# Series and Parallel Circuits

## Series and Parallel Circuits Revision

**Series and Parallel Circuits**

Components can either be connected in **series** or **parallel.** The type of circuit can have an effect on the **current**, **potential difference** and **resistance** of the circuit.

**Series Circuits**

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

The same flow of charge passes through each circuit component and so the **current is the same** in every component:

\textcolor{aa57ff}{\text{I}_{\text{total}}=\text{I}_1=\text{I}_2=\text{I}_3=\text{...}}

The battery or cell provides the supply of potential difference to the circuit. The **potential difference is shared** between the other components. So the total potential difference is equal to the potential difference of the battery:

\textcolor{aa57ff}{\text{V}_{\text{s}}=\text{V}_1+\text{V}_2+\text{V}_3+\text{...}}

**Resistances** in series **adds up**:

\textcolor{aa57ff}{\text{R}_{\text{total}}=\text{R}_1+\text{R}_2+\text{R}_3+\text{...}}

**Parallel Circuits**

In **parallel circuits**, components are connected in **separate loops**.

Each charge can only flow through one of the loops and so **current is shared between loops**. So the supply current in the loop with battery is equal to the sum of the current in the other loops:

\textcolor{f21cc2}{\text{I}_s=\text{I}_1+\text{I}_2+\text{I}_3+\text{...}}

The **potential difference is the same in every loop**:

\textcolor{f21cc2}{\text{V}_1=\text{V}_2=\text{V}_3}

When resistors are connected in parallel, the supply current is shared between the resistors and so the **overall resistance is reduced** as the electrical charges may take many paths.

**Example: Series and Parallel Circuit Rules**

A student builds a circuit containing a battery and three resistors named \text{R}1, \text{R}2 and \text{R}3. A diagram showing their circuit is shown on the right.

**a)** Calculate the current at the arrow marked X on the circuit diagram.

**[2 marks]**

**b)** What is the potential difference across resistor \text{R}1?

**[2 marks]**

**c)** Suggest possible values for the potential difference across resistors \text{R}2 and \text{R}3. Explain your answer.

**[2 marks]**

**Answer: **

**a) **In parallel, current is shared between loops so:

\bold{\text{I}_{\text{s}}=\text{I}_1+\text{I}_2}.

Rearrange for I_{2} :

\text{I}_2=\text{I}_{\text{s}}-\text{I}_1=\textcolor{10a6f3}{6\text{ A}}-\textcolor{aa57ff}{3\text{ A}}=\bold{3\text{ A}}

**b)** \bold{\text{R}=\dfrac{\text{V}}{\text{I}}}

Rearrange to find V:

\text{V}=\text{IR}=\textcolor{10a6f3}{6\text{ A}}\times \textcolor{00bfa8}{1 \, \Omega}=\bold{6\text{ V}}

**c)** R2 and R3 have the same resistance so potential difference must be **equal**.

\text{V}_1 = \text{V}_2=\text{V}_3=6\text{ V}

## Series and Parallel Circuits Example Questions

**Question 1:** State the difference between a series and parallel circuit.

**[2 marks]**

In a series circuit, circuit components are connected in a** single loop** whereas in a parallel circuit, components are connected in **multiple, separate loops**.

**Question 2:** Two lamps are connected in series. The current in one lamp is 5\text{ A}. What is the current in the other lamp.

**[1 mark]**

**\bold{5\text{ A}}**

In series, all components receive the same current.

**Question 3:** Two 3 \Omega resistors are connected in series. What is the total resistance of the circuit?

**[1 mark]**

**Question 4:** A student connects three resistors in a series circuit, and then in a parallel circuit. Which circuit has the least overall resistance? Explain your answer.

**[3 marks]**

**The parallel circuit has the least overall resistance**. This is because in series, each charge carrier must flow through each resistor and so the **resistances add up**. In parallel, the charge carriers have **multiple possible paths** and so resistance is less.

**Question 5:** Three lamps are connected in parallel to a battery that provides a current of 20\text{ A}. The current across two of the lamps is measured to be 5\text{ A} and 7\text{ A}. What current is measured across the third lamp?

**[2 marks]**

\bold{\text{I}_{\text{s}}=\text{I}_1+\text{I}_2+\text{I}_3} (current is shared between the lamps)

Rearrange for I_{3}: