Series and Parallel Circuits

Q: Why are household circuits wired in parallel?

Parallel circuits allow every appliance to receive the full mains voltage, and each appliance can be switched on/off independently without affecting other devices on the circuit.

Q: Do I need to learn the parallel resistance formula for Core tier?

No, Core tier only requires you to know that total parallel resistance is lower than the smallest individual resistor. The reciprocal formula is only required for Extended tier.

Q: What happens if one bulb breaks in a series circuit?

The single loop is broken, so no current flows, and all other bulbs in the series circuit will turn off.

Physics· 4.3.2· 12 min read

1. Core: Series vs Parallel Circuit Structure★☆☆☆☆⏱ 2 min

📘 Definition

Series Circuit

A circuit where all components are connected end-to-end in a single continuous loop, so there is only one path for electric current to flow.

Example:

Two bulbs connected in a single loop to a battery, with no separate branches.

📘 Definition

Parallel Circuit

A circuit where components are connected across separate parallel branches, so there are multiple independent paths for electric current to flow.

Example:

Two bulbs each connected to their own separate branch across a single battery.

📐 Worked Example

Describe the layout of a series and parallel circuit using 1 battery, 2 resistors, and 1 switch.

1
Series circuit: Connect the battery positive terminal to the switch, switch to first resistor, first resistor to second resistor, second resistor back to the battery negative terminal. This forms one single loop with no branches.
2
Parallel circuit: Connect the battery terminals to two separate branches: the first branch contains the switch and first resistor, the second branch contains the second resistor. Both branches connect back to the battery terminals.

2. Core: Rules for Series Circuits★★☆☆☆⏱ 3 min

Two rules for series circuits are required at Core tier:

Current is identical at every point in the circuit: $I_{t o t a l} = I_{1} = I_{2} = ... = I_{n}$
Total resistance equals the sum of individual component resistances: $R_{t o t a l} = R_{1} + R_{2} + ... + R_{n}$

📐 Worked Example

A 3 V battery is connected in series with 2 Ω and 4 Ω resistors. Calculate the total circuit resistance and the current flowing through the circuit.

1
First calculate total resistance using the series resistance rule:
2
$R_{total} = R_1 + R_2 = 2 + 4 = 6 \Omega$
3
Use Ohm's Law ( $I = V / R$ ) to calculate current, which is the same everywhere in the series circuit:
4
$I = \frac{V_{total}}{R_{total}} = \frac{3}{6} = 0.5 A$

3. Core: Rules for Parallel Circuits★★☆☆☆⏱ 3 min

At Core tier, parallel circuits are treated qualitatively. You need to know the following:

A parallel circuit provides more than one path, so the current divides between the separate branches.
The combined (total) resistance of two resistors in parallel is less than the resistance of the smallest individual resistor.
Adding more parallel paths lowers the total resistance of the circuit.
Each parallel branch can be switched on or off independently without breaking the others, which is why household appliances are wired in parallel.

📐 Worked Example

A 6 Ω resistor and a 3 Ω resistor are connected in parallel. Without calculating an exact value, state what you can say about the total resistance of the combination.

1
For any parallel combination, the total resistance is less than the smallest individual resistor.
2
The smallest resistor here is 3 Ω, so the total resistance must be less than 3 Ω.

4. Extended Only: Current, P.D. and Resistance Calculations★★★★☆Extended only⏱ 5 min

At Extended tier you must use these quantitative rules for current and p.d. in series and parallel circuits:

Series p.d.: the supply p.d. equals the sum of the p.d.s across the components: $V_{t o t a l} = V_{1} + V_{2} + ... + V_{n}$
Parallel p.d.: the p.d. across each branch is the same and equals the supply p.d.: $V_{1} = V_{2} = ... = V_{t o t a l}$
Parallel current (junction rule): the supply current equals the sum of the currents in the separate branches: $I_{t o t a l} = I_{1} + I_{2} + ... + I_{n}$

📐 Worked Example

A 6 V supply is connected to two bulbs in parallel. The current in the first bulb is 1 A and the current in the second bulb is 0.5 A. State the p.d. across each bulb and calculate the total current drawn from the supply.

