Energy in Magnetic Fields

An inductor stores energy in the magnetic field produced by the current flowing through it.

When current through an inductor increases, the magnetic field becomes stronger. Because the changing magnetic field produces a self-induced EMF that opposes the increase in current, the power supply must do work to establish the current.

That work is stored as magnetic field energy.

When the current later decreases, the magnetic field collapses and the stored energy can be transferred back into the circuit.

The basic energy transfer is:

electrical energy → magnetic field energy → electrical energy

 

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7

Energy Storage in an Inductor

Consider an inductor connected to a power supply.

When the circuit is first switched on:

• current begins to increase
• the magnetic field becomes stronger
• magnetic flux through the coil increases
• a self-induced EMF is produced
• the self-induced EMF opposes the increase in current

The power supply must therefore transfer energy into the system.

Some of this energy becomes energy stored in the magnetic field surrounding and inside the inductor.

Why Energy Is Required

An inductor opposes a change in current because of Lenz's law.

As current increases, the self-induced EMF acts against that increase.

The source must therefore do work to move charge against the induced EMF.

The work done becomes stored magnetic energy.

This is similar to doing work to compress a spring. The work is not destroyed; it is stored and can later be released.

Energy Stored in an Inductor

The energy stored in an ideal inductor is:

E = ½LI²

where:

• E = stored energy in joules (J)
• L = inductance in henries (H)
• I = current in amperes (A)

This is one of the most important equations for magnetic energy storage.

What the Equation Tells Us

From:

E = ½LI²

the stored energy depends on:

• inductance
• current

For a fixed current:

E ∝ L

For a fixed inductance:

E ∝ I²

Therefore, current has a particularly strong effect on the amount of stored energy.

Effect of Inductance

Suppose the current remains constant.

If inductance doubles:

L → 2L

then:

E → 2E

Therefore:

doubling inductance doubles the stored energy

for the same current.

A larger inductance means the circuit can store more magnetic energy at a given current.

Effect of Current

Stored energy is proportional to the square of current:

E ∝ I²

If current doubles:

I → 2I

then:

E → ½L(2I)²

E → 4(½LI²)

Therefore:

doubling current produces four times the stored energy

If current triples:

stored energy becomes nine times larger

assuming inductance remains constant.

Comparing Current and Inductance

Suppose an inductor initially stores energy E.

If its inductance doubles:

energy doubles

If its current doubles:

energy quadruples

This means that increasing current can have a much greater effect on stored energy than an equal proportional increase in inductance.

Worked Example: Stored Energy

An inductor has:

L = 0.50 H

and carries:

I = 4.0 A

Use:

E = ½LI²

E = ½(0.50)(4.0²)

E = (0.25)(16)

E = 4.0 J

The magnetic field stores:

4.0 J

of energy.

Worked Example: Smaller Inductor

An inductor has:

L = 25 mH

and carries:

I = 2.0 A

First convert:

25 mH = 0.025 H

Then:

E = ½LI²

E = ½(0.025)(2.0²)

E = (0.0125)(4.0)

E = 0.050 J

Worked Example: Finding Current

An inductor stores:

E = 9.0 J

and has:

L = 0.50 H

Start with:

E = ½LI²

Rearrange:

I² = 2E/L

I² = 2(9.0)/0.50

I² = 36

Therefore:

I = 6.0 A

Worked Example: Finding Inductance

An inductor stores:

E = 2.0 J

when carrying:

I = 4.0 A

Use:

E = ½LI²

Rearrange:

L = 2E/I²

L = 2(2.0)/(4.0²)

L = 4.0/16

L = 0.25 H

Why the Factor of One-Half Appears

The induced EMF is not constant while current increases from zero.

For an ideal linear inductor:

ε = L ΔI/Δt

As current builds, energy is progressively transferred into the magnetic field.

The total work required to increase current from zero to I gives:

E = ½LI²

The factor ½ appears because the energy is accumulated as the current and magnetic field build from zero to their final values.

Power During Energy Storage

Power is the rate of energy transfer:

P = VI

For an inductor:

V = L ΔI/Δt

Therefore:

P = LI ΔI/Δt

When current increases, energy is being transferred into the magnetic field.

When current decreases, stored magnetic energy can be transferred out of the inductor.

Energy Is Stored in the Field

It is common to say that energy is "stored in the inductor."

More precisely, the energy is associated with the magnetic field produced by the current.

For a solenoid, much of the magnetic field is concentrated:

• inside the coil
• and, if present, within its magnetic core

The stronger the field, the greater the magnetic energy that can be associated with the system.

 

 

 

7

Magnetic Energy Density

Energy can also be described in terms of the amount stored per unit volume of magnetic field.

For a simple linear magnetic medium:

u = B²/(2μ)

where:

• u = magnetic energy density in J/m³
• B = magnetic field strength in T
• μ = magnetic permeability

For free space:

u = B²/(2μ₀)

This equation shows that stronger magnetic fields contain greater energy density.

Energy in a Solenoid

For an ideal solenoid:

L = μN²A/l

and:

E = ½LI²

Combining these ideas shows that changing the geometry of a solenoid can affect its ability to store magnetic energy.

