Transformers

A transformer is an electrical device that transfers electrical energy from one circuit to another using mutual induction.

Transformers can change alternating voltage without requiring a direct electrical connection between the input and output circuits.

The basic process is:

AC in primary coil → changing magnetic field → changing magnetic flux in core → induced AC voltage in secondary coil

Transformers are essential in electrical power systems because they allow voltages to be increased or decreased efficiently.

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Main Parts of a Transformer

A basic transformer contains:

• primary coil
• secondary coil
• magnetic core

The primary coil is connected to the input AC supply.

The secondary coil provides the output voltage.

The magnetic core helps guide magnetic flux from the primary coil through the secondary coil.

The coils are normally electrically separate but magnetically coupled.

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The Primary Coil

When alternating current flows through the primary coil:

• current continuously changes
• the magnetic field changes
• the direction of the magnetic field periodically reverses
• magnetic flux through the core changes

This changing magnetic flux is necessary for transformer operation.

A steady magnetic field would not continuously induce a voltage in the secondary.

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The Magnetic Core

The transformer core provides a low-reluctance path for magnetic flux.

It helps concentrate the changing magnetic field so that a large fraction of the magnetic flux produced by the primary links the secondary.

This improves magnetic coupling between the coils.

Common transformer core materials are selected to have useful magnetic properties while minimizing energy losses.

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The Secondary Coil

The changing magnetic flux from the primary passes through the secondary coil.

According to Faraday's law:

ε = −N ΔΦ/Δt

Therefore, changing flux through the secondary produces an induced EMF.

Because the magnetic flux repeatedly changes direction and magnitude, the induced voltage in the secondary is also alternating.

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Mutual Induction

Transformer operation is an application of mutual induction.

Mutual induction occurs when:

changing current in one circuit produces an induced EMF in another circuit

The primary current creates the changing magnetic field.

The secondary experiences the resulting changing magnetic flux.

Therefore:

primary circuit → magnetic coupling → secondary circuit

No direct conducting connection between the two windings is required in an ordinary transformer.

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Why Transformers Require Changing Flux

Suppose steady DC is connected to a transformer.

Immediately after switching:

• current changes
• magnetic field changes
• induction can occur briefly

Once the current becomes steady:

ΔI/Δt = 0

The magnetic field becomes approximately constant.

Therefore:

ΔΦ/Δt = 0

and continuous induced secondary voltage stops.

Transformers therefore require changing magnetic flux.

AC naturally provides this.

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AC Transformer Operation

During one part of the AC cycle:

• primary current increases in one direction
• magnetic flux increases
• voltage is induced in the secondary

Later:

• primary current decreases
• magnetic flux changes
• the secondary voltage changes

During the opposite half-cycle:

• primary current reverses
• magnetic field reverses
• induced secondary voltage reverses

The output is therefore also AC.

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Transformer Turns Ratio

The voltage produced in each winding depends on the number of turns.

For an ideal transformer:

V_s/V_p = N_s/N_p

where:

• V_s = secondary voltage
• V_p = primary voltage
• N_s = number of turns in secondary
• N_p = number of turns in primary

The ratio:

N_s/N_p

is called the turns ratio.

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Understanding the Turns Ratio

If:

N_s > N_p

then:

V_s > V_p

The transformer increases voltage.

If:

N_s < N_p

then:

V_s < V_p

The transformer decreases voltage.

If:

N_s = N_p

then ideally:

V_s = V_p

The voltage is unchanged.

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Step-Up Transformers

A step-up transformer increases voltage.

Therefore:

V_s > V_p

and:

N_s > N_p

The secondary has more turns than the primary.

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Worked Example: Step-Up Transformer

A transformer has:

N_p = 200 turns

N_s = 1000 turns

V_p = 24 V

Use:

V_s/V_p = N_s/N_p

V_s/24 = 1000/200

V_s/24 = 5

V_s = 120 V

V_s = 120 V

The transformer increases the voltage from 24 V to 120 V.

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Step-Down Transformers

A step-down transformer decreases voltage.

Therefore:

V_s < V_p

and:

N_s < N_p

The secondary has fewer turns than the primary.

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Worked Example: Step-Down Transformer

A transformer has:

N_p = 1200 turns

N_s = 200 turns

V_p = 240 V

Use:

V_s/V_p = N_s/N_p

V_s/240 = 200/1200

V_s/240 = 1/6

V_s = 40 V

V_s = 40 V

The transformer reduces the voltage from 240 V to 40 V.

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Finding the Number of Turns

The transformer equation can be rearranged to find an unknown number of turns.

Suppose:

V_p = 120 V

V_s = 12 V

N_p = 600 turns

Find N_s.

Use:

V_s/V_p = N_s/N_p

12/120 = N_s/600

0.10 = N_s/600

N_s = 60

N_s = 60 turns

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Finding Primary Turns

Suppose:

V_p = 50 V

V_s = 200 V

N_s = 800 turns

Use:

V_s/V_p = N_s/N_p

200/50 = 800/N_p

4 = 800/N_p

N_p = 200

N_p = 200 turns

This is a step-up transformer.

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Identifying the Transformer Type

A quick way to identify transformer type is to compare the number of turns.

More secondary turns than primary turns:

N_s > N_p

→ step-up

Fewer secondary turns than primary turns:

N_s < N_p

→ step-down

You can also compare the voltages.

V_s > V_p → step-up

V_s < V_p → step-down

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Voltage Ratio and Turns Ratio

Suppose:

N_s/N_p = 4

Then:

V_s/V_p = 4

The secondary voltage is four times the primary voltage.

If:

N_s/N_p = 0.25

then:

V_s/V_p = 0.25

The secondary voltage is one-quarter of the primary voltage.

The voltage changes by the same factor as the number of turns.

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Energy Conservation in an Ideal Transformer

An ideal transformer has no energy losses.

Therefore:

input power = output power

Electrical power is:

P = VI

So for an ideal transformer:

V_pI_p = V_sI_s

where:

• V_p = primary voltage
• I_p = primary current
• V_s = secondary voltage
• I_s = secondary current

This relationship follows from conservation of energy.

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Voltage and Current Trade-Off

A transformer does not create additional electrical power.

If voltage increases, current must decrease.

If voltage decreases, current can increase.

Therefore:

step-up voltage → step-down current

and:

step-down voltage → step-up current

for an ideal transformer supplying a load.

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Current Ratio

From:

V_pI_p = V_sI_s

and:

V_s/V_p = N_s/N_p

we obtain:

I_s/I_p = N_p/N_s

Notice that the current ratio is the inverse of the turns ratio.

This is important.

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Step-Up Transformer Current

For a step-up transformer:

V_s > V_p

but:

I_s < I_p

For example, if voltage increases by a factor of 10, the ideal current decreases by a factor of 10.

Power remains unchanged.

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Step-Down Transformer Current

For a step-down transformer:

V_s < V_p

but:

I_s > I_p

For example, if voltage decreases by a factor of 5, the ideal current can increase by a factor of 5.

Again, the transformer does not create energy.

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Worked Example: Current in an Ideal Transformer

A transformer has:

V_p = 120 V

I_p = 2.0 A

V_s = 24 V

Use:

V_pI_p = V_sI_s

(120)(2.0) = (24)I_s

240 = 24I_s

I_s = 10 A

I_s = 10 A

The voltage decreased by a factor of 5.

The current increased by a factor of 5.

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Worked Example: Step-Up Voltage and Current

A transformer receives:

V_p = 50 V

I_p = 4.0 A

and produces:

V_s = 200 V

Input power:

P_p = V_pI_p

P_p = (50)(4.0)

P_p = 200 W

For an ideal transformer:

P_s = 200 W

Therefore:

I_s = P_s/V_s

I_s = 200/200

I_s = 1.0 A

Voltage increased by a factor of 4 while current decreased by a factor of 4.

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Why Transformers Cannot Create Energy

Suppose a transformer increases voltage from:

100 V → 1000 V

This does not mean the transformer produces ten times as much energy.

If the ideal voltage increases by a factor of 10, current decreases by a factor of 10.

For example:

Primary:

100 V × 10 A = 1000 W

Secondary:

1000 V × 1 A = 1000 W

The power remains:

1000 W

Energy has been transferred and transformed, not created.

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Ideal vs Real Transformers

An ideal transformer assumes:

• no electrical resistance
• no magnetic flux leakage
• no eddy-current losses
• no hysteresis losses
• perfect magnetic coupling

Therefore:

P_input = P_output

Real transformers are not perfect.

Therefore:

P_output < P_input

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Transformer Efficiency

Efficiency can be calculated using:

efficiency = P_output/P_input × 100%

A well-designed transformer can have high efficiency, especially at its intended operating conditions.

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Worked Example: Transformer Efficiency

A transformer receives:

P_input = 500 W

and supplies:

P_output = 450 W

Efficiency:

efficiency = 450/500 × 100%

efficiency = 90%

Power lost:

500 − 450

P_loss = 50 W

This lost energy is mostly transferred into thermal energy.

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Copper Losses

Transformer windings are made from conducting wire.

Real wire has resistance.

Therefore, some electrical energy becomes thermal energy.

The power loss in a winding can be described by:

P_loss = I²R

These losses are often called copper losses.

Reducing winding resistance can improve efficiency.

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Eddy-Current Losses

The changing magnetic flux in the core can induce circulating currents inside conducting core material.

These are eddy currents.

Eddy currents produce unwanted heating.

One way to reduce them is to construct the core from thin insulated layers called laminations.

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Why Laminations Reduce Eddy Currents

A solid conducting core can allow relatively large circulating current loops.

Laminating the core:

• divides it into thin sections
• interrupts large current paths
• increases resistance to circulating currents
• reduces eddy-current heating

This improves transformer efficiency.

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Hysteresis Losses

The transformer core is repeatedly magnetized in opposite directions as AC changes direction.

The magnetic domains inside the material repeatedly rearrange.

Some energy is lost during this process.

This is called hysteresis loss.

Suitable magnetic materials are chosen to reduce this loss.

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Flux Leakage

Ideally, all magnetic flux produced by the primary would link the secondary.

In reality, some magnetic flux does not pass through both windings.

This is called leakage flux.

Flux leakage reduces effective magnetic coupling.

Transformer designs attempt to keep the primary and secondary strongly magnetically coupled.

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Heating

Copper losses, eddy currents, and hysteresis all contribute to heating.

Large transformers therefore require effective cooling.

Cooling methods may include:

• natural air cooling
• forced-air cooling
• insulating cooling fluids
• radiators
• heat exchangers

Managing heat is an important part of transformer design.

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Why Transformers Are Important for Power Transmission

Transformers are extremely important in electrical power grids.

Electrical power is:

P = VI

For a fixed amount of transmitted power:

higher V → lower I

Transmission-line heating is approximately:

P_loss = I²R

Therefore, reducing current greatly reduces energy loss in transmission wires.

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Example: Why High Voltage Helps

Suppose:

P = 100,000 W

If electricity is transmitted at:

V = 1000 V

then:

I = P/V

I = 100,000/1000

I = 100 A

Suppose instead it is transmitted at:

V = 10,000 V

I = 100,000/10,000

I = 10 A

Current has decreased by a factor of 10.

Since:

P_loss = I²R

the resistive loss for the same wire resistance decreases by a factor of:

10² = 100

This demonstrates why high-voltage transmission is so useful.

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Transformers in the Electrical Grid

Electrical power systems use multiple transformers.

A simplified sequence is:

generator → step-up transformer → high-voltage transmission → step-down transformers → consumers

Near the generator, voltage is increased.

Near users, voltage is reduced to levels appropriate for distribution and equipment.

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Step-Up Transformers in Power Stations

Generators produce electrical power at a particular voltage.

A step-up transformer increases this voltage before long-distance transmission.

This allows the same power to be transmitted with lower current.

Lower current reduces:

I²R heating losses

in transmission lines.

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Step-Down Transformers

High transmission voltages are unsuitable for direct use by most equipment.

Step-down transformers progressively reduce voltage during electrical distribution.

This makes the electrical supply appropriate for:

• homes
• businesses
• schools
• factories
• electronic devices

Different systems require different voltage levels.

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Transformers in Chargers and Power Supplies

Many electrical devices require voltages different from the available supply.

Transformers can be part of systems that:

• reduce voltage
• provide electrical isolation
• transfer power
• prepare voltage for further conversion

Modern electronic chargers often use high-frequency switching circuits and relatively small transformers.

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Why High-Frequency Transformers Can Be Small

The induced voltage depends on how rapidly magnetic flux changes.

At higher operating frequencies, the flux changes more rapidly.

This can allow transformers designed for high-frequency switching power supplies to be much smaller than traditional low-frequency transformers handling comparable power.

This is one reason modern chargers can be compact.

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Electrical Isolation

A transformer can transfer energy without a direct electrical connection between the primary and secondary windings.

This can provide galvanic isolation.

Isolation can be useful for:

• electrical safety
• protecting sensitive electronics
• separating circuit grounds
• measurement equipment
• medical and industrial systems

Not every transformer configuration provides isolation; for example, an autotransformer uses a shared winding.

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Isolation Transformers

An isolation transformer may have approximately equal primary and secondary voltages.

For example:

N_s ≈ N_p

so:

V_s ≈ V_p

Its main purpose is therefore not necessarily to change voltage.

Instead, it provides electrical separation between circuits.

This shows that transformers can have functions beyond simply stepping voltage up or down.

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Audio and Signal Transformers

Transformers can also transfer changing electrical signals.

They may be used for:

• impedance matching
• signal isolation
• audio equipment
• communication circuits

These transformers operate using the same principle of mutual induction.

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Instrument Transformers

High-power electrical systems can contain voltages and currents that are too large to measure directly with ordinary instruments.

Special transformers can produce smaller proportional quantities for:

• measurement
• monitoring
• protection systems

Examples include current transformers and voltage transformers.

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Welding Transformers

Some welding equipment requires:

• relatively low voltage
• very high current

A step-down transformer can reduce voltage while increasing available current.

The large current produces intense heating at the welding point.

This is an excellent example of the voltage-current trade-off in transformer operation.

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Doorbells and Low-Voltage Systems

Some low-voltage devices use transformers to reduce supply voltage.

Applications can include:

• doorbells
• control circuits
• lighting systems
• older low-voltage power adapters

The transformer allows equipment to operate at a more suitable voltage.

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Microwave Oven Transformers

Traditional microwave ovens may use transformers to produce a much higher voltage required by the magnetron circuitry.

This is an example of a step-up application.

Such circuits can involve dangerously high voltages and are not suitable for experimentation.

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Transformers and Wireless Charging

Traditional transformers use a magnetic core to strongly couple nearby windings.

Wireless charging uses a related principle with physically separated coils.

The transmitter coil produces changing magnetic flux.

The receiver coil experiences this changing flux and develops an induced EMF.

Both technologies rely on mutual induction.

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Transformer Frequency

Transformers are designed for particular operating frequencies or frequency ranges.

Changing frequency affects:

• magnetic flux
• core behaviour
• losses
• heating
• efficiency

Using a transformer far outside its designed frequency can cause poor performance or damage.

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Magnetic Saturation

Transformer cores can only support a limited magnetic flux density before approaching saturation.

When saturation occurs:

• the core no longer responds proportionally
• effective inductive behaviour decreases
• primary current can increase greatly
• overheating can occur

Transformer design therefore considers voltage, frequency, turns, and core properties together.

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A Complete Transformer Problem

A transformer has:

V_p = 240 V

N_p = 1200 turns

N_s = 100 turns

The primary current is:

I_p = 0.50 A

First calculate secondary voltage:

V_s/V_p = N_s/N_p

V_s/240 = 100/1200

V_s = 20 V

V_s = 20 V

For an ideal transformer:

V_pI_p = V_sI_s

(240)(0.50) = (20)I_s

120 = 20I_s

I_s = 6.0 A

I_s = 6.0 A

The transformer reduces voltage by a factor of 12 and increases current by a factor of 12.

Input power:

P_p = (240)(0.50)

P_p = 120 W

Output power:

P_s = (20)(6.0)

P_s = 120 W

Energy is conserved in the ideal model.

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A Real Transformer Problem

Suppose the transformer above actually produces:

V_s = 20 V

I_s = 5.4 A

Output power:

P_s = V_sI_s

P_s = (20)(5.4)

P_s = 108 W

Input power was:

120 W

Efficiency:

efficiency = 108/120 × 100%

efficiency = 90%

Power lost:

120 − 108

P_loss = 12 W

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A Reliable Strategy for Transformer Problems

First identify:

• V_p
• V_s
• N_p
• N_s
• I_p
• I_s

For voltage and turns:

V_s/V_p = N_s/N_p

For an ideal transformer's power:

V_pI_p = V_sI_s

For current ratio:

I_s/I_p = N_p/N_s

For a real transformer's efficiency:

efficiency = P_output/P_input × 100%

Then determine whether the transformer is:

step-up: V_s > V_p and N_s > N_p

or:

step-down: V_s < V_p and N_s < N_p

Finally, check that the result makes physical sense.

If voltage increases in an ideal transformer, current should decrease.

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Common Mistakes

Thinking transformers create energy

Transformers transfer energy. An ideal transformer conserves energy.

Confusing primary and secondary

The primary receives input. The secondary provides output.

Reversing the turns ratio

Use:

V_s/V_p = N_s/N_p

Keep secondary quantities together and primary quantities together.

Thinking step-up means more current

A step-up transformer increases voltage but decreases current in the ideal loaded case.

Thinking step-down means less power

An ideal step-down transformer has the same input and output power; voltage decreases while current increases.

Thinking transformers work continuously with steady DC

Continuous transformer action requires changing magnetic flux.

Assuming real transformers are 100% efficient

Real transformers lose energy through resistance, eddy currents, hysteresis, leakage, and other effects.

Thinking laminations increase eddy currents

Laminations are used to reduce unwanted eddy currents.

Ignoring units

Use volts for voltage, amperes for current, watts for power, and turns as a simple count.

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Key Terms

Transformer — device that transfers electrical energy between circuits through mutual induction.

Primary coil — winding connected to the input electrical supply.

Secondary coil — winding in which the output voltage is induced.

Mutual induction — induction of an EMF in one circuit caused by changing current and magnetic flux from another circuit.

Magnetic core — material that provides a path for magnetic flux and improves coupling between windings.

Turns ratio — ratio of the number of turns in the secondary to the number in the primary.

Step-up transformer — transformer that produces a higher secondary voltage than primary voltage.

Step-down transformer — transformer that produces a lower secondary voltage than primary voltage.

Ideal transformer — theoretical transformer with no energy losses.

Efficiency — fraction or percentage of input power converted into useful output power.

Copper loss — energy loss caused by electrical resistance in transformer windings.

Eddy current — circulating current induced in conducting material by changing magnetic flux.

Lamination — thin insulated core layer used to reduce eddy currents.

Hysteresis loss — energy loss caused by repeated magnetization and demagnetization of a magnetic material.

Leakage flux — magnetic flux that does not effectively link both windings.

Galvanic isolation — electrical separation between circuits with no direct conductive path.

Magnetic saturation — condition where increasing magnetizing influence produces relatively little additional magnetization in a core.

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Key Takeaways

• Transformers operate using mutual induction.
• Alternating primary current creates changing magnetic flux.
• Changing magnetic flux induces an alternating voltage in the secondary.
• A magnetic core helps couple flux between the windings.
• Transformer voltage depends on the turns ratio.
• The ideal transformer equation is V_s/V_p = N_s/N_p.
• A step-up transformer has more secondary turns and produces higher secondary voltage.
• A step-down transformer has fewer secondary turns and produces lower secondary voltage.
• An ideal transformer conserves power: V_pI_p = V_sI_s.
• Increasing voltage requires decreasing current in an ideal transformer.
• Decreasing voltage allows current to increase.
• Transformers do not create electrical energy.
• Real transformers lose some energy through resistance, eddy currents, hysteresis, leakage, and heating.
• Laminated cores help reduce eddy-current losses.
• Transformers make efficient high-voltage electrical transmission possible.
• High transmission voltage allows lower current for the same power.
• Lower current greatly reduces I²R transmission losses.
• Transformers are used in power grids, chargers, power supplies, welding equipment, measurement systems, isolation systems, and electronic equipment.
• High-frequency transformer operation allows compact transformers in many modern switching power supplies.
• Transformers are one of the most important practical applications of electromagnetic induction.

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Check Your Understanding

1. Explain how mutual induction allows a transformer to transfer electrical energy from the primary to the secondary.
2. Why must the magnetic flux in a transformer change with time?
3. Identify the primary coil, secondary coil, and magnetic core, and describe the function of each.
4. A transformer has N_p = 500 turns and N_s = 2000 turns. Is it a step-up or step-down transformer? Explain.
5. A transformer has V_p = 120 V, N_p = 600 turns, and N_s = 150 turns. Calculate V_s.
6. A transformer changes 20 V to 100 V. If the primary contains 200 turns, calculate the required number of secondary turns.
7. An ideal transformer receives 240 V at 2.0 A and produces 24 V. Calculate the secondary current.
8. Explain why the secondary current of an ideal step-up transformer is lower than its primary current.
9. A transformer receives 800 W and produces 720 W. Calculate its efficiency.
10. Identify three major sources of energy loss in a real transformer and explain how at least one can be reduced.
11. Explain why transformer cores are often laminated.
12. A power line must transmit the same amount of power at either 10 kV or 100 kV. Compare the currents and explain why the higher transmission voltage reduces energy loss.
13. Explain why connecting steady DC directly to a conventional transformer does not produce continuous secondary voltage and may cause problems.
14. Compare a step-up and step-down transformer in terms of turns, voltage, and current.
15. Describe three practical applications of transformers and explain why a transformer is useful in each application.