Auto Transformer MCQ Quiz - Objective Question with Answer for Auto Transformer - Download Free PDF

Explanation:

Use of Single Winding in an Auto Transformer

Definition: An auto transformer is a type of electrical transformer where the primary and secondary windings share a common single winding. Unlike conventional transformers that have separate primary and secondary windings, an auto transformer utilizes a single winding for both input and output, with part of the winding serving as both the primary and secondary. This shared winding configuration significantly reduces the copper consumption compared to conventional transformers.

Working Principle: In an auto transformer, electrical energy is transferred from the input (primary) side to the output (secondary) side through electromagnetic induction. The shared winding allows for direct electrical connection between portions of the primary and secondary circuits. By tapping the winding at different points, varying voltage levels can be achieved. The reduced number of windings results in less material usage, which is one of the primary advantages of an auto transformer.

Advantages:

• Reduced copper consumption due to the use of a single winding for both primary and secondary circuits.
• Compact design with smaller size and lighter weight compared to conventional transformers.
• Higher efficiency due to lower losses in the winding.
• Cost-effective solution for voltage regulation applications.

Disadvantages:

• Limited isolation between primary and secondary circuits, which can be a drawback for applications requiring complete electrical isolation.
• Not suitable for applications where the primary and secondary windings need to handle significantly different power levels.
• Susceptible to fault propagation between the primary and secondary circuits due to the shared winding design.

Applications: Auto transformers are commonly used in applications such as voltage regulation in power systems, motor starting, and laboratory equipment where compactness, efficiency, and cost savings are crucial.

Correct Option Analysis:

The correct option is:

Option 2: Reduced copper consumption

The use of a single winding in an auto transformer significantly reduces the amount of copper required for its construction. In conventional transformers, separate primary and secondary windings are made, which require more copper. Auto transformers share a single winding for both primary and secondary, minimizing the need for additional windings and, consequently, reducing copper consumption. This reduction in material usage results in lower manufacturing costs and contributes to the compact size and lighter weight of auto transformers.

Additional Information

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

Option 1: Higher losses

This option is incorrect because the single winding design of an auto transformer typically results in lower losses compared to conventional transformers. With fewer windings, the resistive losses in the winding are reduced, leading to higher efficiency. Additionally, the compact design minimizes leakage flux, further improving performance.

Option 3: Lower voltage regulation

This option is incorrect because auto transformers generally offer better voltage regulation due to their efficient design and low losses. The shared winding allows for precise voltage adjustment, making auto transformers suitable for applications requiring stable voltage output.

Option 4: Increased size and weight

This option is incorrect because the use of a single winding in an auto transformer results in a more compact design with reduced size and weight compared to conventional transformers. The reduced copper consumption and simplified construction contribute to the smaller dimensions and lighter weight of auto transformers.

Option 5: (Not applicable in this case)

There is no relevant information provided for Option 5 in this context, and it does not align with the operational characteristics of an auto transformer.

Conclusion:

The use of a single winding in an auto transformer is a significant design feature that leads to reduced copper consumption. This reduction not only makes the auto transformer more cost-effective but also contributes to its compact size and higher efficiency. While the shared winding design offers numerous advantages, it also comes with certain limitations, such as reduced electrical isolation. Understanding these trade-offs is essential for selecting the appropriate transformer type for specific applications.

Explanation:

When a Two-Winding Transformer is Converted into an Autotransformer

Definition: A two-winding transformer is a traditional transformer configuration where the primary and secondary windings are electrically isolated from each other. When this type of transformer is converted into an autotransformer, the primary and secondary windings are interconnected, resulting in a single continuous winding that serves both functions. This connection allows for a portion of the power to be transferred directly (conductively) between the input and output, while the rest is transferred inductively via the magnetic field in the core.

Concept: The kVA rating of a transformer indicates its capacity to handle apparent power. In a two-winding transformer, the entire power transfer is achieved inductively. However, in an autotransformer, part of the power is transferred conductively, which significantly increases its kVA rating for the same physical size and thermal capacity. The increase in the kVA rating depends on the voltage ratio of the transformer.

Formula for kVA Rating of an Autotransformer:

The kVA rating of an autotransformer is given by:

kVA_auto = kVA_two-winding × (1 + k)

Where:

• k = Voltage ratio = (V₂ − V₁) / V₁
• V₁ = Lower voltage side
• V₂ = Higher voltage side

This equation shows that the kVA rating of the autotransformer is greater than that of the original two-winding transformer, depending on the voltage ratio.

