# Why Flux in Primary and Secondary Winding is Always Equal?

## Why Flux in the Primary and Secondary Winding of the Transformer is Same?

One of our followers asked “In a transformer, Which one is greater? primary flux or secondary flux? in both cases of step up and step down transformers.

Flux in Primary and Secondary Winding is Always Equal.

In ideal case, the flux produced in primary winding will pass through the secondary winding, so generated flux in primary winding will be same as in secondary winding.

Good to know:

• A transformer doesn’t change the value of power, frequency and flux.
• Transformer only step-up or step-down the value of AC voltage and current. i.e. a Transformer won’t operate on DC.
• Flux is directly proportional to the Ampere-Turns (At) i.e. Φ ∝ At, not proportional to the turns ratio (N). Lest see how is it possible with a solved example.

Transformer Rating and Parameters

A 50Hz Single phase Transformer has 525 Primary turns and 70 Secondary Turns. If the primary is connected to 3300 Volts supply, Find the secondary Voltage. If neglecting losses, What is the primary current when the secondary current is 250 Amperes? Also Prove that the Fluxes produced in Both Primary and Secondary Windings are Same.?

Solution:

Given Data;

• Primary Number of Turns = N1 = 524
• Secondary Number of Turns = N2 = 70
• Primary Input Voltage = V1 = 3300 Volts.
• Secondary Current = I2 = 250 A.
• Frequency = f = 50Hz

Find/Calculate?

1. Secondary Voltage = V2 = ?
2. Primary Current I1 = ?
3.  Φm 1 = Φm 2

1. To Find Secondary Voltage:

We Know that,

N2 / N1 = V2 / V1 ====> V2 = (N2 x V1) / N1

Putting the Values

V2 = (70 x 3300 V) / 525

V2 = 440 Volts

2. To Find Primary Current:

Now if Neglecting Losses,

V1 I1= V2 I2 ====> I1 / I2 = V2 / V1

Or

I1 = (V2 x I2) / V1

Putting the Values,

I1 = 440 V x 250 / 3300 V

I1 = 33.3 Amp

3. Prove that Primary Flux is Equal to the Secondary Flux i.e. Φm 1 = Φm 2

Lets turn around to the EMF Equation of the Transformer.

E1 = 4.44 f N1 Φm1

Φm1 = E1 / 4.44 f N1

Putting the Values

Φm 1 = 3300 V / (4.44 x 50 x 525)

Φm 1 = 0.0283 Weber’s

Φm 1 = 28.3 mWeber’s = Flux in Primary Windings

Same is on the other side,

E2 = 4.44 f N2 Φm 2

Φm 2 = E2 / 4.44 f N2

Plugging the values,

Φm 2 = 440 / (4.44 x 50 x 70)

Φm 2 = 0.0283 Weber’s

Φm 2 = 28.3 mWeber’s = Flux in Secondary Windings

i.e.

Φm 1 = Φm 2

Hence proved that the flux produced in both primary and secondary windings in a transformer is same and equal.

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### Electrical Technology

1. Naveed Aslam says:

But flux is directly proportional to turn ratio ??? Then how possible primary flux = secondary flux ??? Please explain

1. Gandalf says:

Flux is directly proportional to the ampere-turns.

flux produced in primary winding will pass through the secondary winding, so generated flux in primary winding will be same as in secondary winding. Flux is directly proportional to the Ampere-Turns not proportional to the turns ratio (N).

3. Aashutosh singh says:

Flux, low Reluctance path provided by iron core, and both side iron core is similar therefore flux on both sides is equal.

4. Vikas kumar singh says:

Voltage and ratio turn are directly proportional to each other than flux will be constant becouse current do not varies. If current nit varies than electros are not active so no flux generates . so primary and secondary flux are equal