V=-N(dΦ/dt)
Electricity and Magnetism

Transformers

for 14-16

Transformers are vital to the distribution system for electrical power.

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A model transformer

V=-N(dΦ/dt)
Electricity and Magnetism

A model transformer

Practical Activity for 14-16

Class practical

Shows the basic principle of any transformer: a change in current in the primary coil will induce an e.m.f. (voltage) in the secondary coil.

Apparatus and Materials

For each student group...

  • Galvanometer, sensitive to e.g. 3.5–0–3.5 mA., 10 ohm resistance (see note below)
  • C-cores, laminated iron, 2
  • Copper wire, insulated with bare ends, 200 cm, 2 lengths
  • Clip for C-cores
  • Switch
  • Cell, 1.5 V in holder
  • Leads, 4 mm, 4
  • Lamp in lampholder, either 1.25 V or 2.5 V, 2
  • Power supply, low-voltage


Please note: Strictly speaking, we generate e.m.f. but frequently measure the current through the load resistor (i.e. the wire) using a galvanometer (not an ammeter).

Health & Safety and Technical Notes

If a zinc chloride cell is used, it will polarize in 60 s or less and must be left overnight to recover.

If an alkaline manganese cell is used, there is a danger of the cell overheating with a risk of explosion: complete the circuit for 30 s or less.

If a rechargeable cell (NiCd) is used, the wire will get very hot and the cell will be discharged in a few minutes: do the experiment as quickly as possible.

Read our standard health & safety guidance


C-cores should be stored in their original pairs and clipped together to ensure a good fit and to prevent grit and dirt damaging them.

The slightest gap will dramatically reduce the efficiency of the transformer.

Procedure

  1. Wind 10 turns of insulated wire around one arm of a C-core. This forms the primary coil.
  2. Wind 25 turns of insulated wire around one arm of the other C-core. This forms the secondary coil.
  3. Connect the ends of the secondary coil to the galvanometer.
  4. Connect the ends of the primary coil, via the switch, to the cell.
  5. Close the switch. Bring the primary coil up to the secondary coil, as illustrated.
  6. Clip the two C-cores together to form a transformer. Open and close the switch, and watch the galvanometer deflection changing.
  7. Replace the galvanometer with a lamp, and operate the switch.
  8. Connect the primary coil to the a.c. terminals of the power supply (2 V). Connect a second lamp in parallel with the coil, as shown. Switch on. Which lamp glows more brightly?

Teaching Notes

  • Care should be taken not to leave the cells connected for any length of time, as the primary coil may become hot.
  • The lamp connected across the power supply will only glow faintly, whereas the lamp across the secondary glows brightly as long as the length of wire in each coil is the same. To confirm that this is not due to a difference in the two lamps, these should be interchanged.
  • Students could change the numbers of turns of wire on each coil; in this case, the total length should remain constant (so that its resistance does not change).

This experiment was safety-tested in June 2007

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A step-up transformer

V=-N(dΦ/dt)
Electricity and Magnetism

A step-up transformer

Practical Activity for 14-16

Demonstration

Using lamps and meters to compare the voltages in the primary and secondary coils of a transformer.

Apparatus and Materials

  • Demonstration meters, with AC dials (1 A, 5 A, 5 V), 2
  • C-cores and clip, pair of
  • Lamps (2.5 V, 0.3 A) in holders, 2
  • Copper wire, insulated with bare ends, 200 cm, 2 lengths
  • Leads, 4 mm, 4
  • Power supply, low-voltage


Health & Safety and Technical Notes

If general-purpose low voltage power units are used, it is possible that students will increase the voltage applied to the primary above the suggested 2 V. In principle, the secondary voltage could become more than twice the primary one. In practice, the overload cut-out will operate before the secondary voltage becomes hazardous.

Read our standard health & safety guidance


Procedure

  1. Wind 10 turns of insulated wire around one arm of a C-core. This forms the primary coil.
  2. Wind 25 turns of insulated wire around one arm of the other C-core. This forms the secondary coil.
  3. Clip the two C-cores together to form a transformer.
  4. Connect the ends of the secondary coil to a lamp.
  5. Connect the ends of the primary coil to the AC terminals of the power supply. Connect a second lamp in parallel.
  6. Switch on. Both lamps should light; the secondary lamp should be brighter.
  7. Insert the demonstration ammeter and voltmeter in the primary circuit, as shown. Note the readings.
  8. Insert the demonstration ammeter and voltmeter in the secondary circuit, as shown. Note the readings.

Teaching Notes

  • Although the primary current is less than 1 amp, it is advisable to use the 5-amp range of the ammeter. This avoids any marked reduction in input to the transformer (as the meter's resistance will be lower). You might disconnect the lamp from the secondary in order to observe the effect on the meters in the primary circuit. In this case, the 1-amp range of the meter should be used for convenience.
  • With the circuit in operation, you could unclip the two C-cores, and gently separate them. Emphasize that there is no electrical connection between the primary and secondary circuits. They are joined only by the magnetic field in the cores.
  • Step-up and step-down transformers are used in electricity distribution networks to change the voltage output from a power station (e.g. 25 kV) to that needed for high voltage transmission (e.g. 132 kV or 400 kV) and back down again for use in homes, factories and offices (e.g. 230 V). Higher voltages on the power lines make the transmission process much more efficient.

This experiment was safety-tested in July 2007

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Transformer: dependence on number of turns

V=-N(dΦ/dt)
Electricity and Magnetism

Transformer: dependence on number of turns

Practical Activity for 14-16

Demonstration

An intriguing demonstration in which a lamp grows brighter and brighter with more turns on the secondary coil of a transformer.

Apparatus and Materials

  • Demountable (demonstration) transformer with a coil of 1200 turns for mains use
  • Lamp, 2.5 V in holder
  • Copper wire, insulated with bare ends, 4 m

Health & Safety and Technical Notes

The 1,200 turn coil must be designed for connection to the mains with either a permanently-connected mains lead or a fully insulated mains computer used with an IEC connector (as on computer equipment).

Read our standard health & safety guidance


The 1,200 turn coil may overheat if left connected too long.

Procedure

  1. Place the 1200-turn coil on one limb of the laminated U-core of the demountable transformer. Connect this to the a.c. mains.
  2. Connect a long lead (4 metres of insulated copper wire) to the lamp.
  3. With the mains switched on, wind the lead turn by turn round the other leg of the U-core. As more and more turns are wound on, the lamp begins to glow and then to get brighter and brighter. At least 10 turns will be necessary for this.

Teaching Notes

  • This is an intriguing demonstration in which the lamp grows brighter and brighter as the turns increase. The demountable transformer comes with an iron yoke to complete the magnetic circuit, and when that is put in place the lamp glows even more brightly.
  • The transformer kit normally has a collection of coils which can be interchanged, and some extra equipment in order to do further demonstrations such as melting solder or the jumping ring. Read the instructions that come with the kit.
  • When the primary current changes, a potential difference is induced in each turn of the secondary coil on the core. As the secondary is wound, turn upon turn, more potential difference is induced, volt upon volt, so to speak.
  • The relationship Vs / Vp = Ns / Np can be measured with different pairs of coils in the transformer kit. Do remember that the current ratios are the inverse of the potential difference ratios (energy conservation demands that IV is a constant at input and output). It is easy to set up a system which will demand more current from the mains than the QuantityUnit{13}{A} it can supply.
  • Here, Vs and Vp are the potential differences on the secondary and the primary coils and Ns and Np are the number of turns on the secondary and primary coils.

This experiment was safety-tested in April 2006

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Oscilloscope and alternating voltage from transformer

V=-N(dΦ/dt)
Electricity and Magnetism

Oscilloscope and alternating voltage from transformer

Practical Activity for 14-16

Demonstration

A way of showing quantitatively the relationship between the e.m.f. and turns ratios of transformer coils.

