Derive the mutual-inductance of 2-winding IT in terms of the physical parameters of the transformer.

Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
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Chapter5: Components, Symbols, And Circuitry Of Air-conditioning Wiring Diagrams
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Problem 15RQ: What is the purpose of a transformer? Draw the symbols for a transformer.
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Derive the mutual-inductance of 2-winding IT in terms of the physical parameters of the transformer.

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Step 1

To derive the mutual-inductance of 2 winding inductive turn in terms of the physical parameter of the transformer. Let L1 and L2 is the self-inductance of the primary and secondary winding.

Mutual inductance is defines the flux of the coil 2 linking with coil 1, λ12. To the current flowing in coil 2.

Electrical Engineering homework question answer, step 1, image 1

Flux linkage of the coil from the 2 to the coil 1. Hence,

Electrical Engineering homework question answer, step 1, image 2

 

Step 2

Similarly, mutual inductance of coil 1 to the coil 2,

Electrical Engineering homework question answer, step 2, image 1

Now assume that all flux produced by each coil links with the other coil. The implication of this is that there is no leakage flux.

The flux from coil 2 linking with coil 1 is equal to the flux from coil 2 linking with coil 2.

Electrical Engineering homework question answer, step 2, image 2

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