Practise Series and parallel circuits. 14 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
The rules for current, potential difference and resistance in series and parallel circuits, and how to use them in multi-step calculations. You need to explain why adding resistors in series increases the total resistance but adding them in parallel decreases it. You do not need to calculate the total resistance of resistors in parallel.
Grade by grade
What you need to be able to do, from the first marks up to the top grade.
3
Tell series and parallel circuits apartSeries: one loop, one path. Parallel: two or more branches connected across the same two points.
4
State the series and parallel rulesSeries: same current, pd shared. Parallel: same pd across each branch, branch currents add up.
4
Add resistances in seriesUse Rtotal = R1 + R2.
5
Find a missing current or pde.g. the supply pd equals the sum of the pds in series; the total current equals the sum of the branch currents.
6
Explain how added resistors change total resistanceSeries increases the total resistance; parallel decreases it.
7
Solve multi-step series circuit problemsFind the total resistance, then I = V ÷ R, then the pd across each resistor with V = I R.
8
Solve parallel problems using branch currentsEach branch has the full supply pd; find each branch current with I = V ÷ R and add them.
Notes
Series circuits
Components in series are connected one after another in a single loop.
The current is the same through each component.
The total pd of the supply is shared between the components: Vtotal = V1 + V2.
The total resistance is the sum of the resistances: Rtotal = R1 + R2.
The component with the bigger resistance gets the bigger share of the pd, because V = I R and the current is the same.
Parallel circuits
Components in parallel are each on their own branch, connected across the same two points.
The pd across each branch is the same. If each branch is connected straight across the supply, each branch has the full supply pd.
The total current is the sum of the currents through the branches: Itotal = I1 + I2.
The total resistance of two resistors in parallel is less than the smallest of the two resistances.
Each branch can have its own switch, so each component can be turned on and off separately.
Why adding resistors changes the total resistance grade 6+
Series: an extra resistor means the supply pd is shared between more resistors, so the pd across each one is smaller and the current is smaller. A smaller current from the same supply pd means a larger total resistance.
Parallel: an extra resistor adds another path for the charge. The new branch has the full supply pd across it, so it carries its own current and the total current increases. A larger current from the same supply pd means a smaller total resistance.
Solving circuit problems grade 7+
Series: find Rtotal, then I = Vsupply ÷ Rtotal, then the pd across each resistor using V = I R. Check that the pds add up to the supply pd.
Parallel: use the pd across each branch to find each branch current with I = V ÷ R, then add them to get the total current.
Some circuits have series and parallel parts. Work out one part at a time, labelling the diagram as you go.
Cheatsheet
Series: same current through each component
Series: Vtotal = V1 + V2 (pd is shared)
Series: Rtotal = R1 + R2
Parallel: same pd across each branch
Parallel: Itotal = I1 + I2
Parallel: total resistance is less than the smallest resistor
Add a resistor in series → total resistance up; in parallel → total resistance down
How to answer each type of question
Calculate current and pd in a series circuit
4 marks6
Add the resistances to get Rtotal.
Find the current: I = Vsupply ÷ Rtotal.
Find the pd across one resistor: V = I R, using that resistor's resistance only.
Example. A 12 V battery is connected in series with a 4.0 Ω resistor and an 8.0 Ω resistor. (a) Calculate the total resistance of the circuit. (b) Calculate the current in the circuit. (c) Calculate the potential difference across the 8.0 Ω resistor.
Show the model answer
(a) R = 4.0 + 8.0 = 12 Ω (1) (b) I = V ÷ R = 12 ÷ 12 (1) I = 1.0 A (1) (c) V = I R = 1.0 × 8.0 = 8.0 V (1)
Find an unknown resistance in a series circuit
4 marks7
Find the pd across the known resistor with V = I R.
Subtract it from the supply pd to get the pd across the unknown component.
Use R = V ÷ I with the same current (or find Rtotal = V ÷ I and subtract the known resistance).
Example. A 9.0 V supply is connected in series with a lamp and a 15 Ω resistor. The current in the circuit is 0.20 A. Calculate the resistance of the lamp.
Show the model answer
pd across the resistor = 0.20 × 15 = 3.0 V (1) pd across the lamp = 9.0 − 3.0 = 6.0 V (1) R = V ÷ I = 6.0 ÷ 0.20 (1) R = 30 Ω (1)
Calculate the total current in a parallel circuit
3 marks8
Each branch has the same pd as the supply (if connected straight across it).
Find each branch current with I = V ÷ R.
Add the branch currents to get the total current.
Example. A 6.0 V battery is connected to a 3.0 Ω resistor and a 12 Ω resistor in parallel. Calculate the current from the battery.
