# 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 = N
_{1}= 524 - Secondary Number of Turns = N
_{2}= 70 - Primary Input Voltage = V
_{1 }= 3300 Volts. - Secondary Current = I
_{2 }= 250 A. - Frequency =
*f*= 50Hz

**Find/Calculate?**

- Secondary Voltage = V
_{2}= ? - Primary Current I
_{1 }= ? -
**Φ**_{m }_{1 }=**Φ**_{m 2}

**1. To Find Secondary Voltage:**

We Know that,

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

Putting the Values

V_{2 }= (70 x 3300 V) / 525

V_{2} = 440 Volts

- Related Post: Why Transformer Rated In kVA, Not in KW?

**2. To Find Primary Current:**

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 V x 250 / 3300 V

I_{1 }= 33.3 Amp

**3. Prove that Primary Flux is Equal to the Secondary Flux i.e. Φ _{m 1 }= Φ_{m 2}**

Lets turn around to the EMF Equation of the Transformer.

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 V / (4.44 x 50 x 525)

Φ_{m 1} = 0.0283 Weber’s

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

Same is on the other side,

E_{2 }= 4.44 *f* N2 Φ_{m 2}

Φ_{m 2 }= E_{2} / 4.44 *f* N_{2}

Plugging the values,

Φ_{m 2} = 440 / (4.44 x 50 x 70)

Φ_{m 2} = 0.0283 Weber’s

**Φ _{m 2 }= 28.3 mWeber’s = Flux in Secondary Windings**

i.e.

**Φ _{m 1 }= **

**Φ**

_{m 2}**Hence proved that the flux produced in both primary and secondary windings in a transformer is same and equal.**

Related Posts:

- How Find the Rating of Transformer in kVA (Single Phase and Three Phase)?
- Transformer Phasing: The Dot Notation and Dot Convention
- Transformer Efficiency, All day Efficiency & Maximum Efficiency
- TRANSFORMER NAMEPLATE (GENERAL REQUIREMENTS).
- In a Capacitive Circuit, Why the Current Increases When Frequency Increases?
- In an Inductive Circuit, Why the Current Increases When Frequency Decreases?
- Why Power Factor Decreases When Inductance or Inductive Reactance Increases?
- Why Power Factor Decreases When Capacitive Reactance Increases or Capacitance Decreases?

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

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).

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

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