_{1}and R

_{2}respectively (shown external to the windings in the figure). The resistances of the two windings can be transferred to any one side. It is done in order to make the calculations easy.

**The resistance is transferred from one side to the other side in such a manner that percentage voltage drop remains the same on either side.**

# Equivalent Resistance of Transformer Formula

Let

R_{1} = primary winding resistance

R_{2} = secondary winding resistance

K = transformation ratio

Then,

Secondary resistance referred to primary R_{2}’ can be calculated by the formula given below.

**R _{2}’ = R_{2}/K^{2}**

The equivalent resistance of transformer referred to the primary is represented by R

_{01}.

Therefore,

**R**

_{01}= R_{1}+ R_{2}’ = R_{1}+ R_{2}/K^{2}## Equivalent Resistance of Transformer Referred to Secondary

The primary resistance referred to the secondary is denoted by R_{1}’ and can be calculated by the formula given below.

**R _{1}’ = K^{2}R_{1}**

The equivalent resistance of transformer referred to the secondary is represented by R

_{02}.

Therefore,

**R**

_{02}= R_{2}+ R_{1}’ = R_{2}+ K^{2}R_{1}## Equivalent Leakage Reactance of Transformer

**The flux that links with both the windings of the transformer is called mutual flux and the flux which links only with one winding of the transformer is called leakage flux.
** Due to leakage flux of the primary winding and the secondary winding, an EMF is induced in the respective winding. The primary and secondary voltage will have to overcome these induced EMFs. Thus these induced EMFs are considered as the voltage drops across the factitious reactances placed in the series with the primary and secondary windings. These reactances are called as the leakage reactances and they are shown in the figure.

As done in the case of resistances, the reactances can also be transferred to either side.

**The reactance from one side to other is transferred in such a manner that percentage voltage drop remains the same on the either side.**

## Equivalent Reactance of Transformer Referred to Primary

Let

X_{1} = primary winding reactance

X_{2} = secondary winding reactance

K = transformation ratio

Then,

Secondary reactance referred to primary X_{2}’ can be calculated by the formula given below.

**X _{2}’ = X_{2}/K^{2}**

The equivalent reactance of transformer referred to the primary is represented by X

_{01}.

Therefore,

**X**

_{01}= X_{1}+ X_{2}’ = X_{1}+ X_{2}/K^{2}## Equivalent Reactance of Transformer Referred to Secondary

The primary reactance referred to the secondary is denoted by X_{1}’ and can be calculated by the formula given below.

**X _{1}’ = K^{2}X_{1}**

The equivalent reactance of transformer referred to the secondary is represented by X

_{02}.

Therefore,

**X**

_{02}= X_{2}+ X_{1}’ = X_{2}+ K^{2}X_{1}## Impedance of the Transformer

The primary impedance Z_{1} = R_{1} + jX_{1}

And secondary impedance Z_{2} = R_{2} + jX_{2}

The transfer of impedances takes place on the same lines as that of the resistances. The transfer of impedances can take place from primary to secondary and vice versa.

Z_{01} = (R_{01}^{2} + X_{01}^{2})^{1/2} impedance referred to primary side.

Z_{02} = (R_{02}^{2} + X_{02}^{2})^{1/2} impedance referred to secondary side.

## Transformer — 5 | Objective Type Question Answers

### #1 For given applied voltage, with the increase in frequency of the applied voltage

eddy current loss will remain unchanged

### #2 Which of the following statements regarding an ideal single-phase transformer having a turn ratio of 1 : 2 and drawing a current of 10 A from 200 V A.C. supply is incorrect ?

its secondary voltage is 400 V

### #3 The secondary of a current transformer is always short-circuited under operating conditions because

it avoids core saturation and high voltage induction

### #4 In a transformer the resistance between its primary and secondary should be

infinity

### #5 A good voltage regulation of a transformer means

output voltage fluctuation from no load to full load is least

### #6 For a transformer, operating at constant load current, maximum efficiency will occur at

unity power factor

### #7 Which of the following acts as a protection against high voltage surges due to lightning and switching ?

Horn gape

### #8 The efficiency of two identical transformers under toad conditions can be determined by

back-to-beck test

### #9 Which of the following insulating materials can withstand the highest temperature safely ?

mica

### #10 The noise produced by a transformer is termed as

hum

### #11 Which of the following is the most likely source of harmonies in a transformer ?

Core saturation

### #12 If a transformer continuously operated, the maximum temperature rise will occur in

windings

### #13 The hum in a transformer is mainly attributed to

magnetostriction

### #14 The maximum load that a power transformer can carry is limited by its

voltage ratio

### #15 The efficiency of a transformer under heavy loads, is comparatively low because

### #16 An open-circuit test on a transformer is conducted primarily to measure

core loss

### #17 A no-load test is performed on a transformer to determine

magnetizing current and loss

### #18 The voltage transformation ratio of a transformer is equal to the ratio of

secondary induced em.f. to primary induced e.m.f.

Do not forget to click the “finish” button to see the correct answers and result.

- Single Phase Transformer Working Principle
- Ideal Transformer
- Construction of Three Phase Transformer
- Types of Transformers
- Equivalent Resistance and Reactance of Transformer
- Equivalent Circuit of Single Phase Transformer
- Power Loss in a Transformer
- Open Circuit Test of Single Phase Transformer
- Short Circuit Test on Single Phase Transformer
- Transformer Efficiency
- Regulation of Transformer
- Autotransformer
- Instrument Transformers
- Polarity of Transformer Windings
- Significance of Vector Group of Transformer
- Buchholz Relay Construction | Working
- Why current transformer secondary should not be opened
- Dielectric Strength Test of Transformer Oil
- Transformer Moisture Removal Process

## 0 Comments