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Transformer Wiring

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Please help me draw a picture with a description of the solution with a step-by-step analysis using equations:
1) An enclosed transformer has four wire leads coming from it. How could you determine without taking the transformer apart: a) which wires are paired with which and b) what is the ratio of turns on the two coils? Assume that primary and secondary coils' wires are identical.

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Solution Summary

This solution contains an annotated diagram of the transformer and contains step-by-step calculations to determine which wires are paired with which and ratio of turns on the two coils.

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Problem 1

(2x^2-x-20) = 2 - 3x+8
(x^2+x-6 ) (x^2+x-6 )

2 - 3x+8
(x + 3)(x-2)

Taking
3x+8 = 1 + 14
(x + 3)(x-2) 5(x+3) 5(x-2) ...

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