Working Principle:

In a two-winding transformer, the primary and secondary windings are completely separate, and the entire load power is transferred magnetically through the core. In an autotransformer, the windings are interconnected, and part of the power is transferred directly through the winding itself (conductive transfer), while the rest is transferred inductively via the magnetic field. This dual transfer mechanism leads to a more efficient utilization of the winding and core material, thereby increasing the apparent power (kVA) rating.

Example:

Consider a two-winding transformer with a kVA rating of 100 kVA, operating with a primary voltage of 200 V and a secondary voltage of 400 V. When converted into an autotransformer:

• Voltage ratio, k = (400 − 200) / 200 = 1
• kVA_auto = 100 × (1 + 1) = 200 kVA

Thus, the kVA rating of the autotransformer is double that of the original two-winding transformer.

Advantages of Autotransformers:

• Higher kVA rating for the same physical size and material cost compared to a two-winding transformer.
• Better efficiency due to reduced losses in the windings.
• Lower cost and weight, as less copper and core material are required.

Limitations of Autotransformers:

• Lack of electrical isolation between the primary and secondary sides, which may pose safety concerns.
• Not suitable for applications requiring galvanic isolation.

Correct Option Analysis:

The correct option is:

Option 4: Increases

When a two-winding transformer is converted into an autotransformer, its kVA rating increases due to the conductive transfer of power in addition to the inductive transfer. The extent of this increase depends on the voltage ratio, as demonstrated in the formula above. This characteristic makes autotransformers highly efficient and cost-effective for certain applications where electrical isolation is not required.

Additional Information

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

Option 1: Remains same

This option is incorrect because the kVA rating of an autotransformer is always greater than that of the original two-winding transformer. The conductive transfer of power in an autotransformer contributes to this increase, as explained in the formula.

Option 2: Decreases to half of the original rating

This option is incorrect because the kVA rating of an autotransformer does not decrease. On the contrary, it increases due to the efficient utilization of winding material and the dual power transfer mechanism.

Option 3: Decreases to 3/4th of the original rating

This option is also incorrect. As mentioned earlier, the kVA rating of an autotransformer increases compared to the original two-winding transformer. There is no scenario where the rating decreases to 3/4th of the original value.

Conclusion:

The conversion of a two-winding transformer into an autotransformer results in an increased kVA rating due to the combined conductive and inductive power transfer mechanisms. While autotransformers offer significant advantages in terms of efficiency and material utilization, their lack of electrical isolation may limit their use in certain applications. Understanding the principles of operation and the factors influencing the kVA rating is crucial for selecting the appropriate transformer configuration for a given application.

Concept

The ratio of the weight of the conductor material in an autotransformer and two-winding transformer is given by:

. 

where, a = Transformation ratio

Calculation

Given, a = 2

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The correct answer is the volume of copper used = (cross-sectional area) × (length of the conductor used for windings)..

Key Points

• The volume of copper used in an auto-transformer is given by the product of the cross-sectional area of the conductor and the length of the conductor used for the windings.
• The cross-sectional area refers to the thickness or gauge of the copper wire used in the transformer windings.
• The length of the conductor is the total length of the copper wire used in the windings of the transformer.
• In an auto-transformer, the primary and secondary windings are electrically connected, which results in a reduction in the amount of copper required compared to a conventional two-winding transformer.
• This reduction in copper usage makes the auto-transformer more cost-effective and efficient.
• The relationship is mathematically expressed as Volume = Cross-sectional Area × Length, ensuring that the volume of copper used is directly proportional to both the cross-sectional area and the length of the conductor.

 Additional Information

• Auto-Transformer
  • An auto-transformer is a type of transformer with only one winding that acts as both the primary and secondary winding.
  • It is used in applications where a small voltage adjustment is needed.
  • Auto-transformers are more efficient and cost-effective for certain applications, but they do not provide electrical isolation between the primary and secondary circuits.
• Conventional Two-Winding Transformer
  • A conventional two-winding transformer has separate primary and secondary windings.
  • It provides electrical isolation between the primary and secondary circuits.
  • These transformers are typically used in applications requiring significant voltage transformation and electrical isolation.
• Copper Usage in Transformers
  • The amount of copper used in a transformer directly affects its cost, efficiency, and performance.
  • Reducing copper usage without compromising performance is a key design goal in transformer engineering.
  • Using high-quality copper with optimal cross-sectional area and length can enhance transformer efficiency and reduce energy losses.

