# Series and parallel circuits

> IB Physics SL · IB Physics SL
> Source: https://www.owlsprep.com/study/ib-physics-sl-u2-series-and-parallel-circuits/

We cover core rules for series and parallel circuits, resistance calculation methods, and IB SL exam-style problem solving workflows.

**Prerequisites:** [Electric current, potential difference and Ohm's Law](https://www.owlsprep.com/study/ib-physics-sl-u2-ohms-law/)

## Learning objectives

- Distinguish between series and parallel circuit configurations
- Apply core circuit laws to calculate current, potential difference, and total resistance for both circuit types
- Analyze practical operational differences between series and parallel wiring
- Solve IB SL-style mixed series-parallel circuit problems correctly

## Key Properties of Series Circuits

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.

**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.

## Key Properties of Parallel Circuits

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.

**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. $$I = \frac{9}{1} = 9 A$$

> **tip**
>
> For two identical resistors in parallel, total resistance is exactly half the value of one individual resistor, a common IB shortcut.

## Mixed Series-Parallel Circuit Analysis

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:** 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. $$R_{total} = 4 + 3 = 7 \Omega$$

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

**Check your understanding**

Test your understanding of mixed circuits

1. 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

   *Why:* The parallel pair reduces to 5 Ω, added to the 5 Ω series resistor gives 10 Ω total.

## IB Exam Phrasing for Circuit Questions

**Exam command terms**

IB Physics SL uses specific command terms for circuit questions that define what you need to show for full marks

- **Show that** — You must write every calculation step explicitly, no skipped working *(Show that the total resistance of the parallel network is 2 Ω)*

- **Calculate** — Final numerical answer with correct unit is required, 1 mark for working, 1 mark for answer

- **State** — No calculation needed, 1 mark for a 1-sentence factual answer

## Common pitfalls

- **Wrong:** Adding resistors directly when they are in parallel
  - Why it fails: The parallel resistance sum uses reciprocals, not direct addition, leading to a total resistance lower than the smallest individual resistor
  - Correct: Always use the reciprocal sum formula for parallel resistor networks before taking the inverse to get total R.
- **Wrong:** Forgetting that voltage is constant across all parallel branches
  - Why it fails: Students incorrectly divide total voltage across parallel components as if they were in series
  - Correct: Confirm all parallel branches have the exact same potential difference equal to the supply voltage (ignoring internal resistance).
- **Wrong:** Using different current values for different points in a single series loop
  - Why it fails: Charge cannot accumulate or disappear in a closed series path, so current is identical everywhere
  - Correct: Write down that current is constant in series circuits as a separate line in your working to secure the mark.
- **Wrong:** Stopping at the reciprocal sum value for parallel resistance and forgetting to invert it
  - Why it fails: This gives a value of 1/R_total instead of R_total, leading to impossible very large resistance values
  - Correct: After summing all reciprocals, explicitly write the step where you invert the total to get final R_total.

## 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 | $R_{total} = R_1 + R_2 + ...$ | $1/R_{total} = 1/R_1 + 1/R_2 + ...$ |

## 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.

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