Topic B.5 — Current & CircuitsPaper 1 & 2Series & parallel rules~8 min read
Series & Parallel Circuits
Real circuits rarely have just one component. Once you start wiring several together, they can be arranged in two fundamentally different ways — series, where everything sits on one single path, and parallel, where the current gets a choice of routes. Let’s build up the rules for both, together.
📘 What You Need to Know
Series: current is the same everywhere in the loop; potential difference splits across the components; resistances simply add
Parallel: potential difference is the same across every branch; current splits between branches; resistance combines using reciprocals
Adding resistors in series always increases the total resistance
Adding resistors in parallel always decreases the total resistance, giving you a value smaller than the smallest individual resistor
Resistors in Series: one single road
Picture three resistors joined end to end, forming one continuous loop with the cell. Since there’s only one path for charge to take, exactly the same current has to pass through every single component — there’s nowhere else for it to go. But the potential difference works differently: the cell’s total “push” gets shared out across the components, in proportion to how much resistance each one puts up.
One loop, one path — so whatever current leaves the cell is exactly the current flowing through R₁, R₂, and R₃, all the way round.
Combined resistance — seriesR = R₁ + R₂ + R₃ …
It helps to think of it like this: each extra resistor in series is just more corridor for the current to squeeze through — more collisions, more resistance, every time. That’s why the combined resistance always ends up bigger than any single resistor on its own.
Resistors in Parallel: a choice of roads
Now imagine three resistors each connected between the very same two points — like three separate roads all starting at the same junction and ending at the same junction. Because every branch starts and ends at identical points, the potential difference across each one has to be identical too. But the current isn’t forced down one path any more — it splits up, with more current taking the branch that offers the least resistance.
All three branches connect the same two points (the black dots), so they all share the same p.d. — but the total current splits unevenly between them depending on each resistor’s value.
Adding another branch gives the current an extra route to take, so the overall opposition to flow can only go down. That’s why the combined resistance in parallel always ends up smaller than even the smallest individual resistor in the group — there’s simply more room for current to get through overall.
Putting it side by side
The same two questions — “what stays the same?” and “what splits?” — always have opposite answers for series and parallel.
Quick recap: series → same current, split voltage, resistances add; parallel → same voltage, split current, resistances combine by reciprocals and the total always drops.
WE 1
Three resistors of 6.0 Ω, 12 Ω, and 4.0 Ω are connected in parallel. What is their combined resistance?
Use the parallel formula:
1/R = 1/R₁ + 1/R₂ + 1/R₃
Substitute the values:1/R = 1/6.0 + 1/12 + 1/4.0 = 0.5 Ω⁻¹Flip to find R:R = 1 ÷ 0.5R = 2.0 ΩNotice this is smaller than even the smallest resistor, 4.0 Ω — exactly as we’d expect for parallel.
WE 2
A current of 0.72 A enters a junction and splits into two branches. One branch carries 0.25 A, and this branch later splits again: one part carries 0.19 A. What current flows in the final, unnamed part?
Find the second branch first:0.72 − 0.25 = 0.47 ANow split that branch again:0.47 − 0.19 = 0.28 AThe final part carries 0.28 AEvery time current reaches a junction, the parts must always add back up to the whole.
WE 3
A 20 V battery drives a single loop containing a 4.0 V lamp, a 9.0 V lamp, and a resistor. What is the potential difference across the resistor?
In a series loop, all the p.d.s must sum to the total:
20 = 4.0 + 9.0 + VRearrange and solve:V = 20 − 4.0 − 9.0V = 7.0 V
💡 Top Tips
Before doing any calculation, ask yourself “is this one path, or does it split?” — that instantly tells you whether to use the series or parallel rule
Currents flowing into a junction must always equal the currents flowing out — use this to check your working
Don’t forget to flip your answer back over after using the parallel formula — you calculate 1/R first, not R itself
⚠ Common Mistakes
Forgetting to take the reciprocal at the end of a parallel resistance calculation, leaving the answer as 1/R instead of R
Assuming p.d. splits equally between series components — it only splits equally if the resistances themselves are equal
Mixing up the two rules entirely — remember, it’s always “same current” for series and “same voltage” for parallel, never the other way round
Up next: Electrical Power — now we can work out current, voltage, and resistance anywhere in a circuit, let’s see how quickly energy is actually being transferred.
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