Chapter 7 of 8

All 8 chapters
  1. 1Magnetic fields, readunderstood
  2. 2Fields around wires and coils, readunderstood
  3. 3The motor effect, readunderstood
  4. 4Electric motors, readunderstood
  5. 5Electromagnetic induction, readunderstood
  6. 6Generators and dynamos, readunderstood
  7. 7Transformers, readunderstood
  8. 8Speakers and microphones, readunderstood

S4.13.7 Chapter 7

Transformers

A phone charger turns the supply of your home into a few volts. Power lines carry thousands of volts. What changes the voltage, and why do the power lines use so much?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Use the turns ratio to calculate output voltage
  • Explain why power lines carry electricity at very high voltages

A transformer changes the voltage of an alternating current. It has two coils of wire wound on a ring of soft iron, called the core. The coils are not joined to each other. The only link between them is the magnetic field in the core.

The coil joined to the supply is the primary coil. The coil that gives the output is the secondary coil. We write Np and Ns for their numbers of turns, and Vp and Vs for their voltages.

Here is how it works. An alternating current in the primary makes a field that keeps changing. The iron core carries the field through the secondary. A changing field through a coil induces a voltage in it. So the secondary gives an alternating voltage.

A transformer. A ring of iron labelled iron core, with a coil of 5 turns on its left side labelled primary, 5 turns, and a coil of 10 turns on its right side labelled secondary, 10 turns. An AC supply of 6 V is joined to the primary and a lamp showing 12 V is joined to the secondary. Labels: primary, secondary, iron core, lamp, AC supply, 5 turns, 10 turns, 6 V, 12 V.primarysecondaryiron core5 turns10 turnsAC supplylamp6 V12 V
A step-up transformer. The secondary has twice as many turns as the primary, so it gives twice the voltage.

Why does it need alternating current? A steady direct current makes a steady field. The field through the secondary does not change, so no voltage is induced. The lamp stays dark. Only when you switch the current on or off is there a brief change.

Each turn of the secondary gets the same voltage from the changing field. So the more turns, the more voltage. The voltages are in proportion to the turns. This is the rule for the turns ratio:

Vp ÷ Vs = Np ÷ Ns. Rearranged, Vs = Vp × Ns ÷ Np. Check it on the picture: 6 V × 10 ÷ 5 = 12 V. The secondary voltage is the primary voltage times the ratio of secondary turns to primary turns. Take care to put Ns on top.

A transformer with more turns on the secondary is a step-up transformer: it raises the voltage. One with fewer turns on the secondary is a step-down transformer: it lowers the voltage. Many phone chargers have a small step-down transformer inside.

Worked example

A transformer has 50 turns on the primary and 400 on the secondary. The primary voltage is 8 V AC. What is the secondary voltage?

  1. Use Vs = Vp × Ns ÷ Np, with Vp = 8 V, Np = 50 and Ns = 400.
  2. The ratio Ns ÷ Np is 400 ÷ 50 = 8.
  3. So Vs = 8 V × 8 = 64 V.

Answer: 64 V

A transformer. A ring of iron labelled iron core, with a coil of 10 turns on its left side labelled primary, 10 turns, and a coil of 5 turns on its right side labelled secondary, 5 turns. An AC supply of 12 V is joined to the primary and a lamp showing 6 V is joined to the secondary. Labels: primary, secondary, iron core, lamp, AC supply, 10 turns, 5 turns, 12 V, 6 V.primarysecondaryiron core10 turns5 turnsAC supplylamp12 V6 V
A step-down transformer. The secondary has half as many turns as the primary, so it gives half the voltage.

A transformer does not make power. For an ideal transformer, which wastes no energy, the power out equals the power in. Power is voltage times current, so Vp × Ip = Vs × Is. Raise the voltage and the current falls by the same ratio.

Real transformers waste a little energy as heat in the coils and the core. A very large power transformer can be more than 98 percent efficient, so for these sums we treat it as ideal. An ideal transformer is 100 percent efficient.

Now power lines. A power station needs to send a lot of power along wires over long distances. The wires have a resistance, so they get warm and lose energy as heat. The power lost in a wire is P = I² × R, with I the current and R the resistance of the line.

The power sent is P = V × I. To send the same power with a bigger voltage V, you need a smaller current I. Because the heat lost depends on I squared, a small current wastes very little. Make the voltage 10 times as big, and the current becomes a tenth and the loss a hundredth.

Worked example

A town needs 20 000 W sent along a line of resistance 2 Ω. Find the heat lost in the line at 2 000 V, and then at 20 000 V.

  1. At 2 000 V the current is 20 000 ÷ 2 000 = 10 A.
  2. The heat lost is I² × R = 10² × 2 = 200 W.
  3. At 20 000 V the current is 20 000 ÷ 20 000 = 1 A.
  4. The heat lost is I² × R = 1² × 2 = 2 W.

Answer: 200 W, then 2 W

The voltage went up 10 times and the loss went down 100 times. The table shows the same pattern for a bigger case. The power sent is 100 000 W, the line has a resistance of 5 Ω, and the voltage goes up by tens.

A table with the columns Volts, Amps and Heat lost. Rows: 1 000 V, 100 A, 50 000 W. 10 000 V, 10 A, 500 W. 100 000 V, 1 A, 5 W.VoltsAmpsHeat lost1 000 V100 A50 000 W10 000 V10 A500 W100 000 V1 A5 W
100 000 W sent along a line of 5 Ω. At the lowest voltage, half the power is lost. At the highest, almost none is.

So the grid works like this. A step-up transformer at the power station raises the voltage to many thousands of volts. The lines carry a small current. Near towns, step-down transformers lower the voltage in stages, down to the voltage homes use. That is still dangerous: never touch mains wiring. The voltages differ from place to place.

Five boxes joined by arrows pointing down, in this order: power station, step-up, power lines, step-down, homes. Notes beside three of them give example voltages: 25 000 V beside power station, 400 000 V beside power lines and 230 V beside homes.power station25 000 Vstep-uppower lines400 000 Vstep-downhomes230 V
Example voltages. Real grids differ from place to place. High voltage lines are dangerous. Stay away from them and from fallen wires.

Try it

Hear why a transformer needs changing current

You need: a thick iron nail or bolt, thin insulated wire, a torch cell, an old earphone with the plug cut off and the wire ends bared, by an adult, sandpaper or a nail file, tape.

Be safe: Ask an adult to cut off the plug and bare the ends. Clean the wire ends by rubbing them with sandpaper or a nail file, not a knife. Use one torch cell only. Touch the wires to it for one second at a time, because the coil gets warm and drains the cell. Hold the earphone loosely near your ear, not pushed in. Never connect a transformer or coil to mains electricity.

  1. Wind 50 turns of wire along the nail, for the primary. Leave the ends free. Wind 100 turns on the other half of the nail, apart from the primary, for the secondary.
  2. Join the secondary to the earphone wires. Hold the earphone loosely near your ear.
  3. Touch the primary wires to the cell for one second, then take them away.
  4. Now try holding the primary joined to the cell for a moment and listen.

What you will see: You may hear a faint click when the primary is joined to the cell, and another when it is taken away. You hear nothing in between. A steady current makes a steady field, and the secondary needs a changing one. That is why transformers work on AC and not on DC.

If you cannot try it, this is what happens.
A table with the columns Primary and Earphone. Rows: connected, click. held on, silent. disconnected, click.PrimaryEarphoneconnectedclickheld onsilentdisconnectedclick

A wrong idea many people have

A transformer works on a battery just as well as on AC.

Why it feels right: A battery makes a current, and a current makes a field, so the secondary should get a voltage.

The test that breaks it: Join the primary to a cell and hold it on. After a click, the lamp or earphone on the secondary does nothing. A steady current makes a steady field, and a steady field induces no voltage.

What is true: A transformer needs a changing current in the primary. That is why it works on AC. A direct current gives only a brief change when it is switched on or off.

A wrong idea many people have

The turns ratio is Np ÷ Ns for the secondary voltage: Vs = Vp × Np ÷ Ns.

Why it feels right: The ratio Np ÷ Ns appears in the equation, and it is easy to put it the wrong way up.

The test that breaks it: A step-up transformer has more turns on the secondary. It must give a bigger voltage. Using Np ÷ Ns would give a smaller one for 50 turns and 400 turns: 8 V × 50 ÷ 400 = 1 V. That cannot be right.

What is true: The secondary voltage is bigger when the secondary has more turns. Put Ns on top: Vs = Vp × Ns ÷ Np.

A wrong idea many people have

A higher voltage in the power lines means more energy is lost.

Why it feels right: High voltage sounds dangerous and powerful, so it seems it should waste more.

The test that breaks it: Send 20 000 W at 2 000 V and the line loses 200 W. Send it at 20 000 V and it loses 2 W. The current is smaller, and the heat depends on the current squared.

What is true: For the same power, a higher voltage means a smaller current. A smaller current means much less heat in the wires. The energy lost is lower, not higher.

Key words

transformer
a device with two coils on an iron core that changes the voltage of an AC supply.
primary coil
the coil joined to the supply. Np is its number of turns.
secondary coil
the coil that gives the output. Ns is its number of turns.
step-up transformer
a transformer with more turns on the secondary, which raises the voltage.
step-down transformer
a transformer with fewer turns on the secondary, which lowers the voltage.
turns ratio
Vp ÷ Vs = Np ÷ Ns.

