Transformer and Motor Principles: EMF Equation

Posted on Feb 8, 2025 in Audiovisual Communication and Journalism

A transformer is an electrical device used to transfer electrical energy between two or more circuits through electromagnetic induction. It typically steps up or steps down the voltage levels in AC (alternating current) systems. Here’s a breakdown of its working principle:

Working Principle of Transformer:

The transformer works on the principle of Faraday’s Law of Electromagnetic Induction, which states that a change in the magnetic field within a coil of wire induces a voltage (EMF) in the coil.

A transformer consists of two coils, the primary coil and the secondary coil, wound around a common core made of a ferromagnetic material like iron. There is no electrical connection between the two coils; energy is transferred by the changing magnetic field.

Key Components:

• Primary Coil: Connected to the input power source.
• Secondary Coil: Connected to the output load.
• Core: A magnetic material that helps in directing the magnetic flux.

AC Voltage Applied: When an alternating voltage is applied to the primary coil, an alternating current flows through it, generating a time-varying magnetic field.

Magnetic Flux: The changing magnetic field produces a magnetic flux in the core, which links with the secondary coil.

Electromagnetic Induction: Due to this changing flux, an EMF is induced in the secondary coil (according to Faraday’s Law).

Voltage Transformation: The voltage induced in the secondary coil depends on the ratio of turns in the primary and secondary coils. This is known as the turns ratio.

• If the secondary coil has more turns than the primary, the transformer steps up the voltage.
• If the secondary coil has fewer turns, the transformer steps down the voltage.

Given Data:

• N1 = Number of turns in the primary winding.
• N2 = Number of turns in the secondary winding.
• Φm = Maximum flux in the core (in Weber) = Bm × A, where Bm is the maximum flux density and A is the cross-sectional area of the core.
• f = Frequency of the AC input (in Hertz, Hz).

Concepts Behind the EMF Equation:

1. When AC is applied to the primary winding, it produces an alternating magnetic flux in the transformer core.
2. This alternating flux links with both the primary and secondary windings, causing an EMF to be induced in both windings according to Faraday’s Law of Electromagnetic Induction.
3. The magnitude of the induced EMF in any coil is proportional to the rate of change of the magnetic flux linking with the coil.

EMF Equation of a Transformer (Definition):

The EMF equation of a transformer calculates the induced electromotive force (EMF) in the primary and secondary windings of a transformer when alternating current (AC) is applied. The alternating current produces an alternating magnetic flux, which links the windings through mutual induction. According to Faraday’s law, this changing flux induces an EMF in both windings.

The voltage transformation ratio (K) is the ratio between the EMF (or voltage) in the primary and secondary windings, which determines whether the transformer is a step-up (increases voltage) or step-down (decreases voltage) transformer, based on the number of turns in the windings.

In an ideal transformer, V1 = E1 (primary voltage = primary induced EMF) and V2 = E2 (secondary voltage = secondary induced EMF). The flux is the same in both windings, ensuring that the EMF per turn is identical for both.

Working Principle of Induction Motor

The working of an induction motor is based on the principle of electromagnetic induction, and it consists of two primary windings: the stator winding and the rotor winding.

1. Stator Winding

• The input AC supply is connected to the stator winding.
• The current flowing through the stator winding produces a magnetic flux.
• This magnetic flux is rotating; hence, it is referred to as the rotating magnetic field.

2. Rotor Winding

• The rotor winding is typically short-circuited.
• The rotating magnetic flux from the stator cuts across the short-circuited conductors of the rotor winding.

3. Electromagnetic Induction

• According to Faraday’s Law of Electromagnetic Induction, an EMF (Electromotive Force) is induced in the rotor circuit due to the changing magnetic flux.
• This induced EMF causes a current to flow through the rotor winding.

4. Interaction of Magnetic Fluxes

• When the current flows through the rotor winding, it produces another magnetic flux, called the rotor flux.
• Now, the induction motor has two magnetic fluxes: stator flux and rotor flux.
• These two fluxes interact with each other, causing the rotor to experience a torque.

5. Rotor Rotation

• This torque forces the rotor to rotate in the direction of the rotating magnetic field generated by the stator.

Series DC Motor

• A DC motor whose field winding is connected in series with the armature winding, allowing the entire armature current to pass through the field winding, is called a series DC motor.
• Figure-2 shows the connection diagram of a series DC motor.
• In a series DC motor, the field winding carries the entire armature current; therefore, it is made of thick wire with fewer turns to minimize resistance.

Shunt DC Motor

• A DC motor whose field winding is connected in parallel with the armature winding, allowing the total supply voltage to be applied across it, is known as a shunt DC motor.
• Figure-3 shows the connection diagram of a shunt DC motor.
• In a shunt DC motor, the shunt field winding has a large number of turns of thin wire, resulting in high resistance. Thus, only a part of the supply current flows through it, while the rest flows through the armature winding.

Compound DC Motor

• A compound DC motor has two sets of field windings on each magnetic pole: one in series and the other in parallel with the armature winding.

• Compound DC motors are sub-divided into two types:

  1. Short-Shunt Compound DC Motor:

     • Only the shunt field winding is in parallel with the armature winding.

  2. Long-Shunt Compound DC Motor:

     • The shunt field winding is in parallel with both the series field winding and the armature winding.

EMF Equation of a Transformer

Transformer’s EMF Equation

• The magnitude of the induced EMF (or voltage) in a transformer can be found using the EMF equation of the transformer.
• When a source of alternating current (AC) is applied to the primary winding of the transformer (known as magnetizing current), it produces alternating flux in the core of the transformer.
• The alternating flux produced in the primary winding gets linked with the secondary winding by mutual induction. Since this flux is alternating, there must be a rate of change of flux according to Faraday’s law of electromagnetic induction, which states that if a conductor or coil links with any changing flux, there must be an induced EMF in it.
• The same principle applies to transformers as well as induction motors, as an induction motor is fundamentally a transformer.

EMF Equation of Electrical Transformer

To find the magnitude of the induced EMF in a transformer, we use the EMF equation of the transformer. Let’s define the following parameters:

• N1 = Number of turns in the primary winding
• N2 = Number of turns in the secondary winding
• Φm = Maximum flux in the core (in Weber) = Φm = Bm ⋅ A
• f = Frequency of AC input (in Hz)

Here’s a comparison of step-up and step-down transformers presented in a table format: