Unit 5 Notes in English, FEEE 2004, Polytechnic 2nd Semester

 

5. TRANSFORMERS

---

Syllabus of this Unit:

1. Principle of operation, EMF equation, Construction
2. Principle of single-phase transformer, transformation ratio, and step-up and step-down transformers

---

1. Principle of Operation, EMF Equation, and Construction

---

1.1 Principle of Operation:

• Definition: A transformer is a static electrical device that transfers electrical energy between two or more circuits through electromagnetic induction.
• Working: It works on the principle of Faraday’s law of electromagnetic induction, where a change in magnetic flux through a coil induces an electromotive force (EMF) in another coil.

Key Principle:

• When an alternating current (AC) passes through the primary coil, it creates a varying magnetic field around the coil. This varying magnetic field links to the secondary coil, inducing an EMF and thus transferring energy.
• The transformer either steps up or steps down the voltage based on the number of turns in the primary and secondary coils.

Diagram:

         +----------+
   AC    | Primary  |
  Input  | Coil     | 
   ------|          |---- 
         |          |    |  Secondary
         |          |    |  Coil
         +----------+----+  
                      |
                AC Output

---

1.2 EMF Equation of Transformer:

• Derivation: The induced EMF in the secondary coil can be expressed by Faraday’s law of induction.

Formula:

$$E_1=4.44f{N}_1{\mathrm{\Phi }}_{\text{max}}$$

Where:

• E₁ = Induced EMF in the primary coil
• f = Frequency of the AC supply
• N₁ = Number of turns in the primary coil
• Φ_max = Maximum magnetic flux
• E₂ = Induced EMF in the secondary coil (similarly derived)

The above equation shows the relationship between the induced EMF and the number of turns in the coil, frequency, and the magnetic flux.

---

1.3 Construction of a Transformer:

A transformer consists of the following major parts:

1. Core: The magnetic core is made from laminated sheets of silicon steel to minimize eddy currents. The core provides a path for the magnetic flux.
2. Primary Coil: The coil connected to the input AC supply.
3. Secondary Coil: The coil where the output voltage is induced.
4. Insulation: Used to separate the windings to prevent electrical short circuits.
5. Tank: Used for housing the transformer and providing oil for cooling and insulation.

Diagram:

      +-------------------------------+
      |          Transformer           |
      |                               |
      |  +-------------------------+  |  
      |  |                         |  |   
      |  |     Primary Coil        |  |   
      |  |                         |  |  
      |  +-------------------------+  |
      |                               |
      |  +-------------------------+  |
      |  |                         |  |
      |  |     Secondary Coil      |  |
      |  |                         |  |   
      |  +-------------------------+  |
      |                               |
      +-------------------------------+

---

2. Principle of Single-Phase Transformer, Transformation Ratio, and Step-up and Step-down Transformers

---

2.1 Principle of Single-Phase Transformer:

A single-phase transformer works on the same principle as a general transformer. It consists of two coils, the primary and secondary coils, wound on a common core. When an alternating current is passed through the primary coil, it generates a magnetic field that induces a voltage in the secondary coil.

• Step-up Transformer: Increases the voltage from primary to secondary.
• Step-down Transformer: Decreases the voltage from primary to secondary.

---

2.2 Transformation Ratio:

The transformation ratio of a transformer is the ratio of the number of turns in the primary coil to the number of turns in the secondary coil. It can also be expressed in terms of the voltage or current ratio.

Formula:

$$\frac{N_1}{N_2} = \frac{V_1}{V_2} = \frac{I_2}{I_1}$$

Where:

• N₁ = Number of turns in the primary coil
• N₂ = Number of turns in the secondary coil
• V₁ = Voltage in the primary coil
• V₂ = Voltage in the secondary coil
• I₁ = Current in the primary coil
• I₂ = Current in the secondary coil

Explanation:

• For a step-up transformer, $N_1 < N_2$, so the secondary voltage is higher than the primary voltage.
• For a step-down transformer, $N_1 > N_2$, so the secondary voltage is lower than the primary voltage.

---

2.3 Step-up and Step-down Transformers:

1. Step-up Transformer:
   • Definition: A transformer that increases the voltage from the primary side to the secondary side.
   • Construction: Has more turns on the secondary coil compared to the primary coil.
   • Application: Used in power transmission, where the voltage is increased for efficient transmission over long distances.