For the same current:

• more turns generally increase stored energy
• greater cross-sectional area increases stored energy
• suitable magnetic cores can increase stored energy
• changes in coil length affect inductance and therefore stored energy

Building the Magnetic Field

When an inductor is first connected to a DC supply, current does not immediately reach its final value.

Instead:

1. current begins increasing
2. magnetic field begins building
3. self-induced EMF opposes the increase
4. energy is transferred into the magnetic field
5. current gradually approaches its steady value

Once the current becomes constant, the magnetic field becomes constant.

The stored energy remains:

E = ½LI²

as long as the current continues.

Releasing the Stored Energy

Suppose the current through an inductor begins to decrease.

The magnetic field begins collapsing.

According to Lenz's law, the inductor produces an EMF that attempts to maintain the current.

The magnetic field therefore transfers its stored energy back into the electrical circuit.

The sequence becomes:

magnetic field energy → electrical energy

This is why an inductor can continue driving current temporarily even after the original source is disconnected.

 

 

 

9

Energy Conservation

Inductors provide a clear example of conservation of energy.

During current growth:

electrical energy supplied → magnetic field energy

During current decay:

magnetic field energy → electrical energy

In a real circuit, some energy also becomes thermal energy because wires and other components have resistance.

Therefore, a real energy pathway might be:

electrical energy → magnetic field energy → electrical energy + thermal energy

Ideal and Real Inductors

An ideal inductor has no electrical resistance and no energy losses.

It can theoretically store and return magnetic energy without loss.

A real inductor has:

• wire resistance
• magnetic-core losses
• eddy-current losses
• hysteresis losses
• magnetic flux leakage

Therefore, some energy is converted into unwanted thermal energy.

Resistance vs Inductance

Resistance and inductance affect electrical energy differently.

A resistor mainly converts electrical energy into thermal energy:

electrical energy → thermal energy

An ideal inductor temporarily stores energy:

electrical energy → magnetic field energy → electrical energy

This distinction is important.

An inductor does not simply "use up" energy in the same way as a resistor.

Electrical Energy Storage

Electrical systems can store energy in different forms.

Two important components are:

• capacitors
• inductors

A capacitor stores energy in an electric field.

An inductor stores energy in a magnetic field.

These two devices play complementary roles in many electrical circuits.

Capacitors and Inductors

This comparison is extremely useful when studying electrical energy storage.

Similarity Between the Energy Equations

For a capacitor:

E_C = ½CV²

For an inductor:

E_L = ½LI²

Notice the similar structure.

For capacitors:

• C describes the component
• V describes its electrical state

For inductors:

• L describes the component
• I describes its electrical state

In both cases, stored energy depends on the square of the electrical quantity.

Comparing Energy Storage

Consider:

Capacitor: E = ½CV²

Inductor: E = ½LI²

If voltage across a capacitor doubles:

capacitor energy becomes 4 times larger

If current through an inductor doubles:

inductor energy becomes 4 times larger

Both systems therefore show a squared dependence.

Batteries Are Different

A battery also stores energy, but primarily as chemical energy, not as electric or magnetic field energy.

Therefore:

battery → chemical energy

capacitor → electric field energy

inductor → magnetic field energy

These devices can all supply electrical energy to circuits, but they store energy in fundamentally different ways.

Inductor and Capacitor Energy Exchange

A capacitor and inductor can exchange energy with each other.

Suppose a charged capacitor is connected to an inductor.

Initially, much of the energy may be stored in the capacitor's electric field.

As the capacitor discharges:

• current increases
• the inductor's magnetic field strengthens
• energy moves into the magnetic field

Later, the magnetic field collapses and can recharge the capacitor.

In an ideal system:

electric field energy ↔ magnetic field energy

This behaviour is the basis of LC oscillations.

 

 

 

7

Energy in an LC Circuit

At one moment, the capacitor may have maximum voltage and the current may be zero.

Energy is mainly:

electric field energy

Later, the capacitor voltage decreases while current increases.

Energy moves into the inductor.

When current reaches its maximum, energy is mainly:

magnetic field energy

The process can then reverse.

Real circuits gradually lose energy because of resistance.

Practical Use: Switching Power Supplies

Modern electronic power supplies frequently use inductors to temporarily store energy.

A switching circuit rapidly changes the current through an inductor.

During part of the switching cycle:

energy is stored in the magnetic field

During another part:

energy is released to the circuit

This allows efficient conversion between different voltage and current levels.

Inductors are therefore important in devices such as:

• phone chargers
• computer power supplies
• LED drivers
• battery-powered electronics

Buck Converters

A buck converter reduces DC voltage.

An inductor helps maintain relatively smooth current while electronic switches repeatedly turn on and off.

During part of the cycle, the inductor stores magnetic energy.

During another part, it releases energy to the load.

This helps convert electrical power efficiently.

Boost Converters

A boost converter can produce an output voltage greater than its input voltage.

Current first builds through an inductor.

The inductor stores energy in its magnetic field.

When the switching configuration changes, the collapsing magnetic field produces an induced voltage.

The stored energy is transferred to the output.

