EE Questions / AnswersTransformer

# Why Flux in Primary and Secondary Winding of the Transformer is Same? With a Simple Explanation and Example.

Is Flux in Primary Winding always greater than the Secondary winding in Transformer?

Ans:

**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.

**Here is a very simple example to explain my answer.**

**Suppose,**

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 Flux produced in Both Primary and Secondary Winding is Same.?**

**Solution:**

**Given Data;**

Primary Number of Turns N

_{1}= 524,

Secondary Number of Turns N

_{2}= 70

Primary Input Voltage V

_{1}= 3300 Volts.

Secondary Current I

_{2}= 250 A.

**Find/Calculate?**

Secondary Voltage V

_{2}=?

Primary Current I

_{1}=?

**Φ**

_{m 1 = }**Φ**

_{m2}**We Know that,**

N2/N1 = V

_{2}/V_{1}====> V_{2}= (N_{2}x V_{1})/N_{1}

Putting the Values

V

_{2}= (70 x 3300)/525 = 440 Volts Ans.

Now if Neglecting Losses,

V

_{1}I_{1}= V_{2}I_{2}====> I_{1}/I_{2}= V_{2}/ V_{1}…..Or…..I_{1}= (V_{2 }x I_{2}) / V_{1}

Putting the Values,

I

_{1}= 440 x 250/3300 = 33.3 Amp Ans.

**Now turn around the Transformer equation.**

E

_{1}= 4.44 f N_{1}φ_{m1}

φ

_{m1}= E_{1}/ 4.44 f N_{1}

Putting the Values

**Φ**

_{m 1}= 3300 / (4.44 x 50 x 525) = 0.0283 Weber’s

**Φ**

_{m 1 }= 28.3mWeber’s = Flux in Primary Windings

Same is on the other side,

E

_{2}= 4.44 f N2 φ_{m2}

Φ

_{m2}= E_{2}/ 4.44 f N_{2}

Putting the values,

**Φ**

_{m2}= 440 / (4.44 x 50 x 70) = 0.0283 Weber’s

**Φ**

_{m2 }= 28.3mWeber’s = Flux in secondary Windings

**So You can see the flux (Φm) produced in Both Primary and Secondary Winding is same.**

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

Flux is directly proportional to the ampere-turns.