Apparatus and Materials

  • Demountable (demonstration) transformer with coils of 12 000 and 300 turns
  • Leads, 4 mm, 2
  • Oscilloscope


Health & Safety and Technical Notes

The 12,000 coil must be designed for use on the mains, i.e. the mains lead must be permanently attached or connected via an IEC connector.

The mains lead to the 12,000 turn coil should be permanently connected; 4 mm leads connected to a 13 A mains plug are a serious hazard.

If the coil fitted with a mains connector has only 1,200 turns, reduce the secondary to 30 turns. Do not improvise mains connections with 4 mm leads.

Read our standard health & safety guidance


Procedure

  1. Set up the demountable transformer with the 12,000-turn coil on one side of the U-core and the 300-turn coil on the other.
  2. Plug the 12,000-turn coil into the (230 V) mains. There will then be about 6 volts across the secondary coil when the core is completed.
  3. Connect the low-voltage output from the secondary of the demountable transformer to the Y-plates of the oscilloscope by direct connection to the input terminals.

Teaching Notes

  • The frequency of the AC mains can be calculated from the time-base reading.
  • The turns ratio and the voltage ratios can be compared.

This experiment was safety-tested in April 2006

  • A video showing how to use an oscilloscope:

Up next

Model DC power line

V=-N(dΦ/dt)
Electricity and Magnetism

Model DC power line

Practical Activity for 14-16

Class practical

Shows the significant energy losses along any low-voltage transmission line.

Apparatus and Materials

For each student group

  • Power line terminal rods, 2
  • Retort stands and bosses, 2
  • Lamps (12 V, 24 W) in lamp holders, 2
  • Eureka wire, bare (28 SWG), 1.5 m, 2 lengths
  • Power supply, 0 to 12 V, DC
  • DC voltmeters, 2, reading to at least 12 V
  • Ammeter, DC, reading to at least 2 A

Health & Safety and Technical Notes

Read our standard health & safety guidance


Procedure

  1. Fix two of the dowel rods, which form the power line terminals, horizontally in two bosses at a height of about 30 cm above the bench and roughly 1.5 m apart.
  2. Stretch two lengths of resistance wire between the terminals to form the power line.
  3. Connect one of the two lamps directly to the 12 volt DC supply at the power station end.
  4. Connect the supply directly to one of the terminal rods.
  5. Connect the second lamp to the other end of the power line, where it represents the village. Switch on the power supply. The village lamp will just glow, in contrast with the fully-lit pilot lamp at the power station.
  6. Observe the effect of connecting a second lamp in parallel with the single village lamp.
  7. Connect a voltmeter in parallel with each of the lamps, and note the voltages.

Teaching Notes

  • Power lines connect power stations to the consumer. This is convenient, but there is a cost to pay in energy terms. An electric current warms up the transmission cables and so there are energy losses as the atmosphere is warmed up.
  • In this model version, the wire used has significant resistance so that 1.5 m represents many km of transmission line. It is clear that energy is lost along the transmission wires so much so that the village at the end of the transmission wires receives very little energy from the power station at the other end of the wire.
  • As well as measuring voltages, an ammeter (reading to at least 2 amp) can be connected into the supply line. Students can check that the current remains the same around the power line circuit; the current to the power station lamp is greater than that to the village lamp.
  • In order to understand what is happening, students need some quantitative ideas about electricity. A current of 5 amps means a flow of charge of 5 coulombs per second. A voltmeter measures the energy. A potential difference of 3 volts means that 3 joules of energy are given to each coulomb of charge.
  • Thus a volt is defined as a joule/coulomb and an ampere (amp for short) is defined as a coulomb of charge flowing per second. So with V volts and Q coulombs, then the energy transferred is V x Q joules. The current is I = Q/time, and so the energy transferred is V x I joules per second. (A joule per second is also known as a watt, which is a measure of power.)
  • By measuring the current and potential difference at the power station end of the line and at the village end you can calculate the power loss along the line. The potential difference measured across one wire multiplied by the current in the wire will give the power loss of one wire, and so the total power loss of the wires is twice as much. This is a check on the previous calculation. The input energy should now be equal to the energy transferred to the output plus the energy transferred to warming up the transmission wires.
  • The heating effect of a current is proportional to the square of the current. This means that high currents and low potential differences warm up the wires more than low currents and high potential differences. Therefore, the cables transfer more energy to the environment than to the village in the high current case.
  • Another way of reducing lower power losses is to reduce the resistance of the transmission lines. This is done by using wires of low resistivity such as copper or aluminium. (Silver has an even lower resistivity but it would be very expensive!) Increasing the diameter of the cable would use more copper or aluminium and that would be expensive, and they would also be heavier and so need more support.
  • The efficiency of the system can be calculated from:
  • efficiency = power taken by the village/power supplied at the power station

