Transformers MCQ Quiz - Objective Question with Answer for Transformers - Download Free PDF

Additional Information

• Nature of load: The type of connection also depends on the nature of the load. For example, different connections may be suitable for balanced and unbalanced loads.
• Voltage levels: Different voltage levels may require different types of connections.
• Safety: The type of connection may also affect the safety of the transformer and associated equipment.

Explanation:

Ideal Transformer Characteristics

Definition: An ideal transformer is a theoretical concept used to simplify the analysis of transformers in electrical engineering. It assumes certain perfect conditions that do not exist in real-world transformers but help in understanding their basic operation and performance.

Characteristics of an Ideal Transformer:

• Zero resistance of windings.
• No core loss (hysteresis and eddy current losses are absent).
• No leakage flux (all the magnetic flux is confined to the core and links both primary and secondary windings completely).
• Infinite permeability of the core material (ensuring that a very small magnetizing current is required to establish the magnetic flux).
• 100% efficiency (no losses, meaning all the input power is transferred to the output).

Correct Option Analysis:

The correct option is:

Option 4: Zero permeability.

This option is NOT a characteristic of an ideal transformer. In fact, an ideal transformer is assumed to have infinite permeability. Permeability is a measure of how easily a material can become magnetized or how well it can conduct magnetic lines of force. Infinite permeability ensures that the core can carry the magnetic flux with minimal magnetizing current. Zero permeability, on the other hand, would mean that the core cannot be magnetized at all, which is contrary to the operation of a transformer.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Zero resistance of windings.

This characteristic implies that there are no ohmic losses in the windings of the transformer. In a real transformer, the windings have some resistance, leading to copper losses (I²R losses). However, in an ideal transformer, these resistances are assumed to be zero.

Option 2: No core loss.

Core losses in transformers are due to hysteresis and eddy currents in the core material. An ideal transformer assumes that these losses are completely absent, which is not the case in practical transformers. Core losses are a significant factor in the efficiency of real transformers.

Option 3: No leakage flux.

Leakage flux refers to the portion of the magnetic flux that does not link both the primary and secondary windings. In an ideal transformer, it is assumed that all the magnetic flux is confined to the core and links both windings perfectly, meaning there is no leakage flux. In reality, some flux leakage is inevitable, leading to leakage reactance.

Conclusion:

Understanding the ideal characteristics of a transformer is crucial for simplifying analysis and understanding the core principles of transformer operation. While these ideal conditions do not exist in practical transformers, they provide a foundational basis for studying and improving real-world transformer designs. The assumption of infinite permeability is key to the ideal transformer model, and zero permeability would contradict the fundamental operation of a transformer, making option 4 the correct choice as the characteristic that does not belong to an ideal transformer.

Eddy current losses can be significantly reduced by laminating the core of a DC generator.

Concept:

Eddy current losses:

• When an alternating magnetic field is applied to a magnetic material, an EMF is induced in the material itself according to Faraday’s law of Electromagnetic induction.
• Since the magnetic material is a conducting material, these EMFs circulates current within the body of the material. These circulating currents are called Eddy currents. They are produced when the conductor experiences a changing magnetic field.
• The process of lamination involves dividing the core into thin layers held together by insulating materials.
• Due to lamination effective cross-section area of each layer reduces and hence the effective resistance increases.
• As effective resistance increases, the eddy current losses will decrease.

Mathematically, the eddy current loss is given by:

Eddy current loss in the transformer is given by:

Pe = Ke Bm2. t2. f2. V Watts

Where;

K - coefficient of eddy current. Its value depends upon the nature of the magnetic material

Bm - Maximum value of flux density in Wb/m2

t - Thickness of lamination in meters

f - Frequency of reversal of the magnetic field in Hz

V - Volume of magnetic material in m3

From the above formula, we conclude that the Eddy current loss is proportional to the square of the frequency.

Observation:

Since the Eddy current loss is proportional to the square of the thickness of the lamination.

∴ Eddy Current losses in a transformer core can be reduced by reducing the thickness of laminations.

Concept:

Sumpner's Test:

The primary winding of the two transformers are connected in parallel and supplied at rated voltage and frequency.

W₁ gives the iron losses and W₂ gives the full load copper losses of two transformers.

Efficiency = \(output\:power\over output\: power + Iron \: loss + copper \: loss\) × 100 %

Calculation:

Given:

Since W_1​, reads the total iron loss for both the transformers and W₂​ the total copper loss for both the transformers,

W₁ = 8 kW

W₂ = 12 kW

The iron and copper loss for each transformer is  \(\frac{8}{2}\)=4 kW and  \(\frac{12}{2}\)​=6 kW respectively.