This demonstrates a direct practical use of:

E = ½LI²

Practical Use: Electrical Filters

Inductors are also used to smooth current.

Because an inductor opposes rapid current changes, it can reduce unwanted fluctuations.

Energy is alternately stored and released as the current changes.

This is useful in:

• power supplies
• audio circuits
• communication systems
• electronic filters

Practical Use: Ignition Systems

Inductive energy storage can be used to produce large voltages.

Current is first established through a coil.

Energy is stored in its magnetic field.

When the current is interrupted rapidly:

• magnetic field collapses
• flux changes rapidly
• a large induced EMF can be produced

This principle is used in some ignition and pulsed electrical systems.

Practical Use: Electromagnets

An electromagnet stores energy in its magnetic field while current flows.

Examples include:

• relays
• solenoids
• electromagnetic actuators
• lifting magnets
• magnetic valves

When the current is switched off, the stored magnetic energy must go somewhere.

Circuit designers therefore need to manage the released energy safely.

Voltage Spikes

The energy stored in an inductor cannot disappear instantly.

If a current-carrying inductor is suddenly disconnected, the current attempts to decrease very rapidly.

Since:

|ε| = L|ΔI/Δt|

a very rapid change can produce a large voltage.

This voltage may cause:

• sparks
• damage to electronic components
• electrical interference

Protective circuits are often used to provide a safe path for the stored energy.

Flyback Protection

A coil controlled electronically may have a protective path added across it.

When the switch opens:

• the magnetic field collapses
• the inductor attempts to maintain current
• stored energy continues circulating through the protective path
• the current gradually decreases
• the energy is safely dissipated

This helps protect sensitive switching components from large induced voltages.

 

 

 

7

Energy Storage in Electric Vehicles

Inductors are important components in the power electronics used in electric vehicles.

They help:

• convert voltages
• control motor currents
• smooth electrical power
• temporarily store magnetic energy
• manage energy transfer between batteries, motors, and electronic systems

The energy stored in an individual inductor may be temporary, but repeated storage and release can occur thousands of times per second.

Renewable Energy Systems

Power converters used with:

• solar panels
• wind turbines
• battery storage

often contain inductors.

The inductors temporarily store and release magnetic energy as electronic switches control the flow of electrical power.

This helps convert variable electrical inputs into forms suitable for:

• batteries
• electrical grids
• motors
• electronic equipment

Magnetic Energy and Current Changes

The relationship between energy and current helps explain why inductors resist changes in current.

If current increases:

magnetic energy must increase

That requires an energy input.

If current decreases:

magnetic energy decreases

That energy must be transferred elsewhere.

Therefore, changing current involves changing the amount of energy stored in the magnetic field.

Worked Comparison

Inductor A:

L = 0.20 H

I = 4.0 A

Energy:

E_A = ½(0.20)(4.0²)

E_A = 1.6 J

Inductor B:

L = 0.40 H

I = 4.0 A

Energy:

E_B = ½(0.40)(4.0²)

E_B = 3.2 J

Doubling inductance has doubled the stored energy.

Current Comparison

An inductor has:

L = 0.50 H

At:

I₁ = 2.0 A

E₁ = ½(0.50)(2.0²)

E₁ = 1.0 J

At:

I₂ = 4.0 A

E₂ = ½(0.50)(4.0²)

E₂ = 4.0 J

The current doubled, but the stored energy increased by a factor of four.

Multiple-Change Example

Suppose an inductor initially has:

L₁ = L

I₁ = I

Its inductance doubles and its current triples.

Since:

E = ½LI²

the new energy factor is:

2 × 3²

= 2 × 9

= 18

Therefore:

the new magnetic energy is 18 times the original energy.

A Complete Calculation

An inductor has:

L = 0.80 H

The current increases from zero to:

I = 5.0 A

Calculate the final stored energy.

E = ½LI²

E = ½(0.80)(5.0²)

E = (0.40)(25)

E = 10 J

If the current later decreases to:

I = 3.0 A

the remaining energy is:

E = ½(0.80)(3.0²)

E = (0.40)(9)

E = 3.6 J

Energy released:

10 − 3.6

6.4 J

Therefore, 6.4 J of magnetic energy has been transferred out of the inductor.

Comparing an Inductor and Capacitor

An inductor has:

L = 2.0 H

I = 3.0 A

Its energy is:

E_L = ½(2.0)(3.0²)

E_L = 9.0 J

A capacitor has:

C = 0.020 F

V = 30 V

Its energy is:

E_C = ½(0.020)(30²)

E_C = (0.010)(900)

E_C = 9.0 J

Both devices store the same amount of energy, but:

• the inductor stores it in a magnetic field
• the capacitor stores it in an electric field

A Reliable Strategy for Energy Problems

First identify:

• inductance L
• current I

Convert units if necessary.

Then use:

E = ½LI²

If current is unknown:

I = √(2E/L)

If inductance is unknown:

L = 2E/I²

For comparisons, remember:

E ∝ L

and:

E ∝ I²

If the problem asks how much energy is released as current changes:

energy released = E_initial − E_final

Unit Conversions

Inductance must usually be converted into henries.