Show the model answer
The pd across each resistor is 6.0 V (1) I1 = 6.0 ÷ 3.0 = 2.0 A and I2 = 6.0 ÷ 12 = 0.50 A (1) Total current = 2.0 + 0.50 = 2.5 A (1)
Explain why the total resistance changes
2 to 3 marks6
Say what the extra resistor does: shares the pd (series) or adds a path (parallel).
Say what happens to the current from the supply.
Link current to total resistance: same pd with more current means less resistance, and vice versa.
Example. A resistor is connected to a battery. A second resistor is then connected in parallel with the first. Explain why the total resistance of the circuit decreases.
Show the model answer
The second resistor gives an extra path for the charge (1). The pd across each resistor is the same as the battery pd, so both resistors carry a current and the total current from the battery increases (1). The same pd driving a larger current means the total resistance is smaller (1).
Shortcuts and memory tricks
Series: Same current, Shared pd. Parallel: same Pd, current sPlits.
Check a series answer: the pds must add up to the supply pd.
Check a parallel answer: the total current must be bigger than any one branch current.
Parallel sense check: the total resistance is always smaller than the smallest resistor.
Where marks are lost
Adding the resistances of resistors in parallel as if they were in series.
Saying the current is shared in a series circuit. It is the pd that is shared; the current is the same.
Using the whole supply pd with just one resistor in a series circuit.
Thinking the total resistance in parallel is between the two values. It is less than the smallest.
Explaining total resistance with just 'there are more resistors' without mentioning pd and current.
Exam technique
Label the circuit diagram with every value you know or work out (V, I and R).
Write the rule you are using, e.g. 'series, so same current', so the examiner can follow your method.
In 'explain' questions about total resistance, always mention both the pd and the current.
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy4 marks
Components can be connected in series or in parallel.
(a) Which two statements about components connected in parallel are correct? Tick (✓) two boxes.[2]
The potential difference across each branch is the same.
The current in each branch is always the same.
The total current is the sum of the currents through the separate branches.
The total resistance is the sum of the resistances of the components.
(b) The lamps in a house are connected in parallel. Give two advantages of connecting the lamps in parallel.[2]
Show the answer and mark scheme
(a)Answer: The potential difference across each branch is the same.; The total current is the sum of the currents through the separate branches.
(b)Answer: Any two from: each lamp can be switched on and off separately; if one lamp breaks the others stay on; each lamp has the full supply potential difference.
each lamp can be switched on / off separately
if one lamp breaks / blows, the others still work
each lamp has the full (230 V) potential difference across it
Question 2Medium3 marks
The sockets and lights in a house are connected in parallel to the mains supply, not in series.
Give three reasons why household wiring uses parallel circuits rather than series circuits.[3]
Show the answer and mark scheme
Answer: Each appliance/lamp gets the full supply potential difference; each can be switched on/off independently; if one develops a fault or is disconnected, the others are unaffected.
each appliance / lamp receives the full (230 V) supply potential difference, so it works at its rated power regardless of how many others are connected
each appliance / lamp can be switched on or off independently of the others
if one appliance / lamp develops a fault or is disconnected, the others are unaffected and keep working
Question 3Hard8 marks
A student has two identical resistors, each with a resistance of 10 Ω, and a 6.0 V battery.
(a) Explain why connecting the two resistors in series gives a greater total resistance than one resistor on its own.[2]
(b) Explain why connecting the two resistors in parallel gives a smaller total resistance than one resistor on its own.[2]
(c) The two resistors are connected in parallel with the battery. Calculate the current from the battery.[2]
(d) Calculate the total resistance of the two resistors in parallel. Compare your answer with the resistance of one resistor.[2]
Show the answer and mark scheme
(a)Answer: The charge must pass through both resistors one after the other, so the battery's pd is shared between them; the current is smaller for the same pd, so the total resistance is greater (20 Ω).
the current / charge has to pass through both resistors (in turn) / the potential difference is shared between the resistors
so the current is smaller for the same potential difference (total resistance = 10 + 10 = 20 Ω)
(b)Answer: Each resistor provides a separate path for the current and has the full pd across it, so the total current is larger for the same pd — the total resistance is smaller.
there is more than one path for the current / each resistor has the full potential difference across it
so the total current is greater for the same potential difference
(c)Answer: 1.2 A
current in each resistor = 6.0 ÷ 10 = 0.60 (A)
total current = 1.2 (A)
(d)Answer: 5.0 Ω — smaller than the resistance of either resistor (half of 10 Ω). Ω
R = 6.0 ÷ 1.2 = 5.0 (Ω)
smaller than (the resistance of) either resistor / the smallest resistor
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