Series and parallel circuits

IB Physics SL· Topic 2: Electricity and Magnetism· 12 min read

1. Key Properties of Series Circuits★★☆☆☆⏱ 8 min

In a series circuit, every component is connected in a single unbroken loop, so there are no branching paths for charge to flow. If any single component fails or is disconnected, the entire circuit stops operating, as the path for current is broken.

📘 Definition

Series Circuit

A circuit with only one current path, where the same current passes through every component sequentially.

Example:

A simple string of old-style Christmas lights wired in series.

V_{total} = V_1 + V_2 + V_3 + ... + V_n

R_{total} = R_1 + R_2 + R_3 + ... + R_n

📐 Worked Example

Three resistors of 2 Ω, 3 Ω and 5 Ω are connected in series to a 12 V battery. Calculate the total resistance and current flowing through the circuit.

1
Step 1: Sum all individual resistances to find total series resistance
2
$R_{total} = 2 + 3 + 5 = 10 \Omega$
3
Step 2: Apply Ohm's Law I = V/R to find total current, which is identical across all components in series
4
$I = \frac{12}{10} = 1.2 A$

Exam tip:

IB mark schemes almost always award 1 mark for stating that current is constant at all points in a series circuit, even if your final calculation is wrong.

2. Key Properties of Parallel Circuits★★★☆☆⏱ 10 min

In a parallel circuit, all components are connected across the same two terminals of the power supply, creating separate independent current paths for each component. If one component fails, all other branches continue to operate normally.

📘 Definition

Parallel Circuit

A circuit with two or more separate current paths, where all components share the same potential difference across their terminals.

Example:

Standard household electrical outlets, all wired in parallel to the mains supply.

I_{total} = I_1 + I_2 + I_3 + ... + I_n

\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ... + \frac{1}{R_n}

📐 Worked Example

Three resistors of 6 Ω, 3 Ω and 2 Ω are connected in parallel across a 9 V battery. Calculate total circuit resistance and total current drawn from the battery.

1
Step 1: Use the reciprocal sum rule for parallel resistance
2
$\frac{1}{R_{total}} = \frac{1}{6} + \frac{1}{3} + \frac{1}{2} = \frac{1 + 2 + 3}{6} = 1$
3
$R_{total} = 1 \Omega$
4
Step 2: Apply Ohm's Law to find total current
5
$I = \frac{9}{1} = 9 A$

3. Mixed Series-Parallel Circuit Analysis★★★★☆⏱ 12 min

Most IB SL exam circuit questions combine series and parallel segments, requiring you to reduce the network step by step to a single equivalent total resistance.

🔬 Derivation

Goal:

Find equivalent resistance of a 4 Ω resistor in series with a parallel pair of 6 Ω resistors

Starting from:

R1 = 4 Ω, R2 = 6 Ω, R3 = 6 Ω

1
First reduce the parallel 6 Ω resistors to their equivalent value
2
$\frac{1}{R_{parallel}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} \implies R_{parallel} = 3 \Omega$
3
Add this equivalent resistance to the 4 Ω series resistor
4
$R_{total} = 4 + 3 = 7 \Omega$

Result:

The total equivalent resistance of the mixed network is 7 Ω.

✓ Quick check

Test your understanding of mixed circuits

Two 10 Ω resistors in parallel are connected in series with a 5 Ω resistor. What is the total resistance?
- 5 Ω
- 10 Ω
- 15 Ω
- 25 Ω
Reveal answer
10 Ω —
The parallel pair reduces to 5 Ω, added to the 5 Ω series resistor gives 10 Ω total.

4. IB Exam Phrasing for Circuit Questions★★☆☆☆⏱ 5 min

5. Common Pitfalls

Wrong move:

Adding resistors directly when they are in parallel

Why:

The parallel resistance sum uses reciprocals, not direct addition, leading to a total resistance lower than the smallest individual resistor

Correct move:

Always use the reciprocal sum formula for parallel resistor networks before taking the inverse to get total R.

Wrong move:

Forgetting that voltage is constant across all parallel branches

Why:

Students incorrectly divide total voltage across parallel components as if they were in series

Correct move:

Confirm all parallel branches have the exact same potential difference equal to the supply voltage (ignoring internal resistance).

Wrong move:

Using different current values for different points in a single series loop

Why:

Charge cannot accumulate or disappear in a closed series path, so current is identical everywhere

Correct move:

Write down that current is constant in series circuits as a separate line in your working to secure the mark.

Wrong move:

Stopping at the reciprocal sum value for parallel resistance and forgetting to invert it

Why:

This gives a value of 1/R_total instead of R_total, leading to impossible very large resistance values

Correct move:

After summing all reciprocals, explicitly write the step where you invert the total to get final R_total.

6. Quick Reference Cheatsheet

Property	Series Circuits	Parallel Circuits
Current	Same across all components	Sum of currents across all branches
Voltage	Sum of voltages across all components	Same across all branches
Total Resistance	$R_{t o t a l} = R_{1} + R_{2} + ...$	$1/ R_{t o t a l} = 1/ R_{1} + 1/ R_{2} + ...$

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · 1
Resistor network identification
2024 · 2
Total resistance calculation

What's Next

These concepts are frequently combined in 6-8 mark structured exam questions, so practicing mixed circuit analysis will help you maximize marks on Topic 2 assessment items. You can also test your knowledge with our dedicated practice question bank for this sub-topic to identify gaps before your mock exams.