Remember:

1 mH = 10⁻³ H

1 μH = 10⁻⁶ H

For example:

50 mH = 0.050 H

250 mH = 0.250 H

20 μH = 2.0 × 10⁻⁵ H

Current should normally be expressed in amperes.

Energy is then obtained in joules.

Common Mistakes

Forgetting to square the current

The equation is:

E = ½LI²

not ½LI.

Forgetting the factor ½

The factor one-half is essential.

Using millihenries as though they were henries

Always convert units before calculating.

Thinking the energy is stored in the electric current itself

The energy is associated with the magnetic field produced by the current.

Thinking an ideal inductor permanently consumes energy

An ideal inductor can store energy and later return it.

Confusing an inductor with a resistor

A resistor dissipates energy mainly as heat; an ideal inductor stores magnetic energy.

Confusing magnetic and electric energy storage

Inductors store magnetic field energy. Capacitors store electric field energy.

Assuming the energy disappears when current falls

The stored energy must be transferred somewhere else.

Ignoring voltage spikes when interrupting current

A rapid decrease in current can produce a large induced EMF.

Key Terms

Magnetic field energy — energy associated with a magnetic field.

Inductor — circuit component that stores energy in a magnetic field and opposes changes in current.

Inductance — measure of a circuit's self-inductive behaviour, represented by L.

Henry (H) — SI unit of inductance.

Self-induction — production of an EMF caused by changes in a circuit's own current.

Self-induced EMF — voltage produced by changing magnetic flux caused by changing current in the same circuit.

Lenz's law — principle stating that induced effects oppose the change that produced them.

Energy density — energy stored per unit volume.

Capacitor — component that stores energy in an electric field.

Electric field energy — energy associated with an electric field, such as that between capacitor plates.

Magnetic flux — measure of magnetic field passing through a surface.

RL circuit — circuit containing resistance and inductance.

LC circuit — circuit containing inductance and capacitance that can exchange energy between magnetic and electric fields.

Flyback protection — circuit arrangement used to safely manage energy released when current through an inductive load is interrupted.

Energy conservation — principle that energy cannot be created or destroyed, only transferred or transformed.

Key Takeaways

• Inductors store energy in magnetic fields.
• Energy must be supplied to establish the magnetic field around an inductor.
• Self-induction opposes the increase in current while the magnetic field is being established.
• The energy stored in an inductor is E = ½LI².
• Stored energy is directly proportional to inductance.
• Stored energy is proportional to the square of current.
• Doubling inductance doubles the stored energy for the same current.
• Doubling current quadruples the stored energy.
• When current decreases, the magnetic field collapses and stored energy is released.
• Magnetic energy can be transferred back into the electrical circuit.
• Energy conservation applies throughout the storage and release process.
• Real inductors lose some energy through resistance and magnetic-core effects.
• Capacitors store energy in electric fields, while inductors store energy in magnetic fields.
• Capacitor energy is E = ½CV².
• Inductor energy is E = ½LI².
• Inductors oppose rapid changes in current, while capacitors oppose rapid changes in voltage.
• LC circuits can exchange energy between electric and magnetic fields.
• Sudden interruption of current can release stored magnetic energy as a large induced voltage.
• Inductors are important in power converters, filters, motor controllers, renewable-energy systems, and many other electronic devices.
• Magnetic energy storage allows circuits to control and transfer electrical energy efficiently.

Practical Inductance Applications

Inductors are used throughout modern electrical and electronic systems because they oppose rapid changes in current and store energy in magnetic fields.

An inductor is usually made from a coil of conducting wire. Many inductors also contain a magnetic core to increase their inductance.

Their behaviour is based on self-induction:

changing current → changing magnetic field → self-induced EMF

The induced EMF opposes the change in current according to Lenz's law.

This simple effect allows inductors to perform several important jobs:

• storing and transferring energy
• smoothing changing currents
• reducing electrical noise
• filtering signals
• converting voltages efficiently
• controlling current in motors and other devices

 

 

 

6

Inductors in Everyday Electronics

Inductors are found in many familiar devices, including:

• phone chargers
• laptop power supplies
• televisions
• radios
• computers
• Wi-Fi equipment
• LED lighting
• electric vehicles
• electric motors
• audio equipment
• solar power systems

Some inductors are large coils that are easy to recognize.

Others are extremely small components mounted directly onto circuit boards.

Why Inductors Are Useful

The key property of an inductor is that it opposes changes in current.

The induced EMF is related to:

|ε| = L|ΔI/Δt|

where:

• ε = induced EMF
• L = inductance
• ΔI/Δt = rate of current change

Rapid current changes therefore produce larger inductive effects.

This makes inductors particularly useful in circuits containing rapidly changing or switching currents.

Inductors and Steady DC

An ideal inductor behaves differently depending on whether the current is changing.

When DC current is changing:

• the magnetic field changes
• self-induced EMF occurs
• the inductor opposes the current change

When the current becomes steady:

ΔI/Δt = 0

so:

ε = 0

An ideal inductor therefore has zero induced voltage once steady DC conditions are reached.

A real inductor still has some resistance in its wire.

Energy Storage

An inductor stores energy in its magnetic field.

