Parallel Circuits

This lesson covers the rules governing parallel circuits, as required by the Edexcel GCSE Combined Science specification (1SC0). You will learn how current, voltage and resistance behave when components are connected in separate branches.

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What Is a Parallel Circuit?

In a parallel circuit, components are connected on separate branches so that the current has more than one path to follow.

flowchart TD
    A["Battery"] --> B["Junction"]
    B --> C["Lamp 1"]
    B --> D["Lamp 2"]
    C --> E["Junction"]
    D --> E
    E --> A

Each branch provides an independent path. If one branch is disconnected, current can still flow through the other branches.

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Rule 1: Voltage Is the Same Across Each Branch

In a parallel circuit, the potential difference across each branch is the same as the potential difference supplied by the battery.

$V_{\text{battery}} = V_1 = V_2 = V_3$Vbattery​=V1​=V2​=V3​

Why?

Each branch is connected directly to the battery terminals. Every branch therefore receives the full voltage of the supply.

Worked Example 1

A 6 V battery is connected to two lamps in parallel. What is the voltage across each lamp?

$V_1 = V_2 = 6 \text{ V}$V1​=V2​=6 V

Both lamps receive the full 6 V.

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Rule 2: Currents Add Up

In a parallel circuit, the total current from the battery equals the sum of the currents through each branch.

$I_{\text{total}} = I_1 + I_2 + I_3$Itotal​=I1​+I2​+I3​

Why?

At a junction (where the circuit splits), charge is conserved. The charge flowing in must equal the charge flowing out. This is a consequence of the conservation of charge.

Worked Example 2

Two branches in a parallel circuit carry currents of 0.4 A and 0.6 A. What is the total current from the battery?

$I_{\text{total}} = 0.4 + 0.6 = 1.0 \text{ A}$Itotal​=0.4+0.6=1.0 A

Exam Tip: At every junction in a parallel circuit, the current flowing in equals the current flowing out. This principle can be used to find an unknown branch current if you know the total and the other branches.

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Rule 3: Total Resistance Decreases

When resistors are connected in parallel, the total resistance is less than the smallest individual resistance.

For two resistors in parallel:

$\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2}$Rtotal​1​=R1​1​+R2​1​

Why?

Adding another branch gives the current an additional path to flow through. More paths means less overall opposition, so the total resistance falls.

Worked Example 3

Two resistors of 6 $\Omega$Ω and 12 $\Omega$Ω are connected in parallel. Calculate the total resistance.

$\frac{1}{R_{\text{total}}} = \frac{1}{6} + \frac{1}{12} = \frac{2}{12} + \frac{1}{12} = \frac{3}{12}$Rtotal​1​=61​+121​=122​+121​=123​

$R_{\text{total}} = \frac{12}{3} = 4 \; \Omega$Rtotal​=312​=4Ω

The total resistance (4 $\Omega$Ω) is less than either individual resistance.

Worked Example 4

Two identical 10 $\Omega$Ω resistors are in parallel. What is the total resistance?

$\frac{1}{R_{\text{total}}} = \frac{1}{10} + \frac{1}{10} = \frac{2}{10}$Rtotal​1​=101​+101​=102​

$R_{\text{total}} = \frac{10}{2} = 5 \; \Omega$Rtotal​=210​=5Ω

Exam Tip: For two identical resistors in parallel, the total resistance is simply half the value of one resistor. This shortcut saves time in the exam.

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Current in Each Branch

Since the voltage across each branch is the same, the current in each branch depends on the resistance of that branch:

$I_n = \frac{V}{R_n}$In​=Rn​V​

A branch with a lower resistance carries a larger current.

Worked Example 5

A 12 V battery is connected to two resistors in parallel: R₁ = 6 $\Omega$Ω and R₂ = 12 $\Omega$Ω.

$I_1 = \frac{12}{6} = 2.0 \text{ A}$I1​=612​=2.0 A

$I_2 = \frac{12}{12} = 1.0 \text{ A}$I2​=1212​=1.0 A

$I_{\text{total}} = 2.0 + 1.0 = 3.0 \text{ A}$Itotal​=2.0+1.0=3.0 A

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Effect of Adding More Branches

Change	Effect on Total Resistance	Effect on Total Current
Add another branch in parallel	Decreases	Increases
Remove a branch	Increases	Decreases
Add a lamp in parallel	Decreases	Increases (all lamps remain same brightness)

Adding more branches in parallel reduces the total resistance and increases the total current drawn from the battery.

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Advantages of Parallel Circuits

Advantage	Explanation
Each component gets the full supply voltage	Unlike series circuits, where voltage is shared
Components can be switched on and off independently	Removing one branch does not affect the others
If one component fails, others keep working	The remaining branches still form complete circuits

Household wiring is arranged in parallel so that each appliance receives the full mains voltage and can be controlled independently.

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Comparing Series and Parallel

Property	Series	Parallel
Current	Same through all components	Splits between branches; adds at junctions
Voltage	Shared between components; adds to battery voltage	Same across every branch
Total resistance	Sum of individual resistances	Less than the smallest individual resistance
One component fails	Whole circuit stops	Other branches continue

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Summary

• In a parallel circuit, components are on separate branches — there is more than one path for current.
• Voltage is the same across each branch: $V_{\text{battery}} = V_1 = V_2 = V_3$Vbattery​=V1​=V2​=V3​
• Currents add up at junctions: $I_{\text{total}} = I_1 + I_2 + I_3$Itotal​=I1​+I2​+I3​
• Total resistance decreases when resistors are added in parallel: $\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2}$Rtotal​1​=R1​1​+R2​1​
• A branch with lower resistance carries a larger current.
• Parallel circuits are used in household wiring because each device gets the full voltage and can be switched independently.

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Extended Worked Examples

Worked Example 6 — Three Resistors in Parallel

Resistors of 4 $\Omega$Ω, 6 $\Omega$Ω and 12 $\Omega$Ω are connected in parallel across a 24 V battery. Find the current in each branch and the total current from the battery.

Each branch receives the full 24 V (parallel rule). Using $I = V/R$I=V/R: