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Your question is not clear.
Generally one does not talk about a DC transformer although in the generic broad sense of the word it probably applies.
Two major things about wire. The size, #10, relates to current capacity, while insulation and environment may alter that rating to a lower value.
The insulation and environment will determine maximum operating voltage.
If your referenced