Example: If the primary coil has 100 turns and the secondary coil has 1000 turns, the voltage will be increased by a factor of 10.

2. Step-down Transformer:
   • Definition: A transformer that decreases the voltage from the primary side to the secondary side.
   • Construction: Has more turns on the primary coil compared to the secondary coil.
   • Application: Used in devices that operate at low voltage levels, such as in household appliances.

Example: If the primary coil has 1000 turns and the secondary coil has 100 turns, the voltage will be reduced by a factor of 10.

---

MCQ Questions:

1. What is the main principle of working of a transformer?

   • a) Electromagnetic induction
   • b) Electrostatic induction
   • c) Magnetic flux
   • d) Electrolysis
   • Answer: a) Electromagnetic induction

2. Which part of the transformer is responsible for transferring electrical energy?

   • a) Primary Coil
   • b) Secondary Coil
   • c) Core
   • d) Both Primary and Secondary Coils
   • Answer: d) Both Primary and Secondary Coils

3. What does the transformation ratio of a transformer represent?

   • a) Voltage ratio
   • b) Current ratio
   • c) Turns ratio
   • d) All of the above
   • Answer: d) All of the above

4. In a step-up transformer, which coil has more turns?

   • a) Primary coil
   • b) Secondary coil
   • c) Both coils have the same number of turns
   • d) None of the above
   • Answer: b) Secondary coil

5. If the primary coil of a transformer has 100 turns and the secondary coil has 50 turns, what type of transformer is it?

   • a) Step-up transformer
   • b) Step-down transformer
   • c) Isolation transformer
   • d) Power transformer
   • Answer: b) Step-down transformer

6. The transformer works on which of the following laws?

   • a) Coulomb’s law
   • b) Faraday’s law
   • c) Ampere’s law
   • d) Ohm’s law
   • Answer: b) Faraday’s law

7. What is the main material used for the core of a transformer?

   • a) Copper
   • b) Steel
   • c) Iron
   • d) Aluminum
   • Answer: c) Iron

8. What is the frequency of the secondary coil compared to the primary coil in a transformer?

   • a) Higher
   • b) Lower
   • c) Same
   • d) Varies based on turns ratio
   • Answer: c) Same

9. What type of transformer is used for increasing voltage?

   • a) Step-down transformer
   • b) Step-up transformer
   • c) Isolation transformer
   • d) Both
   • Answer: b) Step-up transformer

10. If a transformer has 1000 turns in the primary coil and 500 turns in the secondary coil, what is the transformation ratio?

• a) 1:2
• b) 2:1
• c) 1:1
• d) 2:3
• Answer: b) 2:1

---

Important Practice Questions:

1. Explain the working principle of a transformer and derive the EMF equation.

   • Answer: A transformer works on the principle of electromagnetic induction. When an alternating current passes through the primary coil, it creates a varying magnetic field, which induces an EMF in the secondary coil. The EMF equation is given by $E_1 = 4.44 f N_1 \Phi_{\text{max}}$, where $N_1$ is the number of turns in the primary coil, $f$ is the frequency, and $\Phi_{\text{max}}$ is the maximum magnetic flux.

2. Describe the construction of a transformer and explain the function of each part.

   • Answer: A transformer consists of the core, primary coil, secondary coil, insulation, and tank. The core is made of laminated iron to reduce eddy currents. The primary coil is connected to the AC supply, and the secondary coil delivers the transformed voltage to the load. Insulation is used to separate the coils, and the tank provides oil for cooling.

3. Derive the formula for the transformation ratio and explain its significance.

   • Answer: The transformation ratio is given by $\frac{N_1}{N_2} = \frac{V_1}{V_2} = \frac{I_2}{I_1}$. It determines the relationship between the voltage and current in the primary and secondary coils. A step-up transformer increases the voltage, while a step-down transformer decreases the voltage.

4. Differentiate between a step-up and step-down transformer with examples.

   • Answer: A step-up transformer increases the voltage from primary to secondary, while a step-down transformer decreases the voltage. For example, a step-up transformer is used in power transmission to increase voltage for efficient transmission, while a step-down transformer is used in household devices to reduce voltage.

5. What is the role of the core in a transformer, and why is it made of laminated steel?

   • Answer: The core provides a path for the magnetic flux. It is made of laminated steel to minimize eddy currents, which would otherwise cause energy loss in the form of heat. The lamination ensures that the magnetic flux can pass through efficiently with minimal resistance.