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ELECTRICITY · CHAPTER 11 OF 13

Series and parallel circuits

Components can share one route around a circuit or sit on separate branches. That choice changes the current, potential difference and resistance.

By the end, you’ll be able to…

  • Compare the arrangement of components in series and parallel circuits.
  • Describe how current behaves in series and parallel circuits.
  • Describe how potential difference is shared in each type of circuit.

How many paths can charge take?

Look at the junctions. A series circuit has one continuous route. A parallel circuit contains junctions where the route divides into branches and later rejoins.

ONE ROUTE

Series circuit

Electrons have one continuous route and pass through both bulbs.

− +6 V cell − − − − − −
In series: the two identical bulbs share the 6 V supply. Each bulb has 3 V across it, so the bulbs are dimmer.
MORE THAN ONE ROUTE

Parallel circuit

Electrons split between the branches and later rejoin.

− +6 V cell − − − − − − − −
In parallel: the current splits between the branches, but each bulb has the full 6 V supply across it. Both bulbs are brighter than the bulbs in the series circuit.

In the series circuit, the two identical bulbs share the cell’s 6 V potential difference, so each bulb has 3 V across it. The total resistance is higher, so the current from the cell is smaller and both bulbs are dimmer.

In the parallel circuit, each branch has the full 6 V potential difference across it. The total resistance is lower, so the current from the cell is larger and both bulbs are brighter.

SERIES CIRCUITS

One route for charge

Current

The same current flows through every component because there is only one route.

I₁ = I₂ = I₃

Potential difference

The supply potential difference is shared between the components.

Vₛᵤₚₚₗᵧ = V₁ + V₂

Resistance

The component resistances add together.

Rₜₒₜₐₗ = R₁ + R₂

 

PARALLEL CIRCUITS

More than one route for charge

Current

Current divides between the branches at a junction. When the branches rejoin, the currents combine again.

Iₜₒₜₐₗ = I₁ + I₂

Potential difference

Each branch has the full supply potential difference across it.

Vₛᵤₚₚₗᵧ = V₁ = V₂

Resistance

Adding another branch gives charge another route through the circuit, so the total resistance decreases.

Rₜₒₜₐₗ < resistance of the smallest branch

☆ Current is not used up. If an ammeter reads 0.5 A before a bulb in a series circuit, it also reads 0.5 A after it. The bulb transfers energy, not charge.

At a junction

Current entering a junction equals the total current leaving it.

3 A enters → 1 A + 2 A leave

How to calculate total resistance

Resistance in series

worked example

Two resistors of 4 Ω and 6 Ω are connected in series. Calculate the total resistance.

Rₜₒₜₐₗ = R₁ + R₂

Rₜₒₜₐₗ = 4 + 6

Rₜₒₜₐₗ = 10 Ω

In series, adding resistors increases the total resistance.

Resistance in series

worked example

Two 6 Ω resistors are connected in parallel. Calculate the total resistance.

1/Rₜₒₜₐₗ = 1/R₁ + 1/R₂

1/Rₜₒₜₐₗ = 1/6 + 1/6

1/Rₜₒₜₐₗ = 2/6 = 1/3

Therefore:

Rₜₒₜₐₗ = 3 Ω

In parallel, the total resistance is less than the resistance of either branch.

INTERACTIVE INVESTIGATION

Circuit detective

Use the rules for series and parallel circuits to work out the missing meter readings and total resistances.

Study each circuit, then select an answer for every question to receive immediate feedback.
1
SERIES CIRCUIT

Find the missing meter readings

A 9 V cell supplies two bulbs connected in series. Use the readings shown to work out the two missing values.

− +9 V A₁ 0.5 A A₂ ? V₁ = 4 V V₂ = ?

What does ammeter A₂ read?

Not quite. Current is not divided between components in a series circuit.
Correct. Current is the same at every point in a series circuit.
Not quite. The currents are not added in a series circuit.

What is the potential difference V₂?

Not quite. The two bulbs do not necessarily have equal potential differences.
Correct. The potential differences add to the supply: 4 V + 5 V = 9 V.
Not quite. The 9 V supply is shared between the two components.
Series rule: current is the same everywhere, and the potential differences across the components add to the supply.
2
PARALLEL CIRCUIT

Find the missing branch readings

A total current of 3 A reaches a junction. The two branches are connected across a 6 V cell.

− + 6 V A 3 A I₁ = 1.2 A I₂ = ? V₂ = ?

What is the current I₂?

Not quite. The two branch currents must add to 3 A.
Correct. Current entering the junction equals current leaving: 1.2 A + 1.8 A = 3 A.
Not quite. The total 3 A divides between the two branches.

What is the potential difference V₂?

Not quite. Potential difference is not shared equally between parallel branches.
Correct. Each parallel branch has the full supply potential difference across it.
Not quite. The branch potential differences are not added together.
Parallel rule: current divides between the branches, while every branch has the full supply potential difference across it.
3
TOTAL RESISTANCE

Compare the arrangements

Two identical 6 Ω resistors can be connected in series or in parallel. Select the correct total resistance for each arrangement.

SERIES 6 Ω 6 Ω R total = ? PARALLEL 6 Ω 6 Ω R total = ?

What is the total resistance in series?

Not quite. Adding resistors in series increases the total resistance.
Not quite. In series, the component resistances add together.
Correct. In series, resistances add: 6 Ω + 6 Ω = 12 Ω.

What is the total resistance in parallel?

Correct. Two identical 6 Ω resistors in parallel have a total resistance of 3 Ω.
Not quite. Adding a parallel branch reduces the total resistance.
Not quite. Twelve ohms would be the resistance when the two resistors are connected in series.
Resistance rule: resistances add in series. Adding parallel branches reduces the total resistance because charge has more than one route through the circuit.

Why are appliances in homes connected in parallel?

Appliances in homes are connected in parallel so that they can work independently.

✓ Each appliance receives the full mains potential difference.

✓ Switching one appliance off does not break the circuit for the others.

✓ If one appliance stops working, the others can continue to work.

domestic parallel wiring

This is a simplified diagram. Real household wiring also includes safety features and earth wires where required. Here, only the live and neutral wires are shown to make the parallel arrangement clear.

INTERACTIVE QUICK CHECK

Check your understanding

Answer all three questions about series and parallel circuits.

Select one answer for each question. You will get feedback straight away.
1 A current of 3 A reaches a junction. A current of 1.2 A flows through one branch. What current flows through the other branch?
2 Two lamps are connected in parallel across a 6 V supply. What is the potential difference across each lamp?
3 What happens to the total resistance when another resistor is added in parallel?
INTERACTIVE CHALLENGE

Why does adding a parallel branch increase the total current from the cell?

Think about the number of routes and the total resistance, then reveal the answer.

The extra branch provides another route for charge, reducing the circuit’s total resistance. With the same supply potential difference, a lower total resistance produces a larger total current.

CHAPTER 11

Chapter summary

  • A series circuit has one route for charge, while a parallel circuit has two or more branches.
  • In a series circuit, the current is the same through every component. In a parallel circuit, current divides at junctions and combines again when the branches rejoin.
  • In series, the supply potential difference is shared between the components. In parallel, each branch has the full supply potential difference across it.
  • In series, the total resistance is the sum of the component resistances.
  • Adding another branch in parallel decreases the total resistance. The total resistance is less than the resistance of the smallest branch.

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