Series and Parallel Circuits

This lesson covers the rules for series and parallel circuits, including how current, potential difference and resistance behave in each type of circuit. This is a core part of the AQA GCSE Physics specification (4.2.1.4) and is heavily examined.

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Series Circuits

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.

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

Current in Series Circuits

The current is the same at every point in a series circuit. This is because there is only one path for the charge to flow through — the same charge passes through every component.

I(total) = I(1) = I(2) = I(3)

If you place ammeters at different points in a series circuit, they will all read the same value.

Potential Difference in Series Circuits

The total potential difference from the power supply is shared between the components in a series circuit. The p.d. across each component depends on its resistance — components with higher resistance have a greater share of the total p.d.

V(total) = V(1) + V(2) + V(3)

This makes sense because the total energy supplied by the battery per coulomb must equal the total energy transferred by the components per coulomb.

Resistance in Series Circuits

The total resistance of a series circuit is the sum of the individual resistances:

R(total) = R(1) + R(2) + R(3)

Adding more resistors in series increases the total resistance, which decreases the current (for a given p.d.).

Property	Rule in Series
Current	Same everywhere: I(total) = I(1) = I(2) = I(3)
Potential Difference	Shared: V(total) = V(1) + V(2) + V(3)
Resistance	Adds up: R(total) = R(1) + R(2) + R(3)

Exam Tip: A key consequence of the series rules is that if one component breaks or is removed, the circuit is broken and ALL components stop working. This is why old-fashioned Christmas tree lights used to go out entirely when one bulb failed — they were wired in series.

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Parallel Circuits

In a parallel circuit, components are connected on separate branches. Each branch provides a separate path for the current.

graph LR
    A[Battery] --> B{Junction}
    B --> C[Lamp 1]
    B --> D[Lamp 2]
    B --> E[Lamp 3]
    C --> F{Junction}
    D --> F
    E --> F
    F --> A

Current in Parallel Circuits

The total current from the power supply is divided between the branches. The current through each branch depends on the resistance of that branch — branches with lower resistance carry more current.

I(total) = I(1) + I(2) + I(3)

At a junction, the current splits. The total current entering a junction equals the total current leaving it (this is known as Kirchhoff's first law or the conservation of charge).

Potential Difference in Parallel Circuits

The potential difference across each branch of a parallel circuit is the same and equals the p.d. of the power supply.

V(total) = V(1) = V(2) = V(3)

This is because each branch is connected directly to the power supply.

Resistance in Parallel Circuits

Adding more resistors in parallel decreases the total resistance of the circuit. This is because there are more paths for the current to flow through.

For two resistors in parallel:

1/R(total) = 1/R(1) + 1/R(2)

For three resistors in parallel:

1/R(total) = 1/R(1) + 1/R(2) + 1/R(3)

The total resistance of a parallel combination is always less than the smallest individual resistance.

Property	Rule in Parallel
Current	Shared: I(total) = I(1) + I(2) + I(3)
Potential Difference	Same everywhere: V(total) = V(1) = V(2) = V(3)
Resistance	Decreases: 1/R(total) = 1/R(1) + 1/R(2) + 1/R(3)

Exam Tip: A very common exam question gives you a parallel circuit with two resistors and asks for the total resistance. Use the formula 1/R(total) = 1/R(1) + 1/R(2), then take the reciprocal. For example, two 6-ohm resistors in parallel: 1/R = 1/6 + 1/6 = 2/6, so R = 6/2 = 3 ohms. The total is always less than the smallest individual value.

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Comparing Series and Parallel Circuits

Feature	Series	Parallel
Number of paths	One	Multiple
Current	Same through all components	Splits between branches
Potential difference	Shared between components	Same across all branches
Total resistance	Sum of all resistances	Less than smallest individual resistance
Effect of adding components	Total resistance increases; current decreases	Total resistance decreases; total current increases
If one component fails	Whole circuit stops	Other branches still work
Brightness of identical lamps	Dimmer (less p.d. per lamp)	Brighter (full p.d. across each lamp)

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Worked Examples

Example 1: Series Circuit Calculations

Three resistors of 4 ohms, 6 ohms and 10 ohms are connected in series to a 12 V battery.

a) Calculate the total resistance.

R(total) = 4 + 6 + 10 = 20 ohms

b) Calculate the current in the circuit.

I = V / R = 12 / 20 = 0.6 A

c) Calculate the p.d. across the 6-ohm resistor.

V = I x R = 0.6 x 6 = 3.6 V

d) Verify that the p.d. values add up to the total.

V(4 ohm) = 0.6 x 4 = 2.4 V V(6 ohm) = 0.6 x 6 = 3.6 V V(10 ohm) = 0.6 x 10 = 6.0 V Total = 2.4 + 3.6 + 6.0 = 12.0 V (matches the battery p.d.)

Example 2: Parallel Circuit Calculations

Two resistors of 12 ohms and 6 ohms are connected in parallel to a 6 V battery.

a) Calculate the total resistance.

1/R(total) = 1/12 + 1/6 = 1/12 + 2/12 = 3/12

R(total) = 12/3 = 4 ohms

b) Calculate the total current from the battery.

I(total) = V / R(total) = 6 / 4 = 1.5 A

c) Calculate the current through each resistor.