Inductors

Electromagnetic Induction 

Electromagnetic Induction is the process by which mechanical Work is converted to Electrical Energy.  It is the process by which the generator within a Power station generates Electricity. 

The diagram below shows a simple example of an Inductor (A Coil of Wire) . By moving the Magnet or the Coil) the following results can be obtained :-

1. When the Magnet and the Coil are stationary, the Current reading is zero.

2. When the Magnet moves relative to the Coil, a Current is Induced in the Wire.

3. If the Magnet is moved in the opposite direction, the Current flow reverses.

4. If the Magnet is moved faster, the Induced Current will be larger. 

5. If the Poles of the Magnet are reversed, the Current flow reverses. 

In the above example, a Current flows, apparently without a supply. The reason that a Current flows is that the interaction with the Magnetic field causes an Induced EMF across the coil. The Energy required to move the charges comes from the Work Done moving the Magnet through the Coil. 

The size of the Induced EMF depends on :-

1. The relative speed of the Magnet and Coil

2. The Strength of the Magnet

3. The number of Turns on the Coil

Inductors

The Inductor (described above as a Coil) has a property called Inductance (L). The Inductance of an Inductor is a property of its design, just as the Resistance of a Resistor is. An Inductor will have a large Inductance if it has :-

1. A large area

2. A large number of Turns on the coil

3. An Iron Core

Self Inductance

In the above example, a Current is induced to flow in the coil. This current will itself have a Magnetic field around it, which will Induce a EMF within the Coil. The is called Self-Inductance as the coil is inducing an EMF in itself due to its own changing Current. 

In order to maintain the Law of conservation of Energy, this Self-induced EMF acts to oppose the change that caused it, and as such is referred to as the Back EMF. The fact that this EMF opposes the change that caused it, has implications for turning on or off Inductor circuits. 

This opposition to change is summarised as Lenz's Law :-

"The Induced EMF always acts in such a direction as to oppose the change which produced it. Anything which causes the Magnetic field in a coil to change will be opposed." 

Growth / Decay of Current in an Inductive Circuit

The diagram below shows a simple Inductive circuit, with two control switches S1 and S2 :-

When switch S1 is closed in the above circuit, the Ammeter does not show a instant "jump" to the full Current value, but instead rises to its full value over several seconds. This "delay" is caused by the changing Current inducing a Back EMF across the Inductor, slowing the change in Current. 

The graph below shows how the Current growth is affected by the Inductance (L) of the Inductor :-

As can be seen in the above graph, the greater the Inductance of the Inductor, the greater the Back EMF induced, therefore the lower the rate of change of Current. 

The same effect can be seen if the switch is opened. Again, the Current does not instantly jump to zero, but decays over several seconds. This is again due to a Back EMF being generated slowing the change in Current. 

The graph below shows how the Current decay is affected by the Inductance (L) of the Inductor :-

Magnitude of the Induced EMF

The Magnitude of the Induced EMF is can be found using the following formula :-

Where :-

E  =  Induced EMF (V).

L  =  Inductance of the Inductor (H).

dI / dt  =  Rate of Change of Current (A s-1).

Note - The negative sign in the above equations shows that the Induced EMF will act in the opposite direction to the Current that induced it.

Units of Inductance

The units of Inductance are the Henry (H) . One Henry is defined as follows :-

"The Inductance of an Inductor across which an EMF of 1 Volt is induced when the Current in the conductor changes at a rate of 1 Ampere per second."

Energy Stored in an Inductor

When an Inductor is turned off, the Magnetic field rapidly collapses, generating large Back EMFs. These large Back EMFs can cause sparks across the open contacts of the switch. The Energy required to create the spark comes from the Magnetic field itself. 

When the field was created, Work was done to move the charges setting up the field and this Work Done was stored within the field as Potential Energy. When the field collapses, this Energy is released, causing the spark. This means that a collapsing Magnetic field is a source of Energy . 

The Energy stored in an Inductor can be found using the following formula :-

Where :-

E  =  Energy Stored in the Inductor (J).