This experiment was safety-tested in July 2007

A video showing this practical, plus more efficient transmission at higher voltage:

Up next

AC power line at high voltage

V=-N(dΦ/dt)
Electricity and Magnetism

AC power line at high voltage

Practical Activity for 14-16

Demonstration

This experiment shows clearly why the power transmission lines used for the National Grid operate at high voltage.

Apparatus and Materials

  • Mounted transformers
  • Power supply, 12 V AC
  • SBC sockets fitted with 12 V 24 W lamps, mounted, 2
  • Leads, 4 mm, 6
  • Stands fitted with boss heads, 2
  • Multimeters, 2 (optional)
  • Resistance wire 28 SWG (dia 0.376 mm) e.g. constantan

Health & Safety and Technical Notes

The power line in step 2 will be at 240 volts. Insulation at the transformer boxes and sleeved wire will offer sufficient protection and is essential. Several teachers have ended up in hospital through trying to manage without it.

Read our standard health & safety guidance


Cut two 1.5-metre lengths of resistance wire. This will produce a significant power loss in the low voltage line. Then cut two lengths of transparent sleeving, about 1 cm shorter. Slide them onto the wires.

Cut two lengths of wooden rod as shown. Make slots to take the sleeved resistance wire.

To prevent the wire sagging too much between supports, use elastic bands to attach it to a strip of wood or coil it round wooden rods.

A safe version of this experiment, ready prepared, is available from Irwin Science Education. The Irwin Science Education apparatus allows the same wires (representing long power lines) to be used first at low voltage and then quickly changed to operate at high voltage.

Procedure

  1. Connect the circuit to a 12 V AC supply as shown in figure 1a.
  2. Reconnect the circuit, with a mounted transformer at each end, as shown in figure 1b but do not switch on yet.
  3. Open the transformer boxes. Connect the two lengths of sleeved resistance wire between the two terminal blocks and close the boxes, gripping the sleeved wire between the bottom and the lid.
  4. Support the sleeved wires in the slots in the two rods held in boss heads in stands.
  5. Connect up the two 12 V lamps and the supply as shown.
  6. Switch on.

Teaching Notes

  • Before doing this demonstration, students should understand step-up and step-down transformers. Knowing the turns ratio of the transformers, they will then be able to calculate the voltage in the high tension part of the circuit and at the distant lamp.
  • Transmission lines connect power stations to consumers. This is convenient, but there is a cost to pay in energy terms. An electric current warms up the transmission cables and so there are energy losses as the cables warm the atmosphere. Energy is dissipated so that it is stored thermally in the surroundings.
  • Using a high voltage reduces the energy dissipated in the transmission cables. Energy dissipated in the transmission cable goes as I 2R. Because the product of current I times voltage V is constant (equals electrical power), stepping up the voltage reduces the current. This dramatically reduces energy dissipated by heating the transmission wires.
  • The lamp distant from the power supply should look much dimmer (if it glows at all) than the one directly connected to the supply. In step 3, the distant lamp should now be as bright as the one directly connected to the supply.
  • You could explain that voltmeters measure the energy transfer in joules per coulomb. By connecting across the power supply at the power station, you measure the energy transfer there. The students can then calculate the power used by the consumer and 'the power used by the 'power line + consumer'.
  • You could also connect an AC ammeter (reading at least 2 amps) into the circuits with the lamps. Without the transformers, the current to the power station lamp is greater than that to the consumer lamp.
  • A lower voltage alternative is to use a 4 V AC input at the power station end, with transformers that have a turn ratio of 8:1\. This will produce a transmission voltage of about 30 V. Use 1 2 V lamps, which will just glow at 4 V.

This experiment was safety-tested in July 2007

  • A video showing a demonstration that can be used to illustrate power transmission:

Up next

AC power line at lower voltage

V=-N(dΦ/dt)
Electricity and Magnetism

AC power line at lower voltage

Practical Activity for 14-16

Class practical

Shows the basic principle of any transformer: a change in current in the primary coil will induce an e.m.f. (voltage) in the secondary coil.

Apparatus and Materials

  • 2 V a.c. power supply (fixed output) (‘Westminster pattern’)
  • 1.5 V 0.3 A bulbs in holders, 2
  • 20:1 turns ratio transformers (each made from 120 and 2400 turn coils, C-cores and clip), 2
  • Multimeter (used as a.c. voltmeter), 2
  • 2.0 m length of 28 swg Eureka resistance wire, 2
  • Wooden bar with two 4 mm terminals, 2
  • connecting wires with 4 mm plugs, 10

Health & Safety and Technical Notes

Using a power supply with a fixed, low-voltage output and transformers with a small turns-ratio ensures that no dangerously high voltages are produced. Check the maximum voltage that your equipment can produce is less than about 40 V by multiplying the output voltage of the supply by the turns-ratio of the transformer.

Ensure that the second (step-down) transformer is correctly connected, so that the voltage is not further stepped up.

Read our standard health & safety guidance


Procedure

  1. This method makes use of low voltage (1.5 V) bulbs and transformers constructed using standard lab coils.
  2. Show that, without the use of transformers, the ‘distant’ lamp is dim.
  3. Show that, when step-up and step-down transformers are included, the two lamps have approximately equal brightness.

Teaching Notes

  • Students are likely to be aware that electrical power is transmitted at high voltages. This demonstration shows that this results in less power loss.
  • The equipment models an electrical supply system. The power supply represents a power station; one lamp represents a consumer close to the power station while the other represents a consumer at a distance, at the end of long power lines.
  • The demonstration shows that the distant consumer receives less power (the available p.d. is reduced). This effect can be greatly reduced using step-up and step-down transformers.
  • After the demonstration, you can discuss the current in the circuit. Note that the distant consumer is in a series circuit with the two power lines. (It may look as though the two power lines are in parallel with each other, but tracing the path of the current from the supply shows that they are in series with each other, and with the distant consumer.) With transformers in the circuit, the current is reduced by a factor of 20 and so the power dissipated in the power lines is reduced by a factor of 202 = 400.
  • The approach followed in the film above shows that introducing transformers reduces power loss (as shown by the brightnesses of the bulbs). It then moves on from showing the phenomenon to explaining it. Alternatively, you may wish to include a discussion of the source of power loss (ohmic heating of the power lines) during the demonstration. Many students find this approach confusing because it involves the use of two expressions for electrical power: P = I × V when considering how the current changes when the p.d. of the supply is increased, and P = I 2 × R when considering the ohmic losses in the power lines.
  • Measuring currents in the circuit involves breaking into the circuit to add an a.c. ammeter.
  • A version using d.c., showing appreciable power losses (but without the use of transformers):

    Model DC power line


  • A version of this demonstration in which the voltage is stepped up to 240 V; more safety precautions required:

    AC power line at high voltage


  • This video shows how to set up and demonstrate a model electrical power line where voltages are kept to below 40V:

Up next

Faraday's law

Faraday's Law
Electricity and Magnetism

Faraday's law

Practical Activity for 14-16

Demonstration

Faraday's law of electromagnetic induction is a very important principle. Most of the electrical power in the world is generated by using this principle.

