Electromagnetic Induction » Transformer Calculations
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 6.19P, 6.20P
- Use the turns ratio equation to find a voltage or a number of turns
- Use input power = output power to find a current
- Explain why stepping the voltage up steps the current down
- Solve two-step problems that use both equations
This whole lesson is Paper 2 only content. It is not examined in Paper 1.
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Unlock This CourseThe turns ratio equation
You already know that a transformer has a primary coil and a secondary coil, and that the number of turns decides whether the voltage goes up or down. Now we put numbers on it. The voltages and the turns are linked by this equation:
Learn this (not given in the exam)
input (primary) voltage / output (secondary) voltage = primary turns / secondary turns
Vp / Vs = Np / Ns
The spec says "know and use", so this equation is not printed on the exam paper. You must learn it.
Key terms:
- Turns ratio: the number of turns on the primary coil compared with the number on the secondary coil, Np / Ns.
- Vp, Np, Ip: the voltage across, turns on and current in the primary coil.
- Vs, Ns, Is: the voltage across, turns on and current in the secondary coil.
Rearranging the equation
Do not try to learn four separate equations. Learn one, then cross-multiply. This gives Vp × Ns = Vs × Np. Then divide by whatever sits next to the quantity you want.
| To find | Rearranged equation |
|---|---|
| Output voltage Vs | Vs = Vp × Ns / Np |
| Input voltage Vp | Vp = Vs × Np / Ns |
| Primary turns Np | Np = Vp × Ns / Vs |
| Secondary turns Ns | Ns = Np × Vs / Vp |
A quick check before you start: if the secondary has fewer turns, your answer for Vs must be smaller than Vp. If it has more turns, it must be bigger.
Worked examples: turns and voltages
Worked example 1: a step-down transformer
A transformer has 1000 turns on its primary coil and 50 turns on its secondary coil. The input voltage is 230 V. Calculate the output voltage.
Vp / Vs = Np / Ns
Vs = Vp × Ns / Np = 230 × 50 / 1000
Vs = 11.5 V
The secondary has fewer turns, so the voltage went down, as expected.
Worked example 2: a step-up transformer
A transformer has 100 turns on its primary coil. It changes an input voltage of 12 V into an output voltage of 60 V. Calculate the number of turns on the secondary coil.
Ns = Np × Vs / Vp = 100 × 60 / 12
Ns = 500 turns
The voltage went up by 5 times, so the turns go up by 5 times.
Worked example 3: finding the primary turns
A transformer gives an output of 6 V from a 240 V input. The secondary coil has 25 turns. Calculate the number of turns on the primary coil.
Np = Vp × Ns / Vs = 240 × 25 / 6
Np = 1000 turns
Input power = output power
A transformer does not make energy. For a transformer that is 100% efficient, all the electrical energy going in each second comes out each second. So:
Learn this (not given in the exam)
input power = output power
Vp × Ip = Vs × Is
Each side is just power = current × voltage, which you met in the lesson on Electrical Power and Choosing Fuses. Again the spec says "know and use", so you must learn this one too. Real transformers waste a little energy as heat, but in these questions you use the 100% efficient case.
| To find | Rearranged equation |
|---|---|
| Primary current Ip | Ip = Vs × Is / Vp |
| Secondary current Is | Is = Vp × Ip / Vs |
| Output voltage Vs | Vs = Vp × Ip / Is |
| Input voltage Vp | Vp = Vs × Is / Ip |
Worked example 4: finding a current
A 100% efficient transformer has an input voltage of 230 V and an output voltage of 11.5 V. The current in the secondary coil is 4.0 A. Calculate the current in the primary coil.
Vp × Ip = Vs × Is
Ip = Vs × Is / Vp = 11.5 × 4.0 / 230
Ip = 46 / 230 = 0.20 A
Why a bigger voltage means a smaller current
The power on both sides must be equal. If the voltage is multiplied by a number, the current must be divided by the same number to keep V × I the same.
Worked example 5: a step-up transformer
The input to a 100% efficient transformer is 20 V and 5.0 A. The output voltage is 400 V. Calculate the output current.
Input power = 20 × 5.0 = 100 W, so output power = 100 W.
Is = Vp × Ip / Vs = 100 / 400 = 0.25 A
The voltage went up 20 times (20 V to 400 V). The current went down 20 times (5.0 A to 0.25 A).
So stepping the voltage up steps the current down, and stepping the voltage down steps the current up. A step-up transformer gives a higher voltage but a smaller current. It never gives more power.
Two-step problems
Some questions need both equations. Use the turns equation first to find the missing voltage. Then use the power equation to find the missing current.
Worked example 6: using both equations
A transformer has 2000 turns on its primary coil and 100 turns on its secondary coil. The input voltage is 240 V. The current in the secondary coil is 6.0 A. The transformer is 100% efficient. Calculate the current in the primary coil.
Step 1: find the output voltage.
Vs = Vp × Ns / Np = 240 × 100 / 2000 = 12 V
Step 2: find the output power.
Vs × Is = 12 × 6.0 = 72 W
Step 3: input power = output power, so find Ip.
Ip = 72 / 240 = 0.30 A
Check: the secondary has 20 times fewer turns, so its voltage is 20 times smaller and its current 20 times bigger. 0.30 × 20 = 6.0 A. Correct.
Common mistakes
Common mistakes
- Turning the turns ratio upside down. Primary is on top for both the voltages and the turns, or secondary is on top for both. Never mix them.
- Not checking the answer. A step-down transformer must give a smaller voltage. If your answer is bigger, you have swapped the numbers.
- Thinking a step-up transformer gives out more power. It gives more voltage but less current. The power is the same.
- Writing the answer without a unit. Voltages are in V, currents in A, power in W. Turns have no unit.
- Mixing up the primary and secondary currents in Vp × Ip = Vs × Is. Keep each current with its own voltage.
Exam-style question
A transformer has 600 turns on its primary coil and 30 turns on its secondary coil. The input voltage is 120 V. The transformer is 100% efficient.
(a) Calculate the output voltage. [2 marks]
(b) The current in the secondary coil is 3.0 A. Calculate the output power. [2 marks]
(c) Calculate the current in the primary coil. [2 marks]
(d) State whether this is a step-up or a step-down transformer. [1 mark]
Model answer
(a) Vs = Vp × Ns / Np = 120 × 30 / 600 (1) = 6.0 V (1)
(b) Power = Vs × Is = 6.0 × 3.0 (1) = 18 W (1)
(c) Input power = output power = 18 W, so Ip = 18 / 120 (1) = 0.15 A (1)
(d) Step-down (1).
Exam tip
In a "calculate" question, write the equation, then the numbers, then the answer with its unit. Part (c) needs the answers from parts (a) and (b), so keep your working for every part.