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).

• Related Post: Can We Replace a 110/220 Turns Transformer with 10/20 Turns?

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.  Φ_{m 1} = Φ_{m 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 

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

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 

• Related Post: Is it Possible to Operate a 50Hz Transformer on 5Hz or 500Hz Frequency?

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.

E₁ = 4.44 f N₁ Φ_m1

Φ_m1 = E₁ / 4.44 f N₁

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

• Related Post: Can We Operate a 60Hz Transformer on 50Hz Supply Source and Vice Versa?

Same is on the other side,

E₂ = 4.44 f N2 Φ_{m 2}

Φ_{m 2} = E₂ / 4.44 f N₂

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}

• Related Post: Which Transformer is More Efficient When Operates on 50Hz or 60Hz?

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?