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An n:1 transformer receives a current at its primary and outputs an output voltage

V(out)=V(in)*n and an output current I(out)=I(in)/n

The output power P(out)=V(out)*I(out)=P(in) as expected by the law of conservation of energy.

My question is rather is it necessary to use a thinner (hence narrower cross-section) wire at the secondary so that the transformer works properly? The issue as I understand it, the thinner wire supports a smaller current I(out), but has a longer portion within the magnetic field of the iron core (hence longer or more windings). The electrons are therefore excited over a longer stretch of wire, reach a higher energy level, giving a higher V(out). All of this as expected by conservation of energy laws.

Now, what happens if we used a secondary winding with wire of equal thickness as that of the primary? Which effects will be observed?

  • The secondary will excite a greater number of electrons and will yield an output voltage identical to that of the primary because the energy was dispersed among more electrons. It will behave like a 1:1 transformer instead

  • The secondary will follow the n*voltage and Amperage/n just like a regular n:1 transformer, but will have the advantage of a lower wire resistance at the secondary (because of the thicker wire)

  • Will cause excess current to flow in the primary and overheat the primary windings and eventually cause damage

  • Will yield a lower-than-expected value of n.

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2 Answers 2

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The thickness of the secondary wire is mainly a practical matter. The secondary needs to have more turns, so the wire may need to be made physically thinner to fit on the transformer. In addition, since the secondary current is lower, the secondary usually doesn't need to use a thicker gauge wire to prevent excessive resistive voltage drops or heating. Finally, there is the cost advantage of using less wire. So besides these considerations, the answer to your last question would be #2: the lower secondary resistance would be an advantage in general, unless the design of the circuit that uses the transformer somehow relies on this resistance.

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For an ideal transformer with the coils having zero resistance there is no need to worry about the diameter and composition of the coils.

For a real transformer with the coils having resistance ohmic heating (a lossy process) will occur.
It so happens that fewer turns correspond to a lower voltage but a larger current so to reduce the ohmic heating the windings have a larger cross-sectional area.

One can often identify the coil with the smaller number of turns as it will have wire of a larger diameter than the other coil.
Failing that one can measure the dc resistance of the coils and then surmise that the coil with the lower resistance is the low voltage one.

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