The stored energy is:

E = ½LI²

where:

• E = energy in joules
• L = inductance in henries
• I = current in amperes

When current increases, magnetic energy increases.

When current decreases, the magnetic field can return energy to the circuit.

This temporary energy storage is extremely important in modern power electronics.

Inductors in Power Supplies

One of the most important applications of inductors is in power supplies.

Electronic devices often require a different voltage from the available power source.

For example:

• a battery voltage may need to be reduced
• a battery voltage may need to be increased
• an AC supply may need to be converted to controlled DC
• a varying input may need to produce a stable output

Inductors help accomplish these tasks efficiently.

 

 

 

8

Switching Power Supplies

Modern electronics commonly use switch-mode power supplies.

Instead of continuously wasting excess electrical energy as heat, electronic switches turn on and off rapidly.

Inductors repeatedly:

store magnetic energy → release magnetic energy

during each switching cycle.

This allows electrical energy to be transferred and converted efficiently.

Why Switching Works

Imagine a switch connected to an inductor.

When the switch is turned on:

• current increases
• magnetic field strengthens
• energy is stored

When the circuit switches configuration:

• current begins changing
• magnetic field changes
• the inductor produces an induced voltage
• stored energy is transferred elsewhere in the circuit

This process may occur thousands or millions of times each second in modern electronics.

Buck Converters

A buck converter reduces DC voltage.

For example, a circuit might convert:

12 V → 5 V

The inductor helps maintain a relatively smooth output current while an electronic switch rapidly turns on and off.

During part of the switching cycle, energy is stored in the magnetic field.

During another part, the stored energy is delivered to the load.

This allows efficient voltage reduction.

Boost Converters

A boost converter increases DC voltage.

For example:

5 V → 12 V

During one part of the cycle:

• current increases through the inductor
• magnetic energy is stored

During another part:

• the magnetic field collapses
• the inductor produces an induced voltage
• its voltage contributes to the output

This can produce an output voltage greater than the input voltage.

Buck-Boost Converters

A buck-boost converter can increase or decrease voltage depending on its design and operating conditions.

Inductive energy storage allows energy to be transferred between different parts of the circuit.

Buck-boost systems are useful when battery voltage changes during operation but the electronics require a controlled output.

Phone and Laptop Chargers

Modern chargers commonly contain inductive components as part of their switching power supplies.

Their functions can include:

• temporary energy storage
• voltage conversion
• current smoothing
• noise filtering
• electromagnetic interference reduction

Efficient switching designs allow chargers to be much smaller than older power supplies while still handling significant electrical power.

Smoothing Current

Switching circuits naturally produce rapid variations in current.

Many electronic devices require a much smoother electrical supply.

An inductor resists rapid current changes.

Therefore, it can reduce the size of these fluctuations.

The result is:

rapidly varying current → inductor → smoother current

This is often called current smoothing.

Current Ripple

Small repeated variations around the desired current are often called ripple.

For example, instead of remaining perfectly constant, current might repeatedly rise and fall slightly.

An inductor helps reduce current ripple because:

rapid current change → larger self-induced EMF

The inductor therefore opposes the rapid increase and decrease.

Inductors as Electrical Filters

Inductors can also help separate unwanted high-frequency signals from useful lower-frequency signals.

For sinusoidal AC, the opposition provided by an ideal inductor is described by inductive reactance:

X_L = 2πfL

where:

• X_L = inductive reactance in ohms
• f = frequency in hertz
• L = inductance in henries

As frequency increases:

X_L increases

Therefore, an inductor has a stronger effect on higher-frequency current variations.

Worked Example: Inductive Reactance

An inductor has:

L = 0.020 H

At:

f = 50 Hz

X_L = 2πfL

X_L = 2π(50)(0.020)

X_L ≈ 6.3 Ω

At:

f = 5000 Hz

X_L = 2π(5000)(0.020)

X_L ≈ 628 Ω

The same inductor provides much greater opposition to the higher-frequency signal.

Reducing Electrical Noise

Electronic circuits can contain unwanted rapidly changing signals called electrical noise.

Noise can come from:

• switching circuits
• motors
• radio-frequency signals
• digital electronics
• power lines
• nearby electronic equipment

Because many forms of unwanted noise contain high-frequency components, inductors can help reduce them.

 

 

 

9

Chokes

An inductor designed mainly to reduce unwanted AC or high-frequency signals is often called a choke.

A choke can allow desired DC current to pass while providing greater opposition to rapidly changing current.

Therefore:

desired DC → passes relatively easily

while:

high-frequency noise → strongly opposed

Chokes are widely used in power supplies and communication equipment.

Filtering Power-Supply Noise

A DC power supply may contain:

• useful DC
• unwanted AC ripple
• high-frequency switching noise

An inductor can help separate these components.

The DC component is steady and therefore produces little inductive opposition.

Rapid variations produce larger inductive effects.

This allows an inductor to help create a cleaner DC supply.

Inductors and Capacitors Together

Inductors are often combined with capacitors.

They have complementary behaviour:

Inductor: opposes rapid changes in current.

Capacitor: opposes rapid changes in voltage.

Together, they can form powerful filtering circuits.

