Series Circuits

This lesson covers the rules governing series 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 a single loop.

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What Is a Series Circuit?

In a series circuit, all components are connected one after another in a single loop. There is only one path for the current to follow.

flowchart LR
    A["Battery"] --> B["Lamp 1"]
    B --> C["Lamp 2"]
    C --> D["Lamp 3"]
    D --> A

If any component breaks or is disconnected, the entire circuit stops working because the single loop is broken.

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Rule 1: Current Is the Same Everywhere

In a series circuit, the current is the same at every point in the circuit.

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

Why?

There is only one path, so every coulomb of charge that leaves the battery must pass through every component. Charge is conserved — it is not used up or created anywhere in the circuit.

Worked Example 1

A series circuit contains a battery, a lamp and a resistor. The ammeter reads 0.3 A. What is the current through the resistor?

$I_{\text{resistor}} = 0.3 \text{ A}$Iresistor​=0.3 A

The current is the same at every point, so the current through the resistor is the same as the ammeter reading.

Exam Tip: If you are asked for the current at any point in a series circuit, you only need one ammeter reading. The current is identical everywhere.

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Rule 2: Voltages Add Up

In a series circuit, the potential differences across all components add up to the total potential difference supplied by the battery.

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

Why?

Each component transfers some of the energy provided by the battery. The total energy transferred per coulomb by all the components must equal the energy provided per coulomb by the battery (conservation of energy).

Worked Example 2

A 12 V battery is connected in series with three resistors. The voltage across the first resistor is 3 V and across the second is 5 V. What is the voltage across the third resistor?

$V_3 = V_{\text{battery}} - V_1 - V_2 = 12 - 3 - 5 = 4 \text{ V}$V3​=Vbattery​−V1​−V2​=12−3−5=4 V

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Rule 3: Resistances Add Up

In a series circuit, the total resistance is the sum of all individual resistances.

$R_{\text{total}} = R_1 + R_2 + R_3$Rtotal​=R1​+R2​+R3​

Why?

Each resistor opposes the flow of current. Adding more resistors in series means the current must pass through more obstacles, so the total opposition increases.

Worked Example 3

Three resistors of 4 $\Omega$Ω, 6 $\Omega$Ω and 10 $\Omega$Ω are connected in series. What is the total resistance?

$R_{\text{total}} = 4 + 6 + 10 = 20 \; \Omega$Rtotal​=4+6+10=20Ω

Worked Example 4

The same three resistors are connected to a 12 V battery. What is the current?

Using $V = IR$V=IR:

$I = \frac{V}{R_{\text{total}}} = \frac{12}{20} = 0.6 \text{ A}$I=Rtotal​V​=2012​=0.6 A

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Sharing the Voltage

Because the current is the same through every component, a component with a larger resistance will have a larger share of the voltage.

Using $V = IR$V=IR for each resistor (with the same current I):

Resistor	Resistance	Current	Voltage (V = IR)
R₁	4 $\Omega$Ω	0.6 A	2.4 V
R₂	6 $\Omega$Ω	0.6 A	3.6 V
R₃	10 $\Omega$Ω	0.6 A	6.0 V
Total	20 $\Omega$Ω	—	12.0 V

The voltages (2.4 + 3.6 + 6.0 = 12.0 V) add up to the battery voltage, confirming the rule.

Exam Tip: In a series circuit, the component with the greatest resistance gets the greatest share of the voltage. This is a frequently tested idea.

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Effect of Adding More Components

Change	Effect on Total Resistance	Effect on Current
Add another resistor in series	Increases	Decreases
Remove a resistor from the series	Decreases	Increases
Add another lamp in series	Increases	Decreases (all lamps dimmer)

Adding more components in series increases the total resistance, which reduces the current. If lamps are in series, they all become dimmer when another lamp is added.

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Practical Considerations

• If one lamp in a series circuit blows (filament breaks), the circuit is broken and all lamps go out.
• Older Christmas lights were wired in series — if one bulb failed, the entire string stopped working.
• This is a disadvantage of series circuits for practical applications.

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Series Circuit Calculations — Summary Method

For any series circuit calculation:

1. Find the total resistance: $R_{\text{total}} = R_1 + R_2 + R_3 + \ldots$Rtotal​=R1​+R2​+R3​+…
2. Find the current: $I = \frac{V_{\text{battery}}}{R_{\text{total}}}$I=Rtotal​Vbattery​​
3. Find individual voltages: $V_n = I \times R_n$Vn​=I×Rn​
4. Check: The individual voltages should add up to the battery voltage.

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Summary

• In a series circuit, there is one single loop — one path for current.
• Current is the same at every point: $I_{\text{total}} = I_1 = I_2 = I_3$Itotal​=I1​=I2​=I3​
• Voltages add up to the battery voltage: $V_{\text{battery}} = V_1 + V_2 + V_3$Vbattery​=V1​+V2​+V3​
• Resistances add up: $R_{\text{total}} = R_1 + R_2 + R_3$Rtotal​=R1​+R2​+R3​
• A component with a larger resistance has a larger share of the voltage.
• If one component breaks, the whole circuit stops working.

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Extended Worked Examples

Worked Example 5 — Three Resistors, Full Analysis

A 24 V battery is connected in series with resistors of 2 $\Omega$Ω, 4 $\Omega$Ω and 6 $\Omega$Ω. Find the current and the potential difference across each resistor.

Total resistance:

$R_{\text{total}} = 2 + 4 + 6 = 12 \; \Omega$Rtotal​=2+4+6=12Ω

Current (same everywhere):

$I = \frac{V}{R_{\text{total}}} = \frac{24}{12} = 2.0 \text{ A}$I=Rtotal​V​=1224​=2.0 A

Apply $V = IR$V=IR to each resistor: