Transformer equations
Turns ratio (voltage): — voltage is proportional to the number of turns ( = primary/secondary voltage, = turns). Ideal transformer (power): , so — the current ratio is the inverse of the turns ratio. A step-up transformer raises voltage and lowers current by the same factor, keeping power constant.
Structure and why a.c. only
Two coils (primary, secondary) are wound on a soft-iron core and are electrically isolated — only the magnetic field links them. An alternating current in the primary makes an alternating flux in the core, which induces an alternating e.m.f. in the secondary. Soft iron is chosen because it magnetises and demagnetises easily, following the field. d.c. would not work: it gives a steady flux, and a steady (unchanging) flux induces no e.m.f.
Step-up, step-down and the Grid
Step-up (, so ): used at power stations to raise voltage for the National Grid. High voltage → low current ( constant) → far less energy wasted as heat in the cables (). Step-down (, so ): used near homes to lower voltage to a safe 230 V. Without transformers the Grid would need huge currents and lose enormous energy heating the cables.
Drawn from real examiner reports.
Current ratio is the inverse
Do not apply the turns ratio to current in the same direction. Voltage: ; current is inverted: . A step-up that doubles voltage halves current — because (power is conserved). If your answer makes power rise across the transformer, it is wrong.
June 2024 Paper 2PR Q4(b): many candidates said a step-up transformer raises voltage but wrongly described the current increasing too, losing the current-reduction mark.
No current flows through the core
The primary and secondary coils are electrically isolated — no current passes from one to the other through the iron core. The core carries only magnetic flux. The chain is: a.c. in primary → changing flux in the core → induced e.m.f. in the secondary → current in the secondary's own circuit. Energy moves via the magnetic field, not a wire.
November 2023 Paper 2P Q4(b): the principal misconception was that current from the primary travels through the iron core into the secondary; precision of language mattered.
e.m.f. is energy per unit charge
Defining e.m.f. as "the voltage of the source/supply" scores zero. The mark scheme needs two elements: energy transferred per unit charge, by the source; unit V. A transformer induces an e.m.f. in the secondary — energy given TO charges — as opposed to a p.d., which is energy taken FROM charges by a component.
Transformers need a.c., not d.c.
A transformer works only on alternating current: a.c. gives a continuously changing flux, which induces an e.m.f. in the secondary. Direct current gives a steady flux, which does not change, so it induces no e.m.f. and there is no output. Connecting a transformer to a d.c. cell produces no secondary voltage.
Step-up vs step-down
A step-up transformer has MORE secondary turns () and a HIGHER secondary voltage; a step-down has FEWER secondary turns and a LOWER secondary voltage. The name describes what happens to the voltage, not the current. Memory aid: step-up means the secondary turns go up.
Link low current to less heating
It is not enough to say high-voltage transmission "reduces energy loss". Give the mechanism: high voltage → low current → less power wasted as heat in the cables, because . Halving the current cuts the heating to a quarter. Name the step to earn the mark.
June 2024 Paper 2PR Q4(b): the connection between low current and reduced cable heating ($I^2R$) was seen less often than knowing transformers change voltage.
Draw and label both Grid transformers
For a National Grid diagram, draw TWO transformers — step-up at the power station, step-down near the consumer — and label each. Common losses: only one transformer, swapped labels, or no labels. Draw more loops on the higher-voltage side.
Transformer calculation scaffold
For voltage or turns, use . For current, use the power equation , not the turns ratio in the same direction. Rearrange for the unknown first, substitute, then state the unit (V, A or turns).
Sense-check with power conservation
For an ideal transformer, power in = power out: . After a current answer, check the two powers match. If voltage went up, current must go down (and vice versa); an answer where power rises across the transformer is wrong.
Label the transformer diagram
On a transformer diagram, label the primary and secondary coils, the soft-iron core, and , and show the a.c. supply symbol () on the primary. For step-up/down, draw the turns visibly unequal so the type is clear. A d.c. cell symbol loses the mark.
| Relationship | Formula | What it means |
|---|---|---|
| Turns ratio (voltage) | Voltage is proportional to number of turns | |
| Ideal transformer (power) | Input power = output power (no energy lost) | |
| Current ratio (derived) | Current ratio is the inverse of the turns ratio |
Where = primary voltage (V), = secondary voltage (V), = number of primary turns, = number of secondary turns, = primary current (A), = secondary current (A).
Key definitions:
Define electromotive force (e.m.f.).
A step-up transformer has 400 turns on the primary coil and 2000 turns on the secondary coil. The primary voltage is 240 V.
Calculate the secondary voltage. Give the unit of your answer.