 

 

 

8

LC Filters

An LC filter contains:

• an inductor, L
• a capacitor, C

The inductor helps smooth current.

The capacitor helps smooth voltage.

Together, they can reduce unwanted variations more effectively than either component alone.

LC filters are common in:

• power supplies
• audio systems
• radio circuits
• communication equipment
• motor controllers

Common-Mode Chokes

Some cables carry unwanted high-frequency noise that appears in similar ways on multiple conductors.

A common-mode choke uses coupled windings to strongly oppose this unwanted noise while allowing the intended current or signal to pass.

Common-mode chokes are often found in:

• computer equipment
• power adapters
• communication systems
• USB and other data interfaces
• industrial electronics

They help reduce electromagnetic interference (EMI).

Electromagnetic Interference

Electromagnetic interference, or EMI, is unwanted electromagnetic energy that interferes with the operation of electrical equipment.

EMI can cause:

• distorted signals
• communication errors
• audio noise
• unstable electronics
• interference with nearby devices

Inductive filters help prevent unwanted high-frequency currents from travelling through wires and cables.

Ferrite Components

Ferrite is a magnetic ceramic material commonly used in high-frequency inductive components.

You may have seen a cylindrical or enlarged section near the end of a computer or display cable.

Some of these devices contain ferrite material that helps reduce high-frequency interference.

Ferrite components are useful because they can provide strong magnetic effects while limiting unwanted eddy-current losses at high frequencies.

 

 

 

7

Inductors in Radio Circuits

Inductors are important in radio-frequency circuits.

When combined with capacitors, they can form resonant circuits that respond strongly to particular frequencies.

This allows circuits to:

• select radio frequencies
• reject unwanted frequencies
• tune transmitters
• tune receivers
• filter communication signals

The ability to select frequencies is fundamental to radio and wireless communication.

LC Resonance

In an LC circuit, energy can move between:

• the capacitor's electric field
• the inductor's magnetic field

The capacitor stores energy as:

E_C = ½CV²

The inductor stores energy as:

E_L = ½LI²

This exchange can produce electrical oscillations.

The resonant frequency of an ideal LC circuit is:

f = 1/(2π√(LC))

Example: Radio Tuning

Suppose a radio receives many frequencies simultaneously.

A carefully chosen combination of L and C can have a resonant frequency corresponding to the desired station.

The circuit responds strongly near that frequency while responding less strongly to many other frequencies.

Changing L or C changes the resonant frequency.

This allows the circuit to be tuned.

Inductors in Audio Systems

Inductors can also be used in audio crossover networks.

Different speakers are designed for different frequency ranges.

For example:

• woofers reproduce lower frequencies
• tweeters reproduce higher frequencies

Inductors and capacitors can help direct appropriate frequency ranges to different speakers.

Inductors in Electric Motors

Motor windings are coils and therefore have inductance.

Their inductance affects:

• how quickly current changes
• motor starting behaviour
• current ripple
• electromagnetic torque
• electronic motor control

Modern motor controllers must account for the inductance of the motor windings.

Motor Current Smoothing

Electronic motor controllers often switch voltage rapidly.

Without inductance, current could change very rapidly.

Motor winding inductance helps smooth these changes.

This is especially important in:

• electric vehicles
• drones
• robots
• industrial machines
• computer cooling fans

Relays and Solenoids

Relays and electromagnetic solenoids contain coils.

When current flows:

• a magnetic field develops
• magnetic energy is stored
• magnetic forces can move mechanical components

Examples include:

• electrical switches
• valves
• door locks
• automotive actuators

Because these coils have inductance, switching them off can produce large induced voltages.

Flyback Protection

When current through a coil is suddenly interrupted:

|ε| = L|ΔI/Δt|

If Δt is very small, the induced voltage can become very large.

A flyback diode can provide a temporary path for current when a DC inductive load is switched off.

The stored magnetic energy is then released more safely.

This protects components such as transistors and switches.

 

 

 

7

Transformers

Transformers contain inductive windings.

Alternating current in the primary produces changing magnetic flux.

Mutual induction produces an EMF in the secondary.

Transformers can:

• increase voltage
• decrease voltage
• provide electrical isolation
• transfer signals
• transfer electrical power

Inductance is therefore central to transformer operation.

Wireless Charging

Wireless charging also uses inductive effects.

An alternating current passes through a transmitter coil.

The changing magnetic field reaches a receiver coil.

Mutual induction produces an EMF in the receiver.

Energy can therefore be transferred without exposed electrical contacts.

Applications include:

• smartphones
• smartwatches
• electric toothbrushes
• some medical devices
• some electric vehicle charging systems

Inductive Sensors

Inductors can be used as sensors because nearby materials can affect their magnetic fields.

Applications include:

• proximity sensors
• position sensors
• metal detectors
• vehicle detection systems
• industrial automation

A nearby conducting or magnetic object changes the electromagnetic behaviour of the sensor coil, allowing the electronics to detect its presence.

Induction Heating

Changing magnetic fields can induce currents in nearby conducting materials.

These currents can produce heating.

Induction heating is used in:

• induction cooktops
• industrial metal heating
• metal treatment
• manufacturing

The coil itself creates the changing magnetic field responsible for the induction process.

