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.?
- 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
- Secondary Voltage = V2 = ?
- Primary Current I1 = ?
- 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
- 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
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
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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