# Inductors

*Inductors* are electronic components which store energy in a *magnetic field* as electric current flows through it.

Physically, inductors are insulated wire wound into a **coil** around an insulated core. From physics we know that **currents generate magnetic fields around them** in a direction as determined by the *right hand curl rule*. When wire is coiled, the electromagnetic fields are concentrated in the same direction creating a stronger magnetic field.

## Inductor Operation:

When current flowing through an inductor **changes**, for example turning on a switch or increasing/decreasing current, then the time-varying magnetic field **induces a voltage in a direction which opposes the change**. The induced voltage is described by **Faraday's Law of Induction**, and the direction is given by **Lenz's Law**.

The effect of this is that inductors **oppose any changes in current** flowing through them.

The diagram above shows an inductor in action, once a current begins to flow a magnetic field is produced, B, which increases proportionately with the current and a voltage is induced with polarity to oppose the change in current, i.e. the voltage is created to reduce the current back to zero (the initial state of the inductor to keep it constant). With time this **induced voltage** is reduced and the current increases, until reaching **steady state values**.

**Note:** The induced voltage is also commonly referred to as *back-emf* as the voltage polarity is in the opposite direction to the applied voltage to oppose the change in current.

## Inductance:

The property of **inductance** denotes an inductors ability to store energy in a **magnetic field**, an inductor with *more* inductance will have a *stronger* magnetic field induced for an applied current.

An inductor with **more coils** results in more magnetic fields being created in each loop which sum together to create a stronger field.

When the **length** of the coil is reduced, the coils are closer together which creates a stronger magnetic field.

A larger **surface area** also increases the inductance

Inductance also depends on the **core**, i.e. the material that the coils are wrapped around. Iron and steel cores are great examples of materials that reinforce magnetic fields, they are also referred to as *ferromagnetic materials* which are materials that are highly susceptible to forming magnetic fields..

We can combine these observations into a mathematical relationship relating inductance of a **simple coil** to geometry and the ferromagnetic material as shown below:

Where **μ **(pronounced mew) denotes the *permeability* of the core (ability to support a magnetic field), **μ _{r} **is the

*relative permeability*,

**μ**(mew nought) is the permeability of free space (equal to

_{0}**4π*10^-7**) and

**N**is the number of

*turns*(coils),

**l**is the

*length*of the inductor,

**A**is the area of the coils and

**L**is the

*inductance*which has the units of

**H (Henries)**

The henry unit can further be broken down as shown below:

Where **Wb **is the *Weber*, *magnetic flux*, and **Wb/A** is the magnetic flux per unit area. The second equation is energy per amperes squared. So an inductor with more inductance has more flux for a given area and more energy for a given current which will oppose changes in currents **more strongly** as a result of Faraday's Law of Induction.

What is also interesting to note is that **straight wire inductors** also exhibit inductance which depends on the length and area of the conductor. Note that the inductance is considerably lower than that of a coil however, we will see that this inductance can become significant for high speed circuits. Something to look forward to I assure you :)

Practical inductance values range from uH to mH for large inductors.

## Voltage/Current Relationship:

The **voltage **across the inductor is proportional to the *rate of change* of current and the *inductance*. From this we have the mathematical relationship between current and voltage for an inductor:

**Note:** the negative sign reflects the direction of the voltage and over time the rate of change of current decreases and the induced voltage across the inductor approaches 0V.

## Energy stored in an inductor:

We can also quantify the energy (Work) stored by the inductor in the magnetic field with the equation below:

## Inductors in Series:

Inductance **adds** in series. This can be seen from the formula of inductance where we effectively increase the total number of turns and length with more inductors connected in series which increases the total inductance of the circuit.

## Inductors in Parallel:

Circuit inductance *reduces* as inductors are added in parallel.

**For 2 inductors in parallel **we can use the following formula in a similar manner to calculating **parallel resistance**:

## Inductor Applications:

Like capacitors, there are countless applications for inductors in electronic circuits! Some of the most commonly encountered applications are:

- Filter circuits
- Induction motors
- Oscillators
- Ferrite beads
- Relays
- Many more!

We will learn more about each of the above applications throughout this course.

### Examples:

**1.** Determine the inductance of an inductor made of iron with relative permeability 1000, with 100 turns, area of 10mm^2 and length of 50mm:

**2. **What is the energy stored in an inductor with a current of 100mA and inductance of 50uH?

**3. **What is the total inductance for the circuit below?