Series and Parallel Circuits
Two circuit arrangements with opposite rules for current and voltage. Learn the four rules properly and most circuit questions become bookkeeping — get them the wrong way round and nothing works.
1. The four rules
SERIES — one path. Current: the SAME everywhere. Voltage: SPLITS between components (adds up to the supply).
PARALLEL — multiple branches. Current: SPLITS between branches (adds up to the total). Voltage: the SAME across each branch.
| Series | Parallel | |
|---|---|---|
| Current | same everywhere | splits, and adds back |
| Voltage | splits | same across each branch |
| Total resistance | adds | decreases |
| One component breaks | everything stops | others keep working |
These are the exact opposite of each other, and both were reversed in lessons. Recorded errors included “in parallel the current stays the same and the voltage splits” (backwards) and “voltage stays the same in a series circuit” (also backwards).
A memory hook that works: in series there is only one path, so the current has nowhere else to go — it must be the same everywhere, and the energy (voltage) gets shared out among the components. In parallel, each branch connects to both terminals of the supply, so each gets the full voltage, and the current divides between the routes.
2. Series circuits
Current: the same at every point. An ammeter reads the same wherever you put it.
Voltage: the supply voltage is shared:
V_total = V₁ + V₂ + V₃ …
Resistance:
R_total = R₁ + R₂ + R₃ …
The total is always bigger than any individual resistor.
Worked example. A 12 V supply with a 4 Ω and an 8 Ω resistor in series.
- R_total = 4 + 8 = 12 Ω
- I = V/R = 12 ÷ 12 = 1 A (the same through both)
- V across 4 Ω = IR = 1 × 4 = 4 V
- V across 8 Ω = 1 × 8 = 8 V
- Check: 4 + 8 = 12 V ✓
Find the total resistance first, then the current, then the individual voltages. Trying to find a voltage without the total current was a recorded error — the current is the quantity that links everything in series.
The bigger resistor gets the bigger share of the voltage, in the ratio of the resistances. Tutors recommended this ratio method: with 4 Ω and 8 Ω, the voltage splits 1:2.
Always check that your voltages add up to the supply.
3. Parallel circuits
Voltage: every branch gets the full supply voltage.
Current: splits between branches and recombines:
I_total = I₁ + I₂ + I₃ …
More current flows through the branch with less resistance.
Resistance:
1/R_total = 1/R₁ + 1/R₂ + …
Worked example. 6 Ω and 12 Ω in parallel across 12 V.
- 1/R = 1/6 + 1/12 = 2/12 + 1/12 = 3/12
- R_total = 4 Ω
- I through 6 Ω = 12/6 = 2 A; I through 12 Ω = 12/12 = 1 A
- Total current = 3 A
- Check: V/R_total = 12/4 = 3 A ✓
Remember the final reciprocal. Stopping at 3/12 and calling it the answer is the classic error — you must invert to get 4 Ω. A recorded error even produced a negative resistance, which is impossible and should always trigger a re-check.
The total resistance in parallel is ALWAYS smaller than the smallest branch. Here, 4 Ω is less than both 6 Ω and 12 Ω. If your answer is bigger than the smallest resistor, it is wrong.
Adding more branches DECREASES total resistance, because you are adding more paths for the current. Misunderstanding this, and what happens when a resistor is removed (total resistance increases), were both recorded.
For two resistors only, this is faster:
R = (R₁ × R₂) / (R₁ + R₂) → (6 × 12)/(6 + 12) = 72/18 = 4 Ω ✓
4. Identifying series and parallel
Series: components are on the same single wire, one after another, with no junctions between them. Parallel: the circuit branches — components sit on separate paths between the same two points.
Decide which arrangement you have before calculating. Confusing the two, and adding resistances that were actually in parallel, were both recorded errors — and the wrong choice makes every subsequent number wrong.
Where meters go:
Ammeters in SERIES with the component (they measure the current through it). Voltmeters in PARALLEL across the component (they measure the difference across it).
Not all ammeters in a circuit read the same. A recorded error assumed all ammeters were in parallel. In a parallel circuit, an ammeter in a branch reads that branch’s current, while one in the main line reads the total.
5. Mixed circuits
Work from the inside out:
- Combine the parallel section into a single equivalent resistance
- Add it to any series resistances to get the total
- Find the total current from the supply
- Work back to individual components
The current through the parallel section as a whole equals the series current feeding it, and then splits inside.
6. Effect of switches and changes
Closing a switch that adds a parallel branch:
Total resistance DECREASES, so the total current INCREASES.
But the current in an existing branch is unchanged, because the voltage across it hasn’t changed. A recorded error expected the current through a variable resistor to increase when a parallel switch was closed — it doesn’t, because that branch still has the same voltage and the same resistance.
Increasing a variable resistor in series raises total resistance, so the current falls everywhere in that loop.
7. Advantages of parallel wiring
Household circuits are wired in parallel because:
- Each appliance gets the full mains voltage
- Each can be switched independently
- If one fails, the others keep working
In series, one broken component breaks the whole circuit — which is why old fairy lights all went out together.
8. Mistakes that cost marks
Reversing the current and voltage rules between series and parallel.
Forgetting the reciprocal in the parallel formula.
Getting a parallel total larger than the smallest branch, or negative.
Adding resistances that are actually in parallel.
Not finding the total resistance first.
Thinking removing a parallel resistor lowers total resistance — it raises it.
Expecting an existing branch’s current to change when another branch is switched in.
Putting the ammeter in parallel or the voltmeter in series.
Voltages that don’t add up to the supply.
Using everyday language instead of the technical terms.
Frequently asked questions
What happens to current in a series circuit? It is the same everywhere.
What happens to voltage in a series circuit? It splits between the components and adds to the supply voltage.
What happens to current in a parallel circuit? It splits between branches and adds back together.
What happens to voltage in a parallel circuit? It is the same across each branch — the full supply voltage.
How do I find total resistance in series? Add the resistances.
How do I find total resistance in parallel? 1/R = 1/R₁ + 1/R₂, then take the reciprocal.
Why is parallel resistance smaller? There are more paths for the current.
What happens if I add another parallel branch? Total resistance falls, so total current rises.
Where do ammeters and voltmeters go? Ammeters in series, voltmeters in parallel.
Why are houses wired in parallel? Every appliance gets the full voltage, can be switched separately, and keeps working if another fails.
Quick revision checklist
- I know the current and voltage rules for series
- I know the current and voltage rules for parallel
- I can explain why each rule holds
- I can identify series and parallel sections in a diagram
- I can add resistances in series
- I can combine resistances in parallel, including the reciprocal
- I check the parallel total is smaller than the smallest branch
- I find total resistance → total current → individual values, in order
- I can use the ratio method for voltage in series
- I can handle mixed circuits from the inside out
- I know what happens when a switch adds or removes a branch
- I know where ammeters and voltmeters go
- I can give the advantages of parallel wiring
- I check voltages sum to the supply
These notes cover series and parallel circuits in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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