Apparatus and Materials

  • Ferromagnetic cylindrical rod: diameter 10 mm, length 10 cm
  • Insulated copper wire - SWG 30, 300 g
  • LED
  • Demountable transformer, used as a 'step-down' transformer with primary coil connected to mains, with turns ratio to produce 6-10 V across the secondary coil.

Health & Safety and Technical Notes

NB The primary coil must be designed for connection to the mains, e.g. using an IEC connector and mains lead.

Read our standard health & safety guidance


Procedure

  1. Wind the copper wire on the ferromagnetic rod to form a cylinder with the ferromagnetic rod as axis. Leave 0.5 cm of wire on either side of the rod. This is called the test coil.
  2. Remove the insulation from the two ends of the copper wire and connect an LED in series.
  3. Connect the primary coil of the demountable transformer to the AC mains.
  4. Hold the test coil (ferromagnetic rod with copper wire) in your hand and move the test coil close to the secondary coil, preferably along its axis. (A circular inductor coil will have its magnetic field along its axis.) The LED glows.
  5. If the primary coil is changed for a smaller one connected to the 20 V DC, the LED glows as the test coil is moved towards or away from the secondary coil.

Teaching Notes

  • When an alternating current flows through the secondary coil, it produces alternating magnetic field along its axis.
  • When the test coil is positioned correctly, the flux linking with it changes and a voltage is induced. The LED glows as the magnetic field oscillates due to an alternating supply current.
  • If a DC supply is used, the LED glows only when the test coil is moved.

This experiment was submitted by K.H. Raveesha, Head of Physics at the CMR Institute of Technology in India.

Up next

Explaining how a transformer works

Energy Transferred by Working
Electricity and Magnetism

Explaining how a transformer works

Teaching Guidance for 14-16

When an electric current passes through a long, hollow coil of wire there will be a strong magnetic field inside the coil and a weaker field outside it. The lines of the magnetic field pattern run through the coil, spread out from the end, and go round the outside and in at the other end.

These are not real lines like the ones you draw with a pencil. They are lines that we imagine, as in the sketch, to show the pattern of the magnetic field: the direction in which a sample of iron would be magnetised by the field. Where the field is strongest, the lines are most closely crowded.

With a hollow coil the lines form complete rings. If there is an iron core in the coil it becomes magnetised, and seems to make the field become much stronger while the current is on.

The iron core of a transformer is normally a complete ring with two coils wound on it. One is connected to a source of electrical power and is called the primary coil; the other supplies the power to a load and is called the secondary coil. The magnetisation due to the current in the primary coil runs all the way round the ring. The primary and secondary coils can be wound anywhere on the ring, because the iron carries the changes in magnetisation from one coil to the other. There is no electrical connection between the two coils. However they are connected by the magnetic field in the iron core.

When there is a steady current in the primary there is no effect in the secondary, but there is an effect in the secondary if the current in the primary is changing. A changing current in the primary induces an e.m.f. in the secondary. If the secondary is connected to a circuit then there is a current flow.

A step-down transformer of 1,200 turns on the primary coil connected to 240 V a.c. will produce 2 V a.c. across a 10-turn secondary (provided the energy losses are minimal) and so light a 2 V lamp.

A step-up transformer with 1,000 turns on the primary fed by 200 V a.c. and a 10,000-turn secondary will give a voltage of 2,000 V a.c.

The iron core is itself a crude secondary (like a coil of one turn) and changes of primary current induce little circular voltages in the core. Iron is a conductor and if the iron core were solid, the induced voltages would drive wasteful secondary currents in it (called eddy currents). So the core is made of very thin sheets clamped together, with the face of each sheet coated to make it a poor conductor. The edges of the sheets can be seen by looking at the edges of a transformer core.

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