Inductance

What is Inductance?

Inductance is the property of a circuit whereby there is an emf induced into the circuit by the change of flux linkages produced by a current change. When the emf is induced in the same circuit as that which the current is changing, the property is called self-inductance, L. When the emf is induced in a circuit by a change of flux due to current changing in an adjacent circuit, the property is called mutual inductance, M. The unit of inductance is the henry, H.

A circuit has an inductance of one henry when emf of one volt is induced in it by a current changing at the rate of one ampere per second.

Induced emf in a coil of N turns:

Where dΦ is the change in flux in webers, and dt is the time taken for the flux to change in seconds, that is:

   The induced emf in a coil of inductance L henrys,

Where dI is the change in current in amperes and dt is the time taken for the current to change in seconds, that is:

The minus signs in each of the above two equations, shows the direction given by Lenz’s law.

The proportionality constant L is (the inductance depends on a number of physical parameters, such as coil shape, number of turns, and core makeup).

Typical values of inductance for commercial inductors vary from a few nanohenrys for small air core inductors to 50 H large iron core inductors.

Inductors

A component called inductor is used when the property of inductance is required in a circuit. The basic role of an inductor is to prevent any sudden changes in current flowing through it.

A basic form of an inductor is a simple coil of wire. Examples of practical inductors are shown below

Inductor’s Standard Electrical Circuit Diagram Symbols

The iron-cored inductor is usually called a choke since when used in AC circuits; it has a choking effect, limiting the current flowing through it.

Under AC conditions, an inductor’s impedance (reactance) increases with frequency; an inductor acts to block high-frequency signals while allowing low-frequency signals to pass through it. By selecting the proper inductance value, it is possible to create high frequency chokes e.g. RF/EMI chokes that, when placed in series with power or signal paths will prevent RF (Radio frequency) or EMI (Electromagnetic Interference) from entering the main circuit where they could introduce undesirable hum and false triggering effects.

Low pass and high-pass filters use inductors as the reactive element. In the low pass filter, the inductor ‘chokes’ out high frequency components; while in the high-pass filter the inductor passes the low-frequency components to the ground –high frequency components are prevented from taking the same path and follows the signal path.

Factors which affect the Inductance of an Inductor

We have several factors that affect the inductance of an inductor, and they include:

• The number of turns of wire, the more the turns, the higher the inductance.
• The cross-sectional area of the coil wire, the greater the cross sectional area, the higher the inductance.
• The presence of a magnetic core –when the coil is wound on an iron core, the same current sets up a more concentrated magnetic field and the inductance is increased.
• The way the turns are arranged – a short thick coil of wire has a higher inductance than a long thin one.

Energy stored by an Inductor

The energy W, in the magnetic field of an inductor is given by:

W = ½ LI² joules

Where L = Inductance

I = Current

Related: Key Facts about Resistors, Resistor Colour Codes and Resistor Tolerance

Inductors in Series and Parallel Connections

Inductors in Series Connection

When two or more inductors are in series, the total inductance is equal to the sum of the individual inductances, provided the coils are sufficiently separated so that the coils are not in the magnetic field of one another.

L_T = L₁ + L₂ + L₃ +…+ L_N (Inductors in series)

Fig inductors in series

Inductors in Parallel Connection

If inductors are connected in parallel, and if the coils are separated sufficiently, the total inductance is given by:

When only two inductors are in parallel, we have total inductance:

You can also read: Capacitors, Capacitance and Charge

Inductance in AC circuits

Consider the effect of supplying an iron-cored coil of negligible resistance with an alternating current and voltage.

In this instance the current, and therefore the magnetic field is building up and collapsing (in our case of 50 Hz supply) 50 times every second and hence a continual alternating back emf is produced. As explained in this article, the back emf opposes the change in the circuit current which is producing the emf. Hence under AC conditions the emf produces a continual opposition to the current (Just in the same way as resistance does in a resistive circuit). This opposition is called the inductive reactance (symbol X_L and is measured in ohms).

Inductive reactance X_L = 2ℼfL ꭥ

Where f = frequency in hertz

L = Inductance in henrys

In a purely inductive circuit the voltage leads the current by 90° as illustrated below:

Practical applications of Inductors

The basic role of an inductor is to prevent any sudden changes in current from flowing through it. Under AC conditions, and inductor’s impedance (reactance) increase with frequency; an inductor acts to block high-frequency signals while allowing low-frequency signals to pass through it. By selecting the proper inductance value, it is possible to create high frequency chokes e.g. Radio Frequency (RF) or Electromagnetic interference (EMI) chokes that when placed in series with power or signal paths, will prevent radio frequency or electromagnetic interference from entering the main circuit, where they could introduce undesirable hum and false triggering effects.

Inductors are used in Filter networks. Low pass and high pass filters use an inductor as the reactive element. In the low-pass filter, the inductor ‘’chokes’’ out the high-frequency components; while in the high pass filter the inductor passes the low-frequency to ground while the high frequency components are prevented from taking the same path and follow the signal path. Series-resonant (band pass) and parallel-resonant (Notch) filters use inductors. Parallel-resonant filters are used in oscillator circuits to eliminate from an amplifier any input frequencies that are significantly different from the resonant frequency of the LC filter. These kinds of circuits are usually used to generate carrier signals for transmitters. Resonant filters also act as tuned circuits used in radio reception.

Inductors are used in switching power supplies relying on their energy storage ability e.g. they are used in a step-up switching regulator or boost convertor that is used to increase a 5 V input voltage to a 12 V output voltage.

Coupled inductors that share magnetic flux linkage are used to create transformers –i.e. devices that utilize mutual inductance to step up or step down AC voltages and currents.

A heavily, iron core inductor can be used as an electromagnet that is capable of attracting steel and other ferromagnetic materials. A solenoid is an electromagnetic that has a mechanical mechanism that is pulled when the solenoid is energized by current. This movement mechanism may involve opening or closing a valve i.e. solenoid valve, latching or unlatching a door, making or breaking contacts i.e. electric relay, etc.

Related article: Resistance and Resistivity