mod 3 rg 3.11 inductance and inductors

As described in the previous section, an electric current can produce a magnetic field. A magnetic field can also produce an

electric current, and this reverse effect was discovered in 1831 by two pioneers working independently in England (Michael Faraday) and the USA (Joseph Henry). They both discovered that an Electromotive Force (EMF) can be produced across a conductor in a magnetic field and this effect is known as electromagnetic induction.

an EMF can be induced across a conductor in two ways.

• By the relative movement of a permanent magnet and the conductor (when either one moves).

• By changing the strength of the magnetic field passing through the conductor.

Induction is the principle behind the operation of

electric generators, dynamos, AC motors, and transformers; it is also very important in the operation of radio transmitters and receivers.

Faraday's law can be stated as follows:

A voltage is induced across a conductor whenever relative motion exists between the conductor and a magnetic field. The induced voltage is directly proportional to either:

• The rate of flux cut by a single wire.

• The rate of change of flux passing through a coil of wire.

If a conductor is moved through a magnetic field, an EMF (voltage) is induced across the conductor. This induction will only occur if there is

relative movement between the conductor and the magnetic flux lines, and only in a direction that cuts through the lines.

As this electromagnetic induction is the principle of operation of electrical generators, it is also often referred to as the

“generator principle”.

The direction of the induced voltage depends on:

• The direction in which the conductor is moved.

• The direction of the magnetic field.

An induced EMF in the conductor, when connected to a complete circuit, causes a current to flow in the circuit. A coil of wire provides a more

efficient means of generating currents in this way.

the circuit is completed through a galvanometer. When the bar magnet is moved towards the coil and current flows, the needle of the galvanometer will deflect away from its central position in one direction only. When the magnet stops moving and is held stationary (in relation to the coil), the needle of the galvanometer

returns to zero, as there is no physical movement of the magnetic field.

when the magnet is moved away from the coil, the needle of the galvanometer deflects in the opposite direction; this indicates

a change in polarity. Moving the magnet back and forth repeatedly will cause the needle of the galvanometer to move from side to side. Holding the magnet still while moving the coil back and forth will have the same effect.

he action of moving a coil, or loop of wire, through a magnetic field induces a voltage in the coil with a magnitude that is proportional to

the speed or velocity of the movement.

The faster the movement of the magnetic field, the

greater the induced voltage across the coil. For Faraday’s law to hold true, there must be a relative motion of the coil and magnetic field.

A coil of wire consists of a single wire wound into a series of loops that are electrically insulated from one another so that any current must flow around all the loops. Each loop is known as a

turn

For a coil, it is best to consider the flux passing along the central axis of the coil rather than counting

lines of flux that are cut by the turns (this is possible but very complicated for a coil of wire).

If the magnitude of the flux passing directly along the axis of the coil changes, then

a voltage is induced across the ends of the coil.

The magnitude of the voltage induced across a coil of wire is dependent on three factors:

• The number of turns on the coil – a voltage is induced across each turn; by increasing the number of conductors cutting through the magnetic field.

• The magnitude of the induced voltage is in proportion to the number of turns on the coil e.g. if there are 20 turns on the coil the induced voltage will be 20 times greater than for one turn.

• The relative speeds of the coil compared to the magnet – this will cause the wire to cut the lines of flux at a faster rate, thereby inducing a greater voltage across the coil.

• The strength of the magnetic field – if the same coil of wire is moved at the same speed through a stronger magnetic field, the induced voltage will be greater as there are more lines of flux to cut in the same area (greater flux density).

If a bar magnet is moved in and out of a coil repeatedly, a continuous voltage is induced across the coil, alternating between a positive polarity and a negative polarity; this can be described as an

AC output voltage. This is the basic operating principle of an electrical generator, like those used in dynamos and car alternators.

The simple dynamo-type generator above consists

of a permanent magnet rotating around a central shaft with a coil of wire placed next to this rotating magnetic field. As the magnet spins, the magnetic field around the top and bottom of the coil fluctuates between a north and a south pole. This rotational movement of the magnetic field induces an alternating EMF across the coil, as described by Faraday’s law of electromagnetic induction.

If two coils of wire are brought into close proximity with each other, such that any magnetic field generated by one coil passes through the other, a voltage will be induced across the second coil if the flux changes through the first. This process is called

mutual inductance.

The most common application of mutual induction is in

transformers

Transformers allow power to be transferred between systems which are

galvanically separated by using two coils of wire and an AC supply.

If two systems are galvanically separated or isolated,

no current can flow between them.

Two coils are wound around a common soft magnetic iron coil core but have no electrical connection (as shown below).If the voltage in the first coil (primary) changes, the current will change, along with the strength of the magnetic field established by this coil.

The second coil (secondary) is now

subjected to a changing magnetic field. This change causes a voltage to be induced across the second coil.

It can be shown that the induced voltage across the secondary coil Vs is directly proportional to the rate at which the current changes in the

primary coil

The negative sign indicates that the voltage induced in the secondary coil is in the

opposite direction to that in the primary (see Lenz's law below).

Vs & - the of change of primary current

the constant of proportionality in this relationship is known as the

mutual inductance M.

The greater the mutual inductance the greater the

induced voltage (for the same rate of change of current).

Vs = -M X rate of change of primary current

Several physical factors will increase the mutual inductance M of a pair of coils, including:

Increasing the number of turns on the coils Np and Ns

Increasing the cross-sectional area of the coils A (m²)

Decreasing the length of the coils L (m)

Increasing the permeability of the material used in the common core mu (H/m)

the mutual inductance of a pair of coils M is equal to

M = mu x A x Np x NS/L

the unit of inductance M is henry (H)

This equation only holds true if the two coils share a common core, are very close together, or are wound around the same axis (wound together).

As the distance between the two coils increases the mutual inductance

decreases but non-linearly.

Lenz’s law states that the current caused by an induced voltage always

opposes the cause of the induction.

moving a conductor through a magnetic field will induce a voltage across it; consequently, a current flows, if the conductor is part of a complete circuit. This current

will produce its own magnetic field around the conductor.

This second field around the conductor is always aligned in such a way that

the resultant field becomes denser in front of the conductor. This resultant field opposes the relative motion of the conductor. In the diagrams below, a wire is aligned perpendicular to the plane of this page and is moving to the left.

The wire is part of a complete circuit, so the induced EMF causes a current to flow out of the page. In the left-hand diagram, the two fields (one produced by the magnet and one by the current in the wire) are overlaid; in the right-hand diagram the two fields are added together to show the resultant field (the actual field), and this resultant field exerts a force on the wire to the right, opposing

the motion of the wire.

Lenz's law also applies to mutual inductance (see above) and self-inductance (see below). The induced current will always flow in such a direction as to generate a magnetic field that opposes the change in the original field i.e.,

opposes the change in the field which caused the induction.

It is possible to visualise Fleming's right-hand rule with an open hand, so that

the flux lines coming from the north pole hit the palm, with the thumb pointed in the direction of the conductor movement.

The fingers show the direction of the induced current (conventional current flow), and, therefore, the induced voltage (90 degrees apart)

Just as in mutual induction, a single coil is also subject to the effects of its magnetic field growing or shrinking. As the current through a coil increases, and its magnetic field increases, this induces a voltage across the coil itself. Furthermore, this voltage opposes the change in current flowing in the coil, acting against the current (see Lenz's law above).

Conversely, as the current through a coil decreases, the magnetic field decreases, and this induces a voltage across the coil which opposes this change and acts

to keep the current flowing.

Self-inductance (usually just called inductance) has the symbol

L and the units of henry (H)

if a current is changing at the rate of one ampere per second and is inducing a voltage of one volt across a coil, that coil has an inductance of

one henry.

The inductance of coil L is given by the following formula, which depends only on its geometry and core material.

L= Mu X A X N²/ L

Mu is the permeability of the core in henrys per metre (H/M)

A as the cross-sectional area of the coil in square metres (M²)

N is the number of turns on the coil

L is the length of the coil in metres (m)

Disconnecting coils requires special caution. When a coil is switched off, the rate of change of current is extremely high (i.e., from its original value to zero in a very short time), therefore the induced voltage

is extremely high because the change of the magnetic field is very rapid. The collapsing magnetic field will briefly induce a large voltage across the coil. This voltage can be ten times higher than the voltage originally applied.

As a precaution from back EMF, freewheeling diodes are often

integrated parallel to the coil. In normal operating mode, they are poled in the reverse direction so that no current flows through the diode (see diagram below). When switching off, the back EMF is such that it tries to maintain the current. The diode allows the current to continue to flow for some time (since the voltage is now reversed across the diode a current may flow through the diode) and so the rate of change of current through the coil is much smaller than without the diode, and therefore the back EMF is very much lower (as this depends on the rate of change of current). As the magnetic field decays away the current slowly falls to zero

Sometimes high voltages are intended, e.g. across the ignition coil of an internal combustion engine, and coils are deliberately disconnected without such precautions to create a spark.

Saturation current in an inductor is

the current at which the core is completely filled with magnetic flux and cannot take any more. Scientifically speaking, it is the current at which all the magnetic domains in the core are fully aligned.

You cannot saturate an inductor that does not have

a core

Saturation depends on the quantity of material in the core – if saturation is a problem in a circuit, the usual solution is to

use a physically larger inductor.

Saturation is usually a problem in power supplies because, once it happens,

any additional energy is not stored in the magnetic field but is wasted as heat.

At the saturation point, the magnetic field is no longer increasing, so the induced voltage falls to

zero; the primary current may then increase unchecked and damage the coil.

inductors have several properties that make them essential components in many circuits.

Mutual induction is the principle behind the design of

electrical transformers. By employing different numbers of turns on primary and secondary coils the induced EMF can be selected to be either lower or higher than the primary voltage

Transformers allow AC voltages to be changed in different parts of a circuit or system without

significant loss of energy.

In AC circuits, inductors oppose the changing current and can therefore

reduce or even stop the current in an AC circuit.

For example, inductors can be used to block AC currents but allow DC currents to flow. In this application, the inductor is referred to as

a choke

In radio and television broadcasting, inductors are used in conjunction with capacitors to create tuned circuits. This allows signals of different frequencies to be both broadcast and received, without interference between frequencies. Different frequencies are divided into bands, as seen on the dial of traditional radio. Different values of inductance and capacitance are selected to tune to different bands and different frequencies within those bands. On some radios, the frequency dial is

a variable inductor, where the dial moves a core into or out of a coil, changing its inductance.

Current Transformers (CTs) are single, two and three-phase current-measuring transformers. They measure AC currents without

breaking the current-carrying leads

in a current transformer the primary and secondary sides are

The primary side (input line or feeder line) is the current-carrying lead. The secondary side is the coil on the iron core. The current is now stepped from the input coil down to the output coil, according to the transformer ratio between these two coils.

Current Transformers must always have a load (ammeter), otherwise

a voltage of 100 000 V could be induced across the open terminals.