Energy Storage in Power Electronics

Inductors are particularly useful because they can store and release energy extremely quickly.

Suppose an inductor has:

L = 0.50 H

and carries:

I = 4.0 A

Stored energy:

E = ½LI²

E = ½(0.50)(4.0²)

E = 4.0 J

If current changes, this energy can be transferred elsewhere in the circuit.

Worked Example: Power-Supply Inductor

A power-supply inductor has:

L = 5.0 mH

and carries:

I = 3.0 A

Convert:

5.0 mH = 0.0050 H

Then:

E = ½LI²

E = ½(0.0050)(3.0²)

E = 0.0025(9)

E = 0.0225 J

Although this is a relatively small amount of energy, the inductor may store and release energy thousands of times per second.

The rate of energy transfer can therefore be significant.

Advantages of Inductors

Inductors provide several important advantages.

They can:

• store energy without relying on chemical reactions
• release stored energy very rapidly
• smooth current
• reduce ripple
• suppress high-frequency noise
• help filter signals
• enable efficient switching power supplies
• support voltage conversion
• provide frequency selection
• operate reliably for very large numbers of cycles

These properties make them extremely valuable in modern electronics.

High Efficiency

An ideal inductor does not dissipate energy.

Instead:

electrical energy → magnetic energy → electrical energy

Real inductors do have losses, but efficient designs can transfer a large fraction of their stored energy back into the circuit.

This makes inductors particularly useful in efficient power-conversion systems.

Fast Response

Magnetic energy can be stored and released quickly.

Unlike chemical energy storage, no chemical reaction is required.

This makes inductors suitable for circuits switching at high frequencies.

Modern power converters can therefore repeatedly store and release energy many thousands or millions of times per second.

Reliability

Inductors are often simple components with no moving parts.

This can provide:

• long operating life
• high reliability
• large numbers of operating cycles

This is especially useful in power electronics and industrial equipment.

Limitations of Inductors

Inductors also have disadvantages.

Real inductors can:

• occupy significant circuit-board space
• be relatively heavy
• have wire resistance
• generate heat
• produce electromagnetic interference
• experience magnetic-core losses
• saturate at high currents
• be more expensive than simple resistors

Engineering design involves balancing these disadvantages against the benefits.

Copper Losses

The wire used to make an inductor has resistance.

Therefore:

P = I²R

describes power converted into thermal energy in the winding.

Large currents can therefore cause significant heating.

Using lower-resistance conductors can reduce these losses.

Core Losses

Magnetic cores can experience energy losses.

Two important mechanisms are:

• eddy currents
• magnetic hysteresis

Core materials and construction are selected to reduce these effects.

For example:

• laminated cores can reduce eddy currents
• ferrite materials are useful at higher frequencies

Magnetic Saturation

Magnetic cores cannot always respond proportionally to indefinitely increasing current.

At sufficiently strong magnetic fields, a core may approach magnetic saturation.

When this occurs:

• effective inductance can decrease
• current may increase rapidly
• losses and heating can increase
• circuit performance may deteriorate

Engineers therefore choose inductors with suitable current ratings.

Size and Energy Storage

Storing significant magnetic energy generally requires:

• sufficient inductance
• sufficient current capability
• adequate magnetic core volume
• suitable conductor size

This is one reason high-power inductors can be physically large.

Miniaturizing inductors while maintaining efficiency and current capacity is an important engineering challenge.

Inductors vs Resistors

Inductors vs Capacitors

Inductors and capacitors are often used together because their properties complement each other.

Choosing an Inductor

Engineers may consider:

• inductance
• maximum current
• resistance
• core material
• physical size
• operating frequency
• saturation current
• energy-storage capacity
• heat generation
• electromagnetic interference

The "largest inductance" is therefore not automatically the best choice.

A successful design balances several requirements.

Evaluating Inductors in Modern Electronics

Inductors remain extremely useful because modern electronics increasingly relies on rapid switching.

Switching is used to control energy efficiently rather than continuously dissipating excess energy.

Inductors are well suited to this because they can:

store energy during one part of a switching cycle

and:

release energy during another part

This allows efficient control of electrical power.

Electric Vehicles

Electric vehicles contain numerous inductive components.

They can appear in:

• motor windings
• DC-DC converters
• onboard chargers
• electromagnetic interference filters
• power-conditioning systems

Inductance helps control the very large electrical currents involved in vehicle operation.

Renewable Energy

Solar panels and wind turbines often produce electrical power that must be converted before it can be used or supplied to a grid.

Power-electronic converters use inductors to:

• store energy temporarily
• smooth current
• filter switching noise
• control power flow

Inductors therefore contribute to efficient renewable-energy systems.

Computers and Digital Electronics

Computer processors and other digital components can require low voltages and very large currents.

Voltage-regulator circuits commonly use inductors to convert and control electrical power efficiently.

You may see several small power inductors close to a computer processor or graphics chip.

Their job includes helping deliver stable power despite rapidly changing electrical demand.

 

 

 

7

A Complete Application Example

Consider a computer power circuit that must convert:

12 V → lower controlled voltage

for a processor.

