 120 s.
```
Q = I × t
  = 0.10 × 120
  = 12 C
```

The first resistor is 30 Ω and the total is 90 Ω. The current is 0.10 A. The potential differences are 3.0 V and 6.0 V, and 12 C of charge flows in 2 minutes.

Common mistakes and how to help

Thinking current gets used up as it goes round a circuit

A battery does run down, and the language of “using electricity” makes it sound as if current is consumed.

What helps: Compare the readings of two ammeters placed either side of a lamp: they match. It is the energy carried by the charge that is transferred to the lamp, not the charge or the current itself.

Connecting an ammeter across a component or a voltmeter in the middle of the loop

Both meters look similar, and students remember “in series” and “in parallel” but not which goes with which.

What helps: Remember that current flows through, so the ammeter is in the loop. Voltage is measured across, so the voltmeter is on a side branch. Redraw the circuit diagram and trace the path with a finger.

Assuming every component obeys Ohm’s law

The fixed resistor is the first example that students meet, so its straight-line graph seems to be the rule.

What helps: Look at the filament lamp graph and ask why it curves. The resistance is the voltage divided by the current at each point, not the slope of a curved graph, and a hotter filament has a higher resistance.

Thinking that adding another resistor in series lowers the total resistance

Students recall that adding more paths, as in parallel circuits, makes it easier for current to flow, and apply the idea to every case.

What helps: Imagine a long, narrow corridor. Each resistor in series is another narrow section the current must pass through, so the total can only go up. Check by predicting the ammeter reading in the example.

How to help at home

Build and draw a torch circuit. Using a battery, a bulb in a holder, a switch and some wires, make the simplest working circuit. Have your child draw it with proper symbols, and then add a second bulb in series to see that both glow more dimly. Use batteries only, never mains sockets.
Predict before you test. Before adding a bulb or removing one, ask your child to predict what will happen to the brightness and to the current, and why. Writing a prediction and then testing it is the heart of the practical work done in lessons.
Decode a battery label. A battery rated at 3,000 mAh (milliamp-hours) could in principle supply 3 A for 1 hour, which is 3 × 3,600 = 10,800 coulombs. Look for the rating printed on a rechargeable battery or power bank and help your child convert it to coulombs using charge = current × time.
Spot the sensors. Outside lights that switch on at dusk use a light sensor, and in school circuits that sensor is usually a light-dependent resistor. Many thermostats use thermistors. Talk about what must happen to a sensor’s resistance for it to work, and sketch a graph of resistance against light or temperature.
Test conductors and insulators. With a battery and a bulb, test a range of household items such as a coin, a spoon, a rubber band and a piece of paper by placing each in the circuit. Sort the items by how brightly the bulb glows, and discuss resistance. Always keep the bulb in the circuit: a wire joined straight across the battery gets hot.

Builds on

Key Stage 3: Current, voltage and resistance
Key Stage 3: Static electricity and electric fields
Key Stage 3: Magnetism and electromagnets