L  =  Inductance of the Inductor (H).

I  =  Steady Current within the Inductor (A).

Note - In the two above equations, the letter E is used to represent both Energy and Voltage. Be careful not to confuse these two formula. 

Example 1 - 

Inductors in AC

If an Inductor is connected to an AC Supply, the Current through the Inductor will be continuously changing, therefore, a Back EMF will be continuously induced. 

If the Frequency of the AC Supply is increased, then the rate of change of Current will increase, therefore the Back EMF will increase. 

This means that for an Inductor, the higher the Frequency, the greater the opposition to the flow of Current. 

The graph below shows how the Frequency of an AC affects the Current through an  Inductor :- 

Note - These graphs show the opposite relationship to Capacitors. This has the effect of the following:-

An Inductor blocks AC signals whilst allowing DC signals to pass, as the Inductor produces large Back EMFs at high Frequencies.

A Capacitor blocks DC signals whilst allowing AC signals to pass, as the Current through a Capacitor increases at high Frequencies.

Inductive Reactance

As with the Capacitor, an Inductor can oppose the Current within the circuit. Again, as with the Capacitor, it is not appropriate to refer to this opposition as Resistance. 

The opposition to Current flow through an Inductor is known as the Inductive Reactance, and is again measured in Ohms. 

The Inductive Reactance can be found using the following formula :-

XL  =  2πf L

Where :-

XL  =  Inductive Reactance (Ω) 

f  =  Frequency of the Alternating Signal (Hz)

L  =  Inductance of the Inductor (H) 

Combining Inductive and Capacitive Reactance with Resistance

Even though both Reactances have the unit of Ohms, it is not possible to simply add them together as if they were series resistors. This is because there is a Phase difference between them, and so they can only be added together using Vector addition :-

Where :-

Z  =  Impedance of the Circuit (Ω)

XL  =  Inductive Reactance (Ω) 

XC  =  Capacitive Reactance (Ω) 

R  =  Resistance of the Circuit (Ω) 

Note - As can be seen above, these all have the units of Ohms. This means there are now several different names for the opposition to Current flow :-

1. Resistance - Opposition to Current flow by a Resistor.

2. Capacitive Reactance - Opposition to Current flow by a Capacitor.

3. Inductive Reactance - Opposition to Current flow by an Inductor.

4. Impedance - The overall opposition to Current flow.

Uses of Capacitors and Inductors in Circuits

The diagram below shows and Inductor and a Capacitor in a series circuit :-

This Circuit can be used to filter high and low Frequency signals.

At low Frequency :-

1. Inductor - The opposition to Current is low, so the P.d. across it will be low.

2. Capacitor - The opposition to Current will be high, so the P.d. will be high.

At high Frequency :-

1. Inductor - The opposition to Current is high, so the P.d. across it will be high.

2. Capacitor - The opposition to Current will be low, so the P.d. will be low.

Example 2 - 

A loudspeaker system is connected to a music amplifier. The system contains a Capacitor, Inductor and two loudspeakers, LS1 and LS2, as shown above. 

The circuit is designed so that one loudspeaker emits low Frequency sounds while the other emits high Frequency sounds. By comparing the Capacitive and Inductive Reactances, describe the operation of this system.

Answer :-

In this circuit, LS1 is a Sub-woofer and will emit low Frequency sounds and LS2 is a tweeter and will emit high Frequency sounds.

Loudspeaker 2 - 

At high frequency, Capacitive Reactance is low, and so the high Frequency signal can pass through the Capacitor and be emitted by LS2. 

At low frequency, Capacitive Reactance is high, and so the low frequency signal cannot pass through the Capacitor and is blocked from being emitted by LS2.

Loudspeaker 1 - 

At high Frequency, Inductive Reactance is high, and so the high Frequency signal cannot pass through the Inductor and is blocked from being emitted by LS1. 

At low Frequency, Inductive Reactance is low, and so the low Frequency signal can pass through the Inductor and be emitted by LS1.