Workings of a Transformer
Key idea: G3 Physics and O-Level Physics electromagnetic induction: how an iron-cored transformer works, step-up/step-down equations, and why high voltage transmission reduces cable losses.
By the end, you can
- Describe the structure and induction principle of an iron-cored transformer.
- Apply both ideal-transformer equations.
- Explain why high-voltage transmission reduces cable heating loss.
Topic lessons
- Magnetism (magnets and materials)
- Properties of magnets
- Magnetic field and magnetic field lines
- Induced magnetism and electrical method of magnetisation
- Temporary and permanent magnets
- Magnetic field due to current in a straight wire
- Magnetic field due to current in a solenoid
- Electric bell
- Circuit breaker
- Force on a current-carrying conductor and Fleming's left-hand rule
- D.C. motor
- Electromagnetic induction and Lenz's law
- A.C. generator
- Workings of a transformer
1. Definition
A. Transformer
A transformer changes an a.c. voltage using electromagnetic induction.
B. Step-up and step-down
- Step-up: higher output voltage.
- Step-down: lower output voltage.
O Level expects you to describe the structure and operation of a simple iron-cored transformer, apply the ideal transformer equations, and explain why high voltage transmission reduces cable losses.
2. Key Ideas
- Transformers need a.c. (changing current → changing magnetic field). A steady d.c. does not produce continuous induction.
- Primary coil: input VP, turns NP. Secondary coil: output VS, turns NS.
- Ideal transformer equations (6091 forms):
VP/VS = NP/NS For an ideal transformer only:
VP IP = VS IS
- Step-up: NS > NP so VS > VP.
Step-down: NS < NP so VS < VP.
3. Detailed Explanations
A. How a transformer works (principle)
- An a.c. current in the primary coil produces a changing magnetic field in the iron core.
- The changing magnetic field links the secondary coil.
- This changing flux induces an e.m.f. (voltage) in the secondary coil.
B. Turns ratio controls voltage ratio
More turns on the secondary coil gives a larger induced voltage.
C. Energy loss in cables and high-voltage transmission
Power transmitted is P = VI. Compare transmission systems carrying the same power through cables with the same resistance R.
For fixed transmitted power:
- higher voltage means smaller current, since I = P/V
- cable heating power is Pₗₒₛₛ = I²R
- therefore smaller current gives much less heating loss in the same cables
So power is transmitted at high voltage and then stepped down near homes for safety and use.
VP IP = VS IS assumes no energy loss. A real transformer has VS IS lt VP IP because some energy is dissipated, for example by heating in the coils and core.
Use the Motor, Generator & Transformer Lab to compare primary and secondary turns, then predict whether each setup is step-up or step-down.
4. Common Mistakes
- Using transformer equations for d.c. (needs changing flux, so use a.c.).
- Mixing up NP and NS in the turns ratio.
- Saying a step-up transformer “increases power”. In an ideal transformer, power in equals power out; in a real transformer, output power is lower.
- Saying high voltage alone reduces loss. The comparison must keep transmitted power and cable resistance fixed: high V gives low I, so I²R is smaller.
5. Exam Tips
- Write the ratio equation first: VP/VS = NP/NS.
- If current is asked, use VP IP = VS IS.
- For transmission: “for the same transmitted power, high V → low I; for the same cable resistance, Pₗₒₛₛ = I²R is smaller”.
6. Worked Examples
Example 1: Voltage ratioCore
A transformer has NP = 200 turns and NS = 50 turns. The primary voltage is 240 V. Find the secondary voltage (ideal transformer).
Show Answer
VP/VS = NP/NS = 200/50 = 4
So VS = VP/4 = 240/4 = 60 V.
Example 2: Current ratioCore
In Example 1, if the secondary current is 2.0 A, find the primary current (ideal transformer).
Show Answer
VP IP = VS IS
IP = VS IS/VP = 60 × 2.0/240 = 0.50 A
Example 3: Step-up or step-down?Core
A transformer has NP = 400 turns and NS = 1200 turns. Is it step-up or step-down (for voltage)?
Show Answer
Since NS > NP, it is step-up, so VS > VP.
Example 4: Finding turnsCore
An ideal transformer steps 12 V up to 240 V. The primary coil has 50 turns. How many turns are on the secondary coil?
Show Answer
Using ; fracVPVS =; fracNPNS:
; frac12240 =; frac50NS; Rightarrow NS = 50; times; frac24012 = 1000
So NS = 1000 turns.
Example 5: Transmission current comparisonCore
20 kW of power is transmitted. Compare the current if the voltage is (i) 200 V and (ii) 20 kV.
Show Answer
Use P = VI.
(i) I =; frac20000200 = 100; ,; textA
(ii) I =; frac2000020000 = 1; ,; textA
Higher voltage gives much smaller current, so cable heating losses are much smaller.
If the same cables are used, the current falls from 100 A to 1 A, a factor of 100. Since Pₗₒₛₛ = I²R, the cable heating power falls to 1/100² = 1/10 000 of its original value.
7. Mind Stretchers
Mind stretcher 1: Why step up then step down?Extension
Why are transmission lines typically stepped up and then stepped down again near homes?
Show Answer
Stepping up increases voltage and reduces current for the same power, so cable heating losses are smaller during transmission. Near homes, the voltage is stepped down to safer, usable levels.
Mind stretcher 2: Why d.c. does not workExtension
Why does a transformer not work properly with a steady d.c. supply?
Show Answer
Steady d.c. produces a (nearly) constant magnetic field in the core, so there is no changing flux to induce a voltage in the secondary coil.
8. Practice and next step
Solve a turns-ratio and transmission-loss comparison in the Motor–Generator–Transformer Lab, then complete the Magnetism Structured Practice.
Recommended next step
High-voltage transmission: concept check
Why this will help: Use one focused question set to check that you can apply the lesson without prompts.
About 10 minutes