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), μr is the relative permeability, μ0 (mew nought) is the permeability of free space (equal to 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?

In the circuit above we have inductors L1, L2 and L3 in series and L4 in parallel with R5 hence we can calculate the total inductance with the equation shown below:

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