1
Each parallel branch has the same p.d. as the supply, so the p.d. across each bulb is 6 V.
2
The supply current is the sum of the branch currents:
3
$I_{total} = I_1 + I_2 = 1 + 0.5 = 1.5 \text{ A}$

For Extended tier, you must also calculate the exact total resistance of parallel resistor combinations using the reciprocal formula:

\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}

📘 Definition

Parallel Combined Resistance

$R_{t o t a l}$

The equivalent single resistance that replaces a set of parallel resistors, calculated as the reciprocal of the sum of reciprocals of individual resistances.

Example:

Two 4 Ω resistors in parallel have a total resistance of 2 Ω.

📐 Worked Example

Calculate the total resistance of 3 Ω and 6 Ω resistors connected in parallel.

1
Substitute resistance values into the parallel resistance formula:
2
$\frac{1}{R_{total}} = \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$
3
Take the reciprocal of both sides to find the total resistance:
4
$R_{total} = 2 \Omega$

✓ Quick check

Test your Extended understanding

What is the total resistance of three 3 Ω resistors connected in parallel?
Reveal answer
1 Ω —
1/R_total = 1/3 + 1/3 + 1/3 = 1, so R_total = 1 Ω.

5. Common Pitfalls

Wrong move:

Assuming current is equal across all branches in a parallel circuit

Why:

Current splits across parallel branches, so it varies depending on the resistance of each branch.

Correct move:

Use $I_{t o t a l} = I_{1} + I_{2}$ for parallel circuits, and remember equal current only applies to series circuits.

Wrong move:

Adding parallel resistors directly like series resistors (e.g., 2 Ω + 2 Ω = 4 Ω for parallel)

Why:

Adding parallel branches creates more current paths, so total resistance decreases instead of increasing.

Correct move:

For Core, remember total parallel resistance is lower than the smallest individual resistor; for Extended, use the reciprocal resistance formula.

Wrong move:

Summing voltages across parallel branches to get total supply voltage

Why:

All parallel branches receive the full supply voltage, so voltage across every branch is identical.

Correct move:

Only sum voltages for components connected in series; for parallel, $V_{1} = V_{2} = V_{s u ppl y}$ .

Wrong move:

Assuming a switch on one parallel branch controls the entire circuit

Why:

A switch on a parallel branch only breaks the current path for that specific branch, not the whole circuit.

Correct move:

A switch only controls the entire circuit if it is connected in series with the power supply.

Wrong move:

Forgetting that a broken component in a series circuit turns off all other components

Why:

A broken component breaks the single current loop in a series circuit, stopping all current flow.

Correct move:

Identify if components are in series or parallel first to predict the effect of a broken component.

6. Quick Reference Cheatsheet

Property	Series Circuit	Parallel Circuit
Current	$I_{t o t a l} = I_{1} = I_{2} = ...$ (Core)	$I_{t o t a l} = I_{1} + I_{2} + ...$ (Extended)
Voltage / p.d.	$V_{t o t a l} = V_{1} + V_{2} + ...$ (Extended)	$V_{t o t a l} = V_{1} = V_{2} = ...$ (Extended)
Resistance (Core)	$R_{t o t a l} = R_{1} + R_{2} + ...$	Total R < smallest individual R
Resistance (Extended)	$R_{t o t a l} = R_{1} + R_{2} + ...$	$1/ R_{t o t a l} = 1/ R_{1} + 1/ R_{2} + ...$
Household Use	Used for fuses and main power switches	Used for all appliance wiring

7. Frequently Asked

Why are household circuits wired in parallel?

Parallel circuits allow every appliance to receive the full mains voltage, and each appliance can be switched on/off independently without affecting other devices on the circuit.

Do I need to learn the parallel resistance formula for Core tier?

No, Core tier only requires you to know that total parallel resistance is lower than the smallest individual resistor. The reciprocal formula is only required for Extended tier.

What happens if one bulb breaks in a series circuit?

The single loop is broken, so no current flows, and all other bulbs in the series circuit will turn off.

Going deeper

syllabus_documentCIE IGCSE Physics 0625 2026-2028 SyllabusRefer to section 4.3.2 for official requirements

What's Next

Now that you have mastered series and parallel circuit rules, you are ready to apply these to more complex mixed series-parallel circuit calculations, and analyse circuits with ammeters, voltmeters, and variable components like diodes and thermistors. These concepts are foundational for all electricity topics in your CIE IGCSE Physics 0625 exam, and will be tested in both written and practical paper questions where you may be asked to set up circuits and take measurements. Extended tier candidates will also use these rules to solve electrical power and energy calculations in later topics.