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I am bamboozled after I found that the length of a primary coil of a transformer that I wanted to recoil was approximately 870m.

The wire used was about 0.4mm in diameter, the coil as taking a voltage of 220v, the secondary coil was supposed to give 32v.

When I compared the resistance of the primary coil of a similar transformer (with the same input to output voltage ratio), I found out that the resistance was 120ohms, I plugged the values into the formula for calculating resistivity and I found that the length of the wire I was supposed to use was approximately 870m.

The confusion comes where the length of the wire seems so large but the transformer has a relatively smaller dimensions, of about 5cm in length 2cm in width and 4cm in height.

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    \$\begingroup\$ Obviously, your expectations were wrong. Do you have any actual question for us? It seems you answered the title question yourself. \$\endgroup\$
    – Dave Tweed
    Commented Mar 15 at 11:29
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    \$\begingroup\$ I found out that the resistance was 120ohms how did you measure this? Is it possible that you might have measured a reactance at 50 Hz maybe? Because this corresponds to ~400 mH which sounds reasonable for an iron-core transformer. \$\endgroup\$
    – Rohat Kılıç
    Commented Mar 15 at 11:41
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    \$\begingroup\$ The answer to your question is yes if you know the wire diameter and material resistivity. \$\endgroup\$
    – winny
    Commented Mar 15 at 12:21
  • \$\begingroup\$ Won't the thickness of the insulating coating will be significant too? Whatever distance it contributes to overall wire diameter, the copper cross-section area will be reduced by the square of that. \$\endgroup\$
    – Simon Fitch
    Commented Mar 15 at 14:21

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0.4mm diameter is about AWG26 0.125mm^2 so 870m would be about 110 cubic cm, and would thus weigh about 1kg (copper wire is assumed in this answer). I doubt that seems reasonable for the size of transformer you describe.

Number of turns and wire size are what counts, but if you have an identical transformer to the one that failed and know the exact wire size then you can estimate the length from resistance. One thing that may be flummoxing and/or bamboozling you is if you accidentally measured the wire size of the secondary, which would tend to use much larger wire than the primary in a mains-powered step-down transformer. It would take a lot more 0.4mm wire length to reach 120Ω than (say) 0.2mm wire. With 0.2mm diameter wire the length would drop to 1/4, and the required mass would drop to 1/16 so more like 60g than 1kg of wire.

In any case, accurate measurement of wire diameter is important- preferably a micrometer (with a light touch lest the wire get squished down), but at least vernier or digital calipers.

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