SEAB Original-style practice: A 12\ V battery is connected in series with two resistors, 3.0\ and 9.0\. (a) Find the total resistance. (b) Find the current in the circuit. (c) Find the voltage across the 9.0\ resistor.

(a) Series total: R = 3.0 + 9.0 = 12\. (b) Current: I = VR = 1212 = 1.0\ A. In a series circuit the current is the same everywhere. (c) Voltage across the 9.0\ resistor: V = IR = 1.0 × 9.0 = 9.0\ V. Markers reward the series total, a single current from Ohm's law, and the voltage across one resistor from V = IR, with the same current used throughout.

SingaporePhysicsSyllabus dot point

How do current, voltage, and resistance behave differently in series and parallel circuits?

Analyse series and parallel circuits, including combining resistances and sharing current and voltage

A focused answer to the O-Level Physics outcome on circuits. The rules for current and voltage in series and parallel, combining resistors in each arrangement, and why household appliances are wired in parallel.

Generated by Claude Opus 4.88 min answerUpdated 2026-06-06

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

SEAB wants you to analyse series and parallel circuits: how current and voltage are shared in each, and how to combine resistors. You should be able to find total resistance, currents, and voltages in simple circuits and explain why home appliances are wired in parallel. The big idea is that series and parallel arrangements share current and voltage in opposite ways.

The answer

Series circuits

In a series circuit the components are connected one after another in a single loop.

Current is the same everywhere in the loop.
Voltage is shared between the components, adding up to the supply voltage.
Resistances add: $R = R_1 + R_2 + \dots$

If one component breaks, the loop is broken and everything goes off.

Parallel circuits

In a parallel circuit the components are on separate branches connecting the same two points.

Voltage is the same across each branch (the full supply voltage).
Current is shared between the branches, adding up to the total current from the supply.
Resistances combine by reciprocals: $\dfrac{1}{R} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dots$

The combined parallel resistance is always smaller than the smallest single resistor, because adding branches gives the current more paths to flow through.

Comparing the two

	Series	Parallel
Current	Same throughout	Shared between branches
Voltage	Shared between parts	Same across each branch
One part fails	All go off	Others keep working

Why homes use parallel wiring

Household appliances are wired in parallel so that each gets the full mains voltage, each can be switched on and off independently, and one failing appliance does not switch off the rest. A series arrangement would fail all of these tests.

Worked example

A $6.0\ \text{V}$ battery is connected to two resistors, $10\ \Omega$ and $15\ \Omega$ , in parallel. (a) Find the voltage across each resistor. (b) Find the current in each. (c) Find the total current from the battery.

Step 1: Find the voltage across each branch

In parallel, each resistor has the full supply voltage across it: $6.0\ \text{V}$ each.

Step 2: Find the current in each branch

Use $I = \dfrac{V}{R}$ for each:

I_1 = \frac{6.0}{10} = 0.60\ \text{A}, \qquad I_2 = \frac{6.0}{15} = 0.40\ \text{A}

Step 3: Find the total current

The branch currents add to give the total from the battery:

I_{\text{total}} = 0.60 + 0.40 = 1.0\ \text{A}

Each resistor sees the full $6.0\ \text{V}$ , and the total current ( $1.0\ \text{A}$ ) is the sum of the branch currents. The lower-resistance branch carries the larger current.

Examples in context

Example 1. Christmas lights. Old fairy lights were wired in series, so when one bulb failed the whole string went dark and the faulty bulb was hard to find. Modern lights are wired so the rest stay lit, which is why parallel-style arrangements are preferred where independent operation matters.

Example 2. Home sockets. Every socket in a house is connected in parallel to the mains, so each receives the full $230\ \text{V}$ and any appliance can be switched on or off without affecting the others. If sockets were in series, the voltage would be split among the appliances and turning one off would cut power to all.

Try this

Q1. Two $6.0\ \Omega$ resistors are connected in series. Find their combined resistance. [1 mark]

Cue. In series, $R = 6.0 + 6.0 = 12\ \Omega$ .

Q2. State how the current and voltage behave in a parallel circuit. [2 marks]

Cue. Voltage is the same across each branch; current is shared between the branches and adds to the total.

Q3. Explain why household appliances are connected in parallel rather than in series. [2 marks]

Cue. So each gets the full mains voltage and can be switched independently, and one appliance failing does not switch off the others.

Exam-style practice questions

Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Original4 marksTwo resistors of

4.0\ \Omega

and

6.0\ \Omega

are connected. (a) Find their combined resistance in series. (b) Find their combined resistance in parallel.

Show worked answer →

(a) In series, resistances add: $R = R_1 + R_2 = 4.0 + 6.0 = 10\ \Omega$ .

(b) In parallel: $\dfrac{1}{R} = \dfrac{1}{4.0} + \dfrac{1}{6.0} = \dfrac{3}{12} + \dfrac{2}{12} = \dfrac{5}{12}$ , so $R = \dfrac{12}{5} = 2.4\ \Omega$ .

Markers reward adding resistances in series, the reciprocal rule in parallel, and a parallel result smaller than the smallest individual resistor.

Original5 marksA

12\ \text{V}

battery is connected in series with two resistors,

3.0\ \Omega

and

9.0\ \Omega

. (a) Find the total resistance. (b) Find the current in the circuit. (c) Find the voltage across the

9.0\ \Omega

resistor.