A switching transistor rapidly connects and disconnects the input.

The inductor:

• stores magnetic energy when current increases
• opposes sudden current changes
• releases energy when the switching state changes
• helps maintain continuous current
• reduces current ripple

A capacitor can simultaneously help stabilize voltage.

Together, the switching components, inductor, and capacitor provide efficient power conversion.

Common Mistakes

Thinking inductors simply block electricity

Inductors oppose changes in current, not current itself.

Thinking an inductor always has a large voltage across it

The induced voltage depends on how rapidly the current changes.

Thinking inductors only work with AC

Inductors also affect DC circuits whenever the DC current changes, such as during switching.

Thinking inductors destroy unwanted electrical energy

Filtering often redirects, stores, releases, or dissipates unwanted variations through a combination of circuit components.

Thinking all noise has the same frequency

Electrical noise can contain many different frequencies, so filters must be designed for the particular application.

Thinking an ideal inductor consumes power continuously

An ideal inductor stores and returns energy. Real inductors have resistance and other losses.

Ignoring saturation

Real magnetic cores have limits to how strongly they can be magnetized.

Thinking larger inductance is always better

Greater inductance may also mean greater size, resistance, cost, or slower current response.

Key Terms

Inductor — component that stores energy in a magnetic field and opposes changes in current.

Inductance — measure of the ability of a circuit to produce self-induced EMF when current changes.

Self-induction — production of an induced EMF caused by a circuit's own changing current.

Magnetic energy — energy associated with the magnetic field of an inductor.

Switch-mode power supply — power supply that uses rapid electronic switching to control and convert electrical energy efficiently.

Buck converter — circuit that reduces DC voltage using switching and energy-storage components.

Boost converter — circuit that increases DC voltage using switching and energy-storage components.

Buck-boost converter — switching converter capable of producing an output voltage above or below its input under appropriate operation.

Ripple — unwanted repeated variation in voltage or current.

Choke — inductor designed to oppose unwanted changing currents or high-frequency signals.

Inductive reactance — opposition an ideal inductor provides to sinusoidal alternating current, given by X_L = 2πfL.

Electrical noise — unwanted electrical variations that interfere with desired signals or power.

Electromagnetic interference (EMI) — unwanted electromagnetic disturbance affecting electrical equipment.

LC filter — filter containing an inductor and capacitor.

Ferrite — magnetic ceramic material commonly used in high-frequency inductive components.

Magnetic saturation — condition in which a magnetic core can no longer respond proportionally to increasing magnetizing influence.

Flyback diode — component used to provide a safe current path when a DC inductive load is switched off.

Key Takeaways

• Inductors are used extensively in modern electrical and electronic devices.
• Their key property is opposition to changes in current.
• Changing current produces self-induced EMF.
• Inductors store energy in magnetic fields.
• Stored magnetic energy is given by E = ½LI².
• Inductors can store and release energy repeatedly and rapidly.
• Switching power supplies use inductors for efficient energy transfer.
• Buck converters use inductors while reducing DC voltage.
• Boost converters use inductors while increasing DC voltage.
• Inductors help smooth current and reduce ripple.
• High-frequency signals experience greater inductive reactance because X_L = 2πfL.
• Chokes use inductance to suppress unwanted changing currents and electrical noise.
• Inductors and capacitors are frequently combined to form filters.
• Common-mode chokes can help reduce electromagnetic interference.
• Inductors are important in radios, audio systems, motors, transformers, sensors, wireless chargers, and power converters.
• Motor windings and electromagnetic coils naturally possess inductance.
• Real inductors experience resistance, heating, core losses, and possible saturation.
• Inductors can improve efficiency because energy can be temporarily stored rather than simply dissipated.
• Their disadvantages can include size, weight, resistance, cost, and magnetic interference.
• Modern electronics depends heavily on inductors for efficient power conversion, current control, noise suppression, and signal filtering.

Check Your Understanding

1. Identify five common devices or systems that use inductors.
2. Explain why an inductor opposes rapid changes in current.
3. Explain how an inductor can store energy and later return it to a circuit.
4. Why can an inductor allow steady DC while strongly opposing high-frequency current variations?
5. Calculate the inductive reactance of a 0.050 H inductor at 60 Hz.
6. The same 0.050 H inductor is used at 6000 Hz. Calculate its inductive reactance and compare it with your answer to Question 5.
7. Explain how an inductor can help reduce high-frequency electrical noise.
8. What is a choke, and why is it useful in electronic equipment?
9. Explain why inductors and capacitors are often used together in power-supply filters.
10. Describe the role of an inductor in a buck converter.
11. Describe how magnetic energy stored in an inductor can help a boost converter produce a higher output voltage.
12. A 20 mH power inductor carries 5.0 A. Calculate the energy stored in its magnetic field.
13. Explain why switching off a relay or solenoid can produce a large voltage and how a flyback diode can help protect the circuit.
14. Evaluate two advantages and two disadvantages of using inductors in modern electronic devices.
15. A designer needs a circuit that efficiently converts voltage, reduces current ripple, and suppresses high-frequency noise. Explain why inductors would be useful and identify other components that could be combined with them.