Q9 (16 Marks) Electrical Circuits & Calculations 🔥 Repeated 3x in exams
MET • Written Exam

(a) What is leakage flux as it applies to the iron-core transformer? How is it considered in the analysis of the transformer? (6)

(b) Three conductors fitted side by side in the stator of a salient-pole alternator. Each generates a maximum voltage of 200V (sinusoidal). The angle subtended at the centre of the stator between adjacent conductors is 20 electrical degrees. If the three conductors are connected in series, find

(i) the r.m.s. value of the effective voltage and

(ii) the ‘breadth factor'. Using the theory that is the basis of this problem, give one reason why three-phase current has been introduced. (10)

Appeared In: Feb 2026Jul 2025Feb 2025

Verified Model Answer (Text Solution)

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Part (a)

In an iron-core transformer, when the primary winding is connected to a supply voltage, a current flows through the winding depending on the load and the winding resistance. This current generates a magnetic field, forming a magnetic north and south pole, thereby creating magnetic flux between them.

The magnetic flux consists of lines that ideally pass through the iron core and link both the primary and secondary windings. This mutual flux is responsible for the energy transfer from the primary to the secondary winding and is essential for transformer operation.

However, not all magnetic flux produced by the primary winding links to the secondary winding. Some of the magnetic lines spread into the surrounding air space and do not pass through the secondary coil. This portion of the magnetic flux is known as leakage flux.

Leakage Flux:

  • Leakage flux is the portion of the magnetic flux generated by the primary winding that does not couple with the secondary winding.
  • It occurs due to the physical separation between the windings and non-ideal magnetic coupling.
  • The leakage flux induces an electromotive force (emf) in the primary winding itself, which opposes the current flow in the primary. This results in an additional voltage drop.

How It Is Accounted for in Analysis:

  • The opposition caused by the leakage flux is modeled as an inductive reactance (i.e., a leakage inductance) in series with the primary winding resistance.
  • This series inductance creates a voltage drop equal to the emf generated by the leakage flux.
  • In transformer equivalent circuits, the leakage inductances of both primary and secondary windings are included to reflect this non-ideal behavior.

Minimising Leakage Flux:

Interleaving Technique:

  • Leakage flux can be minimized by arranging the primary and secondary windings closely together on the same leg of the transformer core, a method known as interleaving.
  • This improves magnetic coupling and enhances energy transfer efficiency.
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