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Auto-Transformer:

• An auto-transformer is a type of electrical transformer with only one winding
• .The “auto” prefix refers to the single coil acting alone (Greek for “self”) – not to any automatic mechanism.
• An autotransformer is similar to a two-winding transformer but varies in the way the primary and secondary winding of the transformer are interrelated.
• In an autotransformer, one single winding is used as the primary winding as well as the secondary winding.
• But in two windings transformers, two different windings are used for primary and secondary purposes.
• A circuit diagram of the auto-transformer is shown below

Advantages of an Auto-transformer:

• For transformation ratio = 2, the size of the auto-transformer would be approximately 50% of the corresponding size of two winding transformers. For transformation, the ratio says 20, the size of the autotransformer would be 95% corresponding to two winding transformers. The saving in the cost of the material is of course not in the same proportion. The saving of cost is appreciable when the ratio of transformer is low, that is lower than 2. Thus auto-transformer is smaller in size and cheaper.
• An auto-transformer has higher efficiency than two winding transformers. This is because of less ohmic loss and core loss due to the reduction of transformer material.
• Auto-transformer has better voltage regulation as voltage drop in resistance and reactance of the single winding is less.

Disadvantages of an Auto-transformer:

• Because of the electrical conductivity of the primary and secondary windings, the lower voltage circuit is liable to be impressed upon by higher voltage. To avoid a breakdown in the lower voltage circuit, it becomes necessary to design the low voltage circuit to withstand higher voltage.
• The leakage flux between the primary and secondary windings is small and hence the impedance is low. This results in severer short circuit currents under fault conditions.
• The connections on primary and secondary sides necessarily need to be the same, except when using interconnected starring connections. This introduces complications due to changing primary and secondary phase angles, particularly in the case of delta/delta connections.
• Because of common neutral in a star/star connected auto transformer it is not possible to earth neutral of one side only. Both their sides should have their neutrality either earth or isolated.
• It is more difficult to maintain the electromagnetic balance of the winding when voltage adjustment tappings are provided.
• It should be known that the provision of tapping on an auto-transformer increase considerably the frame size of the transformer. If the range of tapping is very large, the advantages gained in initial cost are lost to a great event.

Concept:

The maximum power rating of the autotransformer is (1 + a) times the power rating of the same device when operated as a regular two-winding transformer.

Sauto = (1 + a) S2-w

Turn ratio 

Sauto = rating of autotransformer

S2-w = rating of two winding transformer

N1 = number of turn at the primary side

N2 = number of turn at the secondary side

Sauto = (1 + a) S2-w

Calculation:

The required output voltage is 2420 i.e. 

Hence it is the case of additive polarity

Alternate Method

Consider the transformation ratio for Autotransformer is 

The kVA rating of autotransformer =  × two winding transformers; for step-up transformer

Note: Maximum kVA rating of Auto-transformer occurs in Additive polarity.

Autotransformer:

• An Autotransformer is a variable output voltage transformer.
• An autotransformer is a kind of transformer where primary and secondary share the same common single winding.
• In an autotransformer, energy transforms taking place through both conduction and induction.
• It works as a variable transformer.
• This type of variable autotransformer is generally used in laboratories and science labs in schools and colleges.
• It is commonly known as Variac.

Important Points

Advantages of auto-transformer over a two-winding transformer:

• More efficient for the same VA rating
• Smaller in size
• Require less copper in their construction
• Cost is less compared to double wound transformers of the same VA rating
• Core and copper losses are lower due to less resistance and leakage reactance giving a superior voltage regulation than the equivalent two winding transformer

Concept:

An Auto-transformer is a kind of electrical transformer where primary and secondary share the same common single winding, i.e. it does not isolate the secondary.

An electrical device that is used to transfer electrical energy from one electrical circuit to another is called a transformer.

In the case of an autotransformer, the power is transferred via both induction & conduction phenomena. While in the case of a two winding transformer, the power is

transferred only by induction phenomena.

For a two-winding transformer, the turns ratio 

For Autotransformer, turns ratio 

Where,

N1 = Number of primary turns of autotransformer

N2 = number of secondary turns of autotransformer

Now from the derivation, we get

The ratio of weights of copper in autotransformer and two winding transformers is given by 

Where,

The transformation ratio for auto transformer is 

Application:

Given: a' = 3, a = N₂/N₁ = 1/3

Therefore,

Additional Information

1) Power transferred inductively is Pind = V2 I1 (1 – K)

2) Power transferred conductively, PC = V2 I2 K

3) Voltage regulation of Auto-transformer = X (1 - K)

Where,

X is the voltage regulation of a two-winding transformer

K is the transformation ratio of the Auto-transformer

Note:

The Capacity (KVA) rating of autotransformer is more than Two winding transformers in both cases of additive and subtractive polarity connection.

The correct answer is option (1)

Concept:

• An Electrical device that is used to transfer electrical energy from one electrical circuit to another is called a Transformer. 
• An Auto-Transformer is a single winding transformer in which a part of the winding is common to both primary and secondary windings.
• In the case of an auto-transformer, the power is transferred through both Induction and Conduction.
• In the case of two winding transformers, the power is transferred only by the Induction phenomenon.
• For the same rating, an auto-transformer needs less conductor material (copper) as compared to an ordinary two-winding transformer.

Explanation:

Weight of copper material required ∝ Current × Number of turns

For the two-winding transformer:

Weight of copper required ∝ (I₁N₁ + I₂N₂)

For the auto-transformer:

Weight of copper required in section ac ∝ I₁(N₁ - N₂)

Weight of copper required in section bc ∝ (I₂ - I₁)N₂

∴ 

Where,

W_auto = Weight of copper required in auto-transformer

W_∘  = Weight of copper required in two-winding transformer

= 

∵ 

= 

Where K = Transformation ratio of auto-transformer

∴ The weight of the copper required in the auto-transformer is:

Weight of copper required in auto-transformer = (1 - K) × Weight of copper required in two-winding transformer

∴ Saving of copper matrerial = W_∘ - W_auto

=W_∘ - (1 - K) W_∘ 

Hence, Saving of copper material = KW_∘ 

Power transferred inductively, Pind = V2 I2 (1 – K)

Power transferred conductively, PC = V2 I2 K

Voltage regulation of Auto-transformer = X (1 - K)

Where X is the voltage regulation of two-winding transformer

K is the transformation ratio of the Auto-transformer

Calculation:

Given that, K = 0.7

P = 49 kVA

Power transferred conductively is 

Pc = 49 × 0.7

Pc = 34.3 kVA

Auto-Transformer:

In an autotransformer, power is transferred through both conduction and induction processes.

EMF induced in the winding is proportional to the number of turns. Therefore, the secondary voltage can be varied by just varying a secondary number of turns. As winding is common in both circuits, most of the energy is transferred by means of electrical conduction and a small part is transferred through induction.

V2(I1 - I2) = Inductive transfer

V2I1 = Conductive transfer

Concept:

• The closer the voltage ratio is to 1, the more economical an auto-transformer becomes due to reduced copper and winding material requirements.
• However, the specific decision depends on the application, load, and other factors, including the voltage difference and the cost of materials, so an economic analysis is typically conducted to determine the most cost-effective transformer configuration for a particular situation.

Concept:

In the case of an autotransformer, the power is transferred via both induction & conduction phenomena. While in the case of a two-winding transformer, the power is transferred only by induction phenomena.

The KVA rating of Autotransformer is more than two winding transformers.

For two-winding transformer, turns ratio 

For Autotransformer, turns ratio 

Where N1 = Number of primary turns of autotransformer

N2 = number of secondary turns of autotransformer

Now,

⇒ (kVA)auto = V1I1 = V2I2

Important Points:

Also, the transformation ratio for Autotransformer is 

Power transferred inductively, Pind = V2 I1 (1 – K)

Power transferred conductively, PC = V2 I2 K

Voltage regulation of Auto-transformer = X (1 - K)

Where X is the voltage regulation of two-winding transformer

K is the transformation ratio of the Auto-transformer

Calculation:

Given that, K = 0.7

P = 3 kW

Power transferred conductively is 

Pc = 3 x 0.7

Pc = 2.1 kW

• An autotransformer is a type of transformer where primary and secondary windings share the same common single winding. So basically it’s a single winding transformer.
• Auto-transformer is used in the transmission and distribution systems when the transformation ratio for voltage is small.
• The rating of the transformer and copper saving can be maximized when the transformation ratio is low, i.e. lower than 2.

Advantages:

• Autotransformer is smaller in size and cheaper.
• An autotransformer has higher efficiency than two winding transformer because of low ohmic loss and core loss due to the reduction of transformer material.
• Autotransformer has better voltage regulation as voltage drop in resistance and reactance of the single winding is less.

The correct answer is option no "2".

Concept:-

The ratio of the weight of the conductor material in an autotransformer and two-winding transformer is given by:

. 

Given: Source, V1 = 600 V. V2 = 200 V 

 = 1 ∶ 1.5

Additional Information Conversion from the two-winding transformer to the autotransformer