Find missing transformer turn counts and input voltages
Rearrange the simple voltage-turn ratio to solve unknown primary or secondary values and check the labelled winding roles.
Section P4.5.6 · The transformer
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Use the transformer voltage ratio.
- Rearrange a proportion.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What must an exact physical turn count be in this simple winding model?
What you will learn
- Rearrange the simple voltage-turn ratio to solve unknown primary or secondary values and check the labelled winding roles.
- Rearrange each named transformer unknown and distinguish compatible turn counts from real design specifications.
Solve the unknown without reversing roles
From Vp/Vs = Np/Ns, a missing primary turn count is Np = Ns × Vp/Vs; a missing secondary count is Ns = Np × Vs/Vp. For Vp = 240 V, Vs = 12 V and Ns = 50, the ratio is 20 and Np = 1000. Primary has more turns in this step-down model.
A missing input voltage can be found from Vp = Vs × Np/Ns. Identify the unknown first and show the rearrangement. Copying a memorised multiplier into every question can invert the ratio when the unknown changes.
Use realistic mathematical checks
Turn counts must be positive whole numbers for an actual winding. A fractional result in a supplied design can indicate an approximate target, inconsistent data or a choice needing refinement; do not silently call a fraction of a physical turn an exact count in the simple whole-turn model.
Questions here use exact compatible supplied counts. The voltage ratio does not specify wire thickness, safe insulation, current capacity or a full real-transformer design. Keep a solved turn count as a mathematical requirement of the given model, not an assembly approval.
Sources for this lesson
Pause and explain
Vp = 120 V, Vs = 24 V and Np = 600. What is Ns?
Worked example
Find Np for a supplied 240 V primary, 12 V secondary and 50 secondary turns.
Show the worked solution
- Rearrange Np = Ns × Vp/Vs.
- Substitute 50 × 240/12.
- The result is 1000 primary turns.
Answer 1000 turns.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find primary turns for 240 V/12 V and 50 secondary turns.
Give me a hint
Multiply secondary turns by the input-to-output voltage ratio.
Compare my reasoning
- 240/12 = 20.
- Np = 50 × 20.
- Primary needs 1000 turns in the model.
1000 turns.
Look for these in your work
- Show the corresponding ratio.
- State turns rather than volts.
Find secondary turns for Vp = 120 V, Vs = 24 V and Np = 600.
Give me a hint
Use the secondary-to-primary voltage ratio.
Compare my reasoning
- 24/120 = 1/5.
- Ns = 600/5.
- The result is 120 turns.
120 turns.
Look for these in your work
- Solve the named unknown.
- Check step-down consistency.
A model has Np = 600, Ns = 150 and Vs = 30 V. Find Vp, then say whether this establishes safe wire ratings.
Give me a hint
Use the primary-to-secondary turn ratio, then separate the design claim.
Compare my reasoning
- Vp = 30 × 600/150.
- The input is 120 V.
- Wire and insulation ratings are not supplied by the ratio.
120 V; safe operating ratings are not established.
Look for these in your work
- Calculate the input voltage.
- Retain the missing-specification limitation.
Common mistakes
- Name the unknown role.
- Show the rearrangement.
- Turn counts do not establish safe ratings.
What can you explain now?
What rearrangement finds secondary turns?
Compare with the explanation
Ns = Np × Vs/Vp
The output-to-input voltage ratio equals the corresponding secondary-to-primary turn ratio.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Rearrange each named transformer unknown and distinguish compatible turn counts from real design specifications.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.