Back to your guess

The answer is B: Power lines use a high voltage so that the current is small and little energy is lost as heat.

The same power can be sent as a high voltage and a small current, or a low voltage and a large current. The heat lost in the wires depends on the current, squared. So a high voltage with a small current wastes much less energy. Transformers change the voltage at each end.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Why does a transformer need alternating current?

    Tap your answer.

    1. Not this one. A direct current makes a field as strong as an alternating one of the same size. The trouble is that the field does not change. Try another.

    2. Not this one. The iron core carries a field of either kind. A transformer needs the field to change. Try another.

    3. Yes, that is right. A voltage is induced only while the field through the secondary is changing. Alternating current makes a field that keeps changing.

    4. Not this one. Heat is a waste in a transformer. It works through a changing magnetic field. Try another.

    See the answer

    Because a steady current makes a steady field, which induces no voltage in the secondary.

    A voltage is induced only while the field through the secondary is changing. Alternating current makes a field that keeps changing.

    • If you chose A: A direct current makes a field as strong as an alternating one of the same size. The trouble is that the field does not change.
    • If you chose B: The iron core carries a field of either kind. A transformer needs the field to change.
    • If you chose D: Heat is a waste in a transformer. It works through a changing magnetic field.

  2. Which equation links the voltages and the turns of a transformer?

    Tap your answer.

    1. Yes, that is right. The voltage on each coil is in proportion to its number of turns, so Vp ÷ Vs = Np ÷ Ns.

    2. Not this one. That has the turns the wrong way up. A secondary with more turns gives a bigger voltage, so Vs is on top with Ns: Vs ÷ Vp = Ns ÷ Np. Try another.

    3. Not this one. The voltages and turns are in proportion. They are not multiplied together. Try another.

    4. Not this one. The voltages and turns are in proportion, so the equation is a ratio, not a sum. Try another.

    See the answer

    Vp ÷ Vs = Np ÷ Ns

    The voltage on each coil is in proportion to its number of turns, so Vp ÷ Vs = Np ÷ Ns.

    • If you chose B: That has the turns the wrong way up. A secondary with more turns gives a bigger voltage, so Vs is on top with Ns: Vs ÷ Vp = Ns ÷ Np.
    • If you chose C: The voltages and turns are in proportion. They are not multiplied together.
    • If you chose D: The voltages and turns are in proportion, so the equation is a ratio, not a sum.

  3. What is the same on both sides of an ideal transformer?

    Tap your answer.

    1. Not this one. The voltage changes. That is the job of a transformer. Try another.

    2. Yes, that is right. An ideal transformer wastes no energy, so the power out equals the power in: Vp × Ip = Vs × Is.

    3. Not this one. If the voltage goes up, the current goes down by the same ratio, so the current changes. Try another.

    4. Not this one. The turns are different on the two coils. The ratio of turns decides how much the voltage changes. Try another.

    See the answer

    The power.

    An ideal transformer wastes no energy, so the power out equals the power in: Vp × Ip = Vs × Is.

    • If you chose A: The voltage changes. That is the job of a transformer.
    • If you chose C: If the voltage goes up, the current goes down by the same ratio, so the current changes.
    • If you chose D: The turns are different on the two coils. The ratio of turns decides how much the voltage changes.

  4. Why do power lines use a very high voltage?

    Tap your answer.

    1. Not this one. The speed of the energy does not depend on this. The reason is the size of the current. Try another.

    2. Yes, that is right. The power sent is V × I, so a higher V needs a smaller I. The heat lost is I² × R, which falls very quickly as I falls.

    3. Not this one. The resistance of the wires does not depend on the voltage. The loss is smaller because the current is smaller. Try another.

    4. Not this one. It is the other way. For the same power, a higher voltage means a smaller current and less heat lost. Try another.

    See the answer

    A higher voltage means a smaller current, so much less energy is lost as heat.

    The power sent is V × I, so a higher V needs a smaller I. The heat lost is I² × R, which falls very quickly as I falls.

    • If you chose A: The speed of the energy does not depend on this. The reason is the size of the current.
    • If you chose C: The resistance of the wires does not depend on the voltage. The loss is smaller because the current is smaller.
    • If you chose D: It is the other way. For the same power, a higher voltage means a smaller current and less heat lost.

  5. The transformer in the picture has 6 turns on its primary and 2 turns on its secondary. The primary voltage is 30 V. What is the secondary voltage?

