# M6-S5: Transformers and Other Applications of Induction

• Transformers operate using Faraday’s law of induction
• AC supply in the primary coil generates a magnetic field that changes in orientation
• Rate of change is dependent on the frequency of AC
• The secondary coil experiences change in magnetic flux and hence a current is induced

• Current carrying conductor’s magnetic field is stronger (higher in flux density, B) inside the coil’s core, and weaker outside as the flux is more spread apart (lower in flux density, B)
• Therefore, it is more efficient to utilise the flux inside the core for induction
• Soft iron core joining the primary and secondary coils achieves this as it helps transmit this magnetic flux to the core of the secondary coil
• In essence, the iron core increases the strength of the magnetic field

• Transformers can only function using AC as DC would not cause a change in magnetic flux, so Faraday’s law of induction would not apply.
• The ratio of turns of primary and secondary coil dictates the ratio of potential difference (voltage) of the two coils:

• Given that the change in magnetic flux experienced by the secondary coil equals the change in flux produced by the primary coil:

• Given that the transformer is ‘ideal’ and has 100% efficiency during this process of electromagnetic induction:

• Voltage and current are therefore inversely proportional. Increase in voltage during transformation is accompanied by a reduction in current
• For a 100% efficient transformation with no power loss, the above equations can be combined to give:

• Lenz’s law also applies in transformers in that the induced current in the secondary coil is always opposite in direction as the one in primary coil. These causes the two currents to be out-of-phase

• DC supply can induce current via a non-practical and non-sustainable strategy
• Constant switching-on and -off of DC supply causes the magnetic field to appear and disappear
• This generates a ‘change’ in magnetic flux experienced by the secondary coil
• Induced emf for DC and AC supplied transformers are shown below. (1) AC and (2) DC. Notice momentarily spikes in emf when DC is used.

• The relationship between coil turn and voltage heavily depends on the efficiency of flux linkage
• In a realistic transformer, flux which is not transmitted through the soft iron core is generally not experienced by the secondary coil

• Solution: Utilise material that has high magnetic susceptibility, so a higher density of flux can be transmitted from primary to secondary coil
• Magnetic susceptibility: the degree of magnetisation of a particular material under the influence of an external magnetic field

Problem 2 Resistive heat production

• Iron core can conduct current
• Change in magnetic flux in primary coil induces production of eddy current in the iron core.
• Using right-hand grip rule, the direction of these eddy currents circulates in a perpendicular plane to the direction of magnetic flux
• Disordered motion of eddy currents in the soft iron core generates unwanted heat
• Disordered current = higher frequency of electron collision
• Electron collision causes kinetic energy of electrons (electric energy) to be lost as heat

• Solution: Lamination of iron core
• Iron core is split into slices of equal thickness. Slices must be made perpendicular to the plane of eddy current of movement
• Insulating layers are inserted between slices
• Iron core is reconstructed by combining the pieces such that a ‘slice’ of iron core is always between two insulating layers.
• This method restricts the movement and reduces the size of eddy currents. Overall, the collision between electrons is reduced.

• Power loss due to heat is dependent on:
• the magnitude of current in the coil (movement of electrons)
• resistance of coil

• Resistance of the coil is dependent on:
• Length of the conductor (coil)
• Increase length = greater resistance
• Cross-sectional area of the conductor
• Increase cross sectional area = lower resistance
• Temperature
• Increase temperature = greater resistance
• Conductivity of material
• Materials have different intrinsic resistivity due to differences in chemical structure.
• Step-up transformers reduce power loss
• Step-up transformers increase the voltage in the secondary coil so that the current is reduced.
• Reduced current is associated with less power loss

#### Transformers in Power Transmission

• Power transmission over long distances is associated with significant power loss due to length of transmission wire and temperature
• Step-up transformers are used to compensate for this loss during transmission
• Thus, power can be transmitted over long distances with relatively high efficiency
• Voltage of each transformer is dependent on the stage of power transmission
• With subsequent distribution at substations e.g. zone substation, the voltage of each transformation tower decreases.
• In Australia, the gradual decrease during transmission terminates at 240 V when it reaches households
• Factories tend to have slightly higher voltage usage ~400 V

Transformers in Households

• Step-down transformers are usually present in households to reduce the voltage size so that it becomes suitable for smaller devices such as:
• Chargers for laptops and phones
• Toaster
• Hair dryer
• Lamp
• Step-up transformers are necessary for much larger appliances and devices simply due to higher energy demand
• Refrigerator
• Television

• Lenz’s law is seen as back emf in DC motors whereby the rotation speed of the armature decreases until it reaches an equilibrium state.
• The mechanical energy of the motor’s rotation is partially converted into electrical energy which opposes the direction of rotation. Thus, rotation decreases & efficiency of motor is reduced.

Faraday and Lenz’s Law are applied in many other applications

Magnetic Braking

• In vehicles equipped with magnetic braking systems, the wheels are made of material that is high in electrical conductivity.
• When the brake is off: the electromagnets near the spinning wheel is turned off – no application of Faraday’s and Lenz’s law
• When the brake is on: the electromagnets are turned on to create an external magnetic field
• As a consequence of this newly generated field, the spinning motion of the wheel causes itself to experience a chance in magnetic flux as it is cutting through magnetic flux lines of the electromagnet.
• Faraday’s law: eddy currents are induced in the wheel due to its relative movement to the magnetic field
• Lenz’s law: eddy currents form in a direction such that the resultant force opposes the change in flux. The force resists the motion of the wheel which in turn causes the vehicle to slow down.
• No friction involved during braking thus, less frequent or no maintenance
• The magnitude of resisting force is proportional to the induced current which is dependent on change in flux experienced by the wheel. This means the greater the speed the vehicle was formerly travelling out, the greater the resisting force.
• Vehicles with very high speeds can be brought to a stop more effectively compared with using conventional friction-based brakes.
• Energy conversion: mechanical energy to electrical energy to heat energy (negligible)

Induction stove/cooktop

• Induction cooktops utilise AC to power electromagnets found beneath the stove.
• Electromagnets generate a magnetic field that is alternating in orientation periodically
• Pans which are made of the right conductive material, when brought into close proximity to the electromagnets, experience a change in magnetic flux
• Faraday’s law: eddy currents are induced in the pan
• Lenz’s law: applies along with Faraday’s law but is not considered in this case because only heat is required for an induction stove
• Far more efficient compared with conventional gas stoves. In conventional stoves, the heat energy produced by the flame is partially lost during its transmission to the cooking utensil. This problem is greatly minimized in an induction stove
• ‘Safe’ – since eddy currents can only be induced in conductive material, accidental contact with the stove surface will not lead to consequences that are as severe in cases of flame. After usage, the stove will still contain residual heat, but this is often not harmful upon contact
• Disadvantage: only utensils made of certain types of conductive material can be used.
• Energy conversion: electrical to heat (thermal)
• the technology is not 100% efficient, heat will be partially lost during transmission.

Practice Question 1

(a) All transformers which operate using the principle of Faraday’s electromagnetic induction have less than 100% efficiency. Explain why this is the case. (4 marks)

(b) Explain one strategy that is used to overcome the problem(s) you outlined in (a). (2 marks)

Practice Question 2

The primary coil of a transformer has 4800 turns and is supplied by 240 V AC. The secondary circuit operates a small electric motor of resistance 192 ohms which requires 0.5 A.

(a) Calculate how many turns the secondary coil should have.

(b) The current flowing in the primary circuit is 0.21 A. Calculate the efficiency of the transformer.

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