The efficiency of each transformer at full load is

η= \(400 \over 400+4+6\) ​×100

=97.56%

• High-frequency transformers typically operate within a range of 20 kHz to 30 MHz, depending on their application.
• Transformers used in radio frequency (RF) applications reach up to 30 MHz, beyond which traditional designs lose efficiency due to core losses and parasitic effects.
• Above this frequency, alternatives like waveguides or resonators are preferred.
• Therefore, Option 3: 30 MHz is the most appropriate choice, as it reflects the practical upper limit for high-frequency transformers used in RF and communication systems.

• Delta – star connection type three-phase transformer is used for both large and low voltage rating transformers.
• Delta – star transformer is used at the generator side to step up the voltage levels and Star – delta transformer is used at the load side of distribution systems to step down the voltage levels.
• Star – star connection transformers are used for small, high voltage transformers.
• Delta – delta connection transformers are used for large, low voltage transformers.

Additional InformationAs the line voltage is √3 times of the phase voltage, hence star connection is used to give the output.

• An isolation transformer is a transformer used to transfer electrical power from a source of alternating current (AC) power to some equipment or device while isolating the powered device from the power source
• Isolation transformers provide galvanic isolation and are used to protect against electric shock, to suppress electrical noise in sensitive devices, or to transfer power between two circuits which must not be connected
• Isolation transformers block transmission of the DC component in signals from one circuit to the other but allow AC components in signals to pass
• Transformers that have a ratio of 1 to 1 between the primary and secondary windings are often used to protect secondary circuits and individuals from electrical shocks between energized conductors and earth ground

Delta – star connection type three-phase transformer is used for both large and low voltage rating transformers.

Delta – star transformer is used at the load side of distribution systems to step down the voltage levels to provide a neutral connection.

Star – star connection transformers are used for small, high voltage transformers.

Silicon steels are used for electrical transformer cores the following reasons:

1) Low hysteresis loss

2) High permeability

3) High resistance

4) Virtually eliminated ageing

5) Lower thickness of lamination

Concept:

In a transformer, the voltage & number of turns are related as

\(\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{{{N}_{1}}}{{{N}_{2}}}\)

Where,

 V₁ = Voltage across primary side of the transformer

V₂ = Voltage across the secondary side of the transformer

N₁ = Number of turns in primary side of transformer

N₂ = Number of turns in secondary side of transformer

Calculation:

V₁ = 2000

V₂ = 200

N₂ = 100

\(\frac{2000}{200}=\frac{{{N}_{1}}}{100}\)

⇒ N₁ = 1000

The dielectric strength of transformer oil is mainly determined by the presence of acids, water, and other contaminates.  It is therefore, important to keep the transformer oil as free from such contaminates as possible.  The dielectric strength of the oil will decrease with time and based on the service conditions where the transformer is located. The dielectric strength of transformer oil is expected to be 33 kV.

The correct answer is option 4
Concept:

A transformer has mainly two types of losses

• core losses
• copper losses.

Core loss, which is also referred as iron loss, consists of hysteresis loss and eddy current loss.

These two losses are constant when the transformer is charged. That means the amount of these losses does not depend upon the condition of secondary load of the transformer. In all loading condition, these are fixed.

Copper losses are directly proportional to the square of the load on the transformer.

\({W_{cu}} = {x^2}{W_{cufl}}\)

Here, x is the percentage of a full load of the transformer.

Wcufl­ is the copper losses at the full load.

Calculation:

Given that, x = 50% = 0.5

Copper losses at full load = 400 W

Copper loss at 50% of full load = (0.5)2 × 400 = 100 W

Construction of transformer

• The transformer consists of a central core on which primary and secondary winding is placed.
• The core of a shell-type transformer is made up of a ferromagnetic material such as soft iron.
• In most types of transformer construction, the central iron core is constructed from a highly permeable material commonly made from thin silicon steel laminations. 
• These thin laminations are assembled together to provide the required magnetic path with the minimum magnetic losses.
• The resistivity of the steel sheet itself is high, thus reducing any eddy current loss by making the laminations very thin.

The transformer will give the maximum efficiency when their copper loss is equal to the iron loss.

Copper loss:

A loss in a transformer that takes place in the winding resistance of a transformer is known as the copper loss.

Copper loss = i2R

Iron loss:

Iron losses = Eddy current loss + hysteresis loss

Eddy current loss = Ke t2 f2 B2

Hysteresis loss = Kh f B^η

Where, K_e & K_h are constant

f = Supply frequency

B = Flux density

t = thickness

Efficiency is maximum at some fraction x of full load:

\(x = \sqrt {\frac{{{W_i}}}{{{W_{cu}}}}}\)

Where Wi = iron losses

Wcu = copper losses

Load at maximum efficiency \(= Full\;load \times \sqrt {\frac{{{W_i}}}{{{W_{cu}}}}} = Full\;load \times \sqrt {\frac{B}{A}} \)

kVA at maximum efficiency is given by,

\(kVA\;at\;{η _{max}} = full\;load\;kVA \times \sqrt {\frac{{{W_i}}}{{{W_{cu}}}}}\)