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4.6 Parallel Circuits

GCSE Physics · AQA · Chapter 4: Electric Circuits

A free GCSE Physics lesson for AQA (8463) from OBA School: current and potential difference in parallel circuits, branch currents and total resistance. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • State that components in parallel have the same p.d. across them
  • State that the total current is the sum of the currents in the separate branches
  • Calculate the current in each branch using I = V ÷ R and the total current
  • Explain why adding resistors in parallel decreases the total resistance, and why it is less than the smallest resistor
  • Compare series and parallel circuits

Key words

  • Parallel: Components connected on separate branches, so charge passes through one branch or another.
  • Branch: One of the separate paths in a parallel circuit.
  • Junction: A point where the current splits or joins (shown with a dot).
  • Total resistance: Supply p.d. ÷ total current; for components in parallel it is less than the smallest single resistance.

Current in a parallel circuit

In a parallel circuit the current splits at a junction and joins up again. Charge is not lost, so the total current is the sum of the currents through the separate branches.

Potential difference in a parallel circuit

Each coulomb of charge goes through one branch only, so it transfers all the energy it was given in that branch. Components in parallel have the same p.d. across them – equal to the supply p.d. when each branch has only one component.

So the current in each branch depends only on that branch’s resistance:

I = V ÷ R for each branch. The bigger the resistance, the smaller the current through it.

Worked example: branch currents and total current

4.0 Ω: I = 12 ÷ 4.0 = 3.0 A; 6.0 Ω: I = 12 ÷ 6.0 = 2.0 A; 12 Ω: I = 12 ÷ 12 = 1.0 A
total current = 3.0 + 2.0 + 1.0 = 6.0 A

Answer: the battery supplies 6.0 A

Total resistance in parallel

Adding another resistor in parallel adds another path for the charge. The p.d. across each branch stays the same, so the existing branch currents do not change – but there is now extra current in the new branch. The total current increases, and since Rtotal = V ÷ Itotal, the total resistance decreases.

Worked example: total resistance of the three resistors above

Rtotal = V ÷ Itotal = 12 ÷ 6.0

Answer: Rtotal = 2.0 Ω – less than the smallest resistor (4.0 Ω)

Exam tip: The total resistance of resistors in parallel is always less than the smallest individual resistance. Find it by working out the total current first, then R = V ÷ I.

Comparing series and parallel

  • current; Series same through each component; Parallel splits: total = sum of branch currents
  • p.d.; Series shared: Vtotal = V₁ + V₂; Parallel same across each branch
  • total resistance; Series R₁ + R₂ (bigger than each); Parallel less than the smallest resistor
  • adding a resistor; Series total resistance increases, current falls; Parallel total resistance decreases, current rises
  • one component breaks; Series everything stops; Parallel other branches keep working

Lights and sockets in a house are connected in parallel: each appliance gets the full mains p.d. and can be switched on or off on its own.

Common mistakes

  • Splitting the supply p.d. between parallel branches. Each branch gets the full p.d.
  • Adding resistances in parallel as if they were in series. In parallel the total is smaller than any one resistor.
  • Thinking the biggest resistor carries the most current. In parallel it carries the least.
  • Forgetting that the current through the battery is the total of all the branch currents.

Revision questions

Try these, then check your answers below each one.

Question 1. In a parallel circuit, the ammeter next to the battery reads 1.20 A. One branch carries 0.45 A. There are two branches. What is the current in the other branch?

Answer: 0.75 A

Working: 1.20 − 0.45 = 0.75 A.

Question 2. A 10 Ω resistor and a 40 Ω resistor are connected in parallel. Their total resistance is… (Choose from: less than 10 Ω, between 10 Ω and 40 Ω, exactly 50 Ω, more than 40 Ω.)

Answer: less than 10 Ω

Working: The total resistance of resistors in parallel is always less than the smallest one (here it is 8 Ω).

Question 3. True or false? Components connected in parallel always have the same current through them.

Answer: False

Working: False. Parallel components have the same p.d.; the currents depend on their resistances.

Related lessons

Continue in the full course

This lesson is section 4.6 (AGCPH0406) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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