Parallel Circuits
Three rules — almost the opposite of series. Mix them up and you'll lose marks every paper. Get them locked in here.
SPEC 8463 • 4.2.2 • PAPER 1 ⭐
What is a Parallel Circuit?
A parallel circuit has more than one loop. Components sit on separate branches, so charge flowing from the cell can take different routes back.
Definition
Parallel circuit: a circuit where components are connected across the same two points, so each branch has the same potential difference.
Two resistors, each on its own branch between junctions A and B. The cell drives the whole circuit.
Rule 1 — Same pd Across Each Branch
The potential difference across each parallel branch is the same, and equals the supply pd.
Rule 1
V_supply = V_branch 1 = V_branch 2 = V_branch 3 = …
Example: a 12 V battery with two parallel branches. Each branch has 12 V across it. Not 6 V each — 12 V each.
Why?
Each branch connects directly to both terminals of the supply. Both ends of every branch are at the same two voltage levels — so the pd across them must be the same.
Rule 2 — Branch Currents Add Up
The currents in the branches add to give the total current from the supply.
Rule 2
I_total = I₁ + I₂ + I₃ + …
Example: if 1.5 A flows in one branch and 0.75 A in another, the cell supplies 2.25 A in total.
Why?
Charge that leaves the cell must come back to it. At each junction, the charge splits between branches; at the next junction, it recombines. Conservation of charge.
Rule 3 — Total R is LESS Than Smallest Branch
This one is counterintuitive. The total resistance of resistors in parallel is less than the smallest individual branch resistance.
Rule 3
R_total < smallest individual R
Common Misconception
Adding more resistors does not always increase total resistance. In series it does. In parallel, adding more branches gives current more routes, so total resistance falls.
Worked check: two 12 Ω resistors in parallel give R_total = 6 Ω. Three 12 Ω in parallel give 4 Ω. More branches = less total resistance.
Useful pattern
For n identical resistors of value r in parallel, R_total = r ÷ n. So n × R_total = constant — number of resistors and total resistance are inversely proportional. Examiners have asked students to spot this pattern in tabulated data.
Why Adding Branches Reduces Total R
The spec explicitly asks you to explain qualitatively why adding resistors in parallel decreases total resistance. The AQA mark scheme for this question is 2 marks — and only 11% of students get both marks.
Mark-scheme answer (2 marks)
An additional parallel branch provides another path for current (or charge) to flow. (1 mark)
The total current is greater for the same potential difference. (1 mark)
Bonus / 3-mark extension
Finish with: "Since R = V ÷ I, a larger total current for the same pd means the total resistance is smaller." This earns the 3rd mark on extended versions and shows full reasoning.
Weak (0/2)
"The resistance gets shared between the resistors."
Strong (2/2)
"Each new branch provides another path for current. With more paths, the total current is greater for the same pd."
The 1/R Formula — STRETCH ONLY
You may have seen this formula at A-level or in textbooks. It is not required by the AQA GCSE spec.
[STRETCH] — not required by AQA GCSE
1 ÷ R_total = 1/R₁ + 1/R₂
The AQA spec states explicitly: "Students are not required to calculate the total resistance of two resistors joined in parallel."
What you do instead
Solve every parallel-circuit problem using the three rules — work out the current in each branch separately using V = IR, then add the branch currents to get the total. Total R drops out as V_supply ÷ I_total.
Examiner Warning
If asked to explain qualitatively why R decreases, do not write down the 1/R formula. Examiners have flagged this as a common error that scores zero — the formula is not an explanation.
Worked Example — ESUA
Two resistors, 4 Ω and 8 Ω, are connected in parallel across a 6 V cell. Find the total current and the total resistance.
- EEquation: Each branch has the supply pd across it (Rule 1). Use V = I × R rearranged to I = V ÷ R for each branch. Total current is the sum of branch currents (Rule 2).
- SSubstitute:Branch 1: I₁ = 6 ÷ 4 = 1.5 ABranch 2: I₂ = 6 ÷ 8 = 0.75 ATotal: I_total = 1.5 + 0.75
- UUnits: amperes (A) for current, ohms (Ω) for resistance.
- AAnswers: I_total = 2.25 A. Then R_total = V ÷ I = 6 ÷ 2.25 = 2.67 Ω (3 s.f.).
Sanity check
2.67 Ω is less than 4 Ω, the smallest branch resistance. Rule 3 confirmed.
Series vs Parallel — All Three Rules
Lock this table in. Confusing series and parallel rules is the most-flagged error in this topic across examiner reports.
QuantitySeriesParallel
CurrentSame at every pointBranch currents add to total
Potential differenceShared between components (adds to supply)Same across each branch
Total resistanceR₁ + R₂ + … (always increases)Less than smallest branch (decreases)
Rule of thumb
Read the diagram first. One loop = series. More than one loop = parallel. Don't pattern-match — count the loops.