    A transformer. A ring of iron labelled iron core, with a coil of 6 turns on its left side labelled primary, 6 turns, and a coil of 2 turns on its right side labelled secondary, 2 turns. An AC supply of 30 V is joined to the primary and a lamp showing a question mark is joined to the secondary. Labels: primary, secondary, iron core, lamp, AC supply, 6 turns, 2 turns, 30 V, ?.primarysecondaryiron core6 turns2 turnsAC supplylamp30 V?
    Tap your answer.

    1. Not this one. You put the turns ratio upside down. The secondary has fewer turns, so the voltage must fall. Try another.

    2. Not this one. You added the turns. The voltage is multiplied by the ratio Ns ÷ Np, not added to. Try another.

    3. Not this one. You took the turns away from the volts. The voltage is multiplied by the ratio of the turns. Try another.

    4. Yes, that is right. Vs = Vp × Ns ÷ Np = 30 V × 2 ÷ 6 = 10 V.

    See the answer

    10 V

    Vs = Vp × Ns ÷ Np = 30 V × 2 ÷ 6 = 10 V.

    • If you chose A: You put the turns ratio upside down. The secondary has fewer turns, so the voltage must fall.
    • If you chose B: You added the turns. The voltage is multiplied by the ratio Ns ÷ Np, not added to.
    • If you chose C: You took the turns away from the volts. The voltage is multiplied by the ratio of the turns.

  6. An ideal step-up transformer raises the voltage from 100 V to 400 V. How does the current in the secondary compare with the current in the primary?

    Tap your answer.

    1. Yes, that is right. Vp × Ip = Vs × Is. The voltage is four times as big, so the current is a quarter as big.

    2. Not this one. Power stays the same, so if the voltage becomes four times as big, the current must become a quarter. Try another.

    3. Not this one. It cannot. Power is voltage times current, and an ideal transformer keeps the power the same. Try another.

    See the answer

    It is a quarter as big.

    Vp × Ip = Vs × Is. The voltage is four times as big, so the current is a quarter as big.

    • If you chose B: Power stays the same, so if the voltage becomes four times as big, the current must become a quarter.
    • If you chose C: It cannot. Power is voltage times current, and an ideal transformer keeps the power the same.

  7. From an earlier chapter

    Which machine has a split ring and gives direct current in pulses?

    Tap your answer.

    1. Not this one. An alternator has slip rings and gives alternating current. Go to S4.13.6. Try another.

    2. Not this one. A transformer has no moving parts. It changes the voltage of an alternating supply. Go to S4.13.6. Try another.

    3. Not this one. An electromagnet is a coil with a core. It makes a field and gives no current. Go to S4.13.6. Try another.

    4. Yes, that is right. A dynamo is a generator with a split ring. It swaps the brushes every half turn, so the current outside always goes the same way.

    See the answer

    A dynamo.

    A dynamo is a generator with a split ring. It swaps the brushes every half turn, so the current outside always goes the same way.

    • If you chose A: An alternator has slip rings and gives alternating current. Go to S4.13.6.
    • If you chose B: A transformer has no moving parts. It changes the voltage of an alternating supply. Go to S4.13.6.
    • If you chose C: An electromagnet is a coil with a core. It makes a field and gives no current. Go to S4.13.6.

  8. A transformer has 40 turns on its primary and 100 turns on its secondary. The primary voltage is 12 V. What is the secondary voltage?

    See the answer

    30 V

    Vs = Vp × Ns ÷ Np = 12 × 100 ÷ 40 = 30 V.

  9. A step-down transformer has 600 turns on its primary and is joined to a 120 V supply. It must give 24 V. How many turns does its secondary need?

    See the answer

    120 turns

    Ns = Np × Vs ÷ Vp = 600 × 24 ÷ 120 = 120 turns.

  10. An ideal transformer has a secondary voltage of 20 V and a secondary current of 10 A. The primary voltage is 100 V. What is the primary current?

    See the answer

    2 A

    Vp × Ip = Vs × Is, so Ip = 20 × 10 ÷ 100 = 2 A.

  11. A power line has a resistance of 3 Ω and carries a current of 20 A. How much power is lost as heat in the line?

    See the answer

    1 200 W

    P = I² × R = 20² × 3 = 400 × 3 = 1 200 W.

  12. A town needs 60 000 W sent along a line of resistance 4 Ω. The line voltage is 6 000 V. How much power is lost as heat in the line?

    See the answer

    400 W

    The current is P ÷ V = 60 000 ÷ 6 000 = 10 A. The heat lost is I² × R = 10² × 4 = 400 W.

Keep it

Copy this into your exercise book.

A transformer needs AC. Vp ÷ Vs = Np ÷ Ns. Ideal: Vp × Ip = Vs × Is. Power lines: high voltage, small current, little heat (I² × R).

Draw: A transformer with two coils on a core, with turns and volts written beside it.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

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