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Electricity and magnetism · Subtopic 4 of 8

Series and Parallel Circuits

In series, the current is the same everywhere, p.d.s add up to the supply, and resistances add. In parallel, each branch gets the full p.d., the branch currents add up to the total, and the combined resistance is less than any single branch. A potential divider shares the supply p.d. in the ratio of its resistances.

Cambridge 5054 Paper 1Cambridge 5054 Paper 2Cambridge 0625 Papers 2, 4Cambridge 0625 Papers 1, 3Edexcel 4PH1 Paper 1PEdexcel 4PH1 Paper 2P≈ 35 minRevision 5 · updated 2026-10-27

Section 1 of 14

Learning objectives

State the current and p.d. rules for series and parallel circuits.
Calculate combined resistance in series and for two resistors in parallel.
Solve circuits combining series and parallel parts.
Use potential dividers, including with thermistors and LDRs.

Pause and think

In an old string of fairy lights, if one bulb failed, they all went out. In your house, if one lamp blows, the others stay on. What's different about the wiring?

Section 2 of 14

Core idea

Start hereOld fairy lights

In old Christmas lights, one dead bulb made the whole string go dark: they were in series. Houses are wired in parallel so one lamp failing leaves the rest on.

The big idea

Series: same current, voltages add, $R=R_1+R_2$ . Parallel: same voltage, currents add, $\frac1R=\frac1{R_1}+\frac1{R_2}$ (less than the smallest).

1. Series and parallel

Series (left) and parallel (right)

Series: 1.2 A through both; the 4 Ω gets 4.8 V and the 6 Ω gets 7.2 V. Parallel: each gets 12 V; currents 3 A and 2 A add to 5 A, so the total resistance is

\dfrac{12}{5}=2.4

Ω.

Combining resistors

$V=V_1+V_2=IR_1+IR_2\Rightarrow R=R_1+R_2$
Series: same $I$ , voltages add.
$I=I_1+I_2=\frac V{R_1}+\frac V{R_2}$
Parallel: same $V$ , currents add.
$\frac1R=\frac1{R_1}+\frac1{R_2}$
Divide by $V$ .

Worked example4 Ω and 12 Ω on 12 V

In series, then in parallel.

Goal: Currents and voltages.
Strategy: Combine, then $V=IR$ .

$R=16\ \Omega,\ I=0.75\text{ A}$
Series.
$V_1=3\text{ V},\ V_2=9\text{ V}$
$0.75\times4$ , $0.75\times12$ .
$\tfrac1R=\tfrac14+\tfrac1{12}=\tfrac13\Rightarrow R=3\ \Omega$
Parallel.
$I_1=3\text{ A},\ I_2=1\text{ A},\ I=4\text{ A}$
Each gets 12 V.

AnswerSeries:

0.75

3

V and

9

V. Parallel:

3

A +

1

A =

4

✓ Check

12/3=4

A ✓;

3+9=12

V ✓.

2. Potential dividers

Worked example9 V across 2 kΩ and 1 kΩ

Output voltages.

Goal: Two voltages.
Strategy: Voltage shares in the ratio of resistances.

$2:1\Rightarrow6\text{ V and }3\text{ V}$
Thirds of 9 V.
$\text{LDR in the dark: }R\uparrow$
It takes more of the voltage: a light sensor.

Answer

6

V and

3

✓ CheckSum 9 V ✓.

Common misconceptionParallel total

\frac1R=\frac13

means

R=3

, not

\frac13

Pause and think

Why are house lights in parallel?

Summary

Series: add.
Parallel: reciprocals.
Dividers share voltage.

Potential divider: Resistors splitting a voltage.

HistoryKirchhoff's rules. In

1845

, as a

21

-year-old student, Gustav Kirchhoff stated two rules: currents into a junction equal currents out, and p.d.s round any loop add up to the e.m.f. These are the series and parallel rules you use today, and they work for any circuit.

Fun factBirds on power lines. A bird sitting on a single high-voltage wire is safe because both its feet are at almost the same potential: there's no p.d. across its body, so no current flows through it. Touching two wires at once would be a different story.

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