Mixed circuits
The spec states: "Some circuits include both series and parallel parts." When you see one, identify each section's topology first, then apply the right rules to each section. Treat a parallel combination as an "equivalent resistor" with its own equivalent resistance, then apply series rules to combine it with anything in series. AQA examines this regularly (e.g. Jun 2024 Paper 1, Q5).
Practice Q1
A 9.0 V battery is connected to two resistors in parallel: R₁ = 6.0 Ω and R₂ = 12 Ω. Calculate the current supplied by the battery.3 marks
E
Each branch has 9.0 V across it. I = V ÷ R per branch. Add branch currents.
S
I₁ = 9.0 ÷ 6.0 = 1.5 A | I₂ = 9.0 ÷ 12 = 0.75 A | I_total = 1.5 + 0.75
U
Amperes (A).
A
I_total = 2.25 A
Practice Q2
Explain why connecting an additional resistor in parallel decreases the total resistance of the circuit.2 marks
1
An additional parallel branch provides another path for current (or charge) to flow. (1 mark)
2
The total current is greater for the same potential difference. (1 mark)
+
3-mark extension: "Since R = V ÷ I, a larger I for the same V means total resistance is smaller."
Examiner Alert
Nov 2020 Paper 1H · Q08.4
The 2-mark question "Explain why adding resistors in parallel decreases the total resistance" was answered correctly by only 11% of students. Another 26% scored just 1 mark. Almost two-thirds got zero.
"The most common answer was that 'the resistance is shared'. Another common answer was to use the equation for resistors in parallel as an explanation." — AQA Examiner Report, Nov 2020 Paper 1H
Two killer errors
"The resistance is shared" — wrong concept entirely. Resistance isn't shared; total resistance decreases.
Writing the 1/R formula as your explanation — examiners want qualitative reasoning, not algebra. Scores zero.
Lock-in answer
"Another path for current; total current is greater for the same pd." Two clauses, two marks. Memorise the structure.
Weak vs Strong — The Classic Error
Same question. Two answers. The first treats parallel like series and loses every mark.
Question: Two parallel resistors, 4 Ω and 8 Ω, connected to a 6 V cell. Find the total current.
Weak (0/3)
R_total = 4 + 8 = 12 Ω
I = 6 ÷ 12 = 0.5 A ❌
Adds resistances as if they were in series. Wrong rule, wrong answer.
Strong (3/3)
Each branch has 6 V across it.
I₁ = 6 ÷ 4 = 1.5 A
I₂ = 6 ÷ 8 = 0.75 A
I_total = 2.25 A ✓
Mark Scheme Language
The exact phrases that score marks on parallel-circuit questions. Use these — not paraphrases.
Don't writeWrite
"voltage is shared""the potential difference across each branch is the same and equals the supply pd"
"current splits""the total current is the sum of the currents in the branches"
"resistance gets less""another parallel branch provides another path for current, so total resistance decreases"
"adds in parallel""the total resistance of two resistors in parallel is less than the smallest individual resistance"
6-Mark Style — Compare & Contrast
A typical 6-marker on this topic asks you to describe the difference between series and parallel circuits. Plan three points before writing — one per pair of rules.
Three-point template
Current: series — same everywhere; parallel — branch currents add to total.
Potential difference: series — shared between components; parallel — same across each branch.
Total resistance: series — sum of resistances; parallel — less than smallest individual, with the explanation that extra branches provide extra paths for current.
Level 3 finish
End with the practical consequence: e.g. "this is why house lighting is wired in parallel — each lamp has the full mains pd, and one lamp failing doesn't break the circuit for the others." Linking theory to application pushes the answer into Level 3.
Recap — Three Parallel Rules
Same pd
V across each branch = supply pd
Currents add
I_total = I₁ + I₂ + …
R total falls
R_total < smallest branch R
Method for any parallel calculation
1
Identify the supply pd — that's the pd across every branch.
2
Use I = V ÷ R for each branch separately.
3
Add the branch currents to get I_total.
4
If asked for R_total, divide V_supply by I_total.
Checkpoint
You can now:
State the three parallel rules for pd, current, and total resistance.
Calculate branch currents and total current in any parallel circuit.
Recognise that total R is less than the smallest branch and explain why qualitatively.
Avoid the killer misconception "the resistance is shared" flagged in the Nov 2020 examiner report.
Use mark-scheme language — "another path for current; total current is greater for the same pd".
Recognise mixed series-parallel circuits and apply the right rules to each section.
Next lesson
2.07 — Direct & alternating potential difference; mains electricity. AC vs DC, the UK 230 V / 50 Hz mains, and the three-pin plug.
Next: What is a Parallel Circuit?