Physics › Magnetic fields › Transformers

Transformers

Two coils share one core, and Faraday's law does the rest: the turns ratio sets the voltage ratio, imperfections drain a little power as heat, and the whole national grid is built on one consequence, that high voltage means small current and tiny transmission losses.

Year 13AQA 3.7.5.6OCR A 6.3.3

Builds on Electromagnetic induction: Faraday and Lenz and Alternating currents.

IN THIS TOPIC

  • Explain transformer operation through alternating flux and induced emf.
  • Use the turns-ratio and efficiency equations, and name the causes of inefficiency.
  • Calculate transmission-line power losses and explain the high-voltage grid.

WHAT YOU PROBABLY THINK

A transformer can step up power.

Two coils, one flux

one shared flux, always changingprimary a.c.secondary emffive turnseight turns
FIG. 1Alternating current in the five-turn primary drives a magnetic flux round the iron core, pulsing and reversing with the supply. The eight-turn secondary links that same ever-changing flux, so an emf appears across it, a quarter cycle out of step because emf follows the rate of change, not the flux itself. Stop the change and the secondary dies: transformers run on a.c. or not at all. More secondary turns than primary makes this one step up the voltage.

A transformer is two coils wound on one iron core. Alternating current in the primary drives an alternating flux round the core, and the core delivers that same changing flux through every turn of the secondary, where Faraday's law induces an emf in each turn. More turns collect more emf, and the voltages sit in the turns ratio:

NsNp = VsVpON YOUR DATA SHEET

More secondary turns step up the voltage; fewer step it down. The mechanism also explains the one absolute restriction: a transformer needs changing flux, so it works on ac only. A steady dc primary current makes a steady flux, and a steady flux induces nothing.

Where the power leaks

An ideal transformer passes power through untouched, and with the output power IsVs and input power IpVp, the report card is

efficiency = IsVsIpVpON YOUR DATA SHEET
Why cores are laminated: a solid core lets large eddy currents swirl and heat it; thin insulated sheets cut the loops smallsolid core: large eddy currentslaminated: loops cut smallthe changing flux induces currents in the core itself
FIG. 2The changing flux induces eddy currents in the core itself; laminations cut the loops small and starve the loss.

Real transformers reach the high nineties of percent, and the shortfall has nameable causes. The windings have resistance and warm up as current flows. The changing flux induces eddy currents in the iron core itself, swirling charge that heats the metal; building the core from thin insulated laminations cuts those loops small and is the standard fix. A little flux leaks, missing the secondary, and a little energy is spent repeatedly re-magnetising the core each cycle. Four causes, four marks, whenever the question asks. The opening claim has it backwards: stepping up the voltage steps the current down by at least the same factor, because the power out can never exceed the power in.

The grid's one big idea

Why the grid runs at hundreds of kilovolts: for the same power, raising the voltage lowers the current, and cable loss falls as the current squaredstationstepuphigh V, small Istepdownhomesloss = I²R: current is the villain, so the grid starves it25× the volts, the same power, 625× less lost
FIG. 3Step up, transmit at high voltage and small current, step down: cable loss goes as the current squared.

Transmission cables have resistance, and the power they waste is P = I2R: the current, squared, is the villain. For a fixed power delivered, P = IV, raising the voltage lowers the current in proportion, and the squared dependence turns a modest voltage increase into a dramatic loss collapse: twenty-five times the voltage means six hundred and twenty-five times less power lost in the same cables. This is the entire logic of the national grid: step up to hundreds of kilovolts at the power station, cross the country at small current, and step back down near the user. The transformer's existence is why mains electricity is ac at all.

THE EXAM BIT

  • The operation answer is a Faraday chain: alternating primary current, alternating core flux, changing flux linkage in the secondary, induced emf. Four links, in order.
  • Transformers work on ac only, because induction needs changing flux. The dc case scores as its own mark: steady flux, no emf.
  • The four inefficiency causes are a list question: winding resistance, eddy currents (laminations reduce them), flux leakage, and the energy of repeatedly magnetising the core.
  • Grid questions want the argument in symbols: fixed P = IV, so higher V means lower I, and cable loss I2R falls as the square. Name the square.
  • In efficiency calculations keep primary and secondary quantities strictly apart; the subscripts are where the marks hide.

CHECK YOURSELF

A station sends 10 MW down cables of total resistance 5.0 Ω. Find the power lost when transmitting at 25 kV, and at 400 kV, as a percentage of the power sent each time.

Show a hint

Current first from P = IV; then the loss is that current squared times R.

Show the answer

At 25 kV: I = P/V = 107/2.5 × 104 = 400 A, so loss = I2R = 4002 × 5.0 = 8.0 × 105 W: 0.80 MW, 8.0% gone.

At 400 kV: I = 25 A, so loss = 252 × 5.0 = 3.1 × 103 W: 3.1 kW, 0.031%.

Sixteen times the voltage, 256 times less loss: the square at work, and the reason pylons carry hundreds of kilovolts.

Turns set the voltage ratio; power only ever passes through.

The grid starves I²R: high volts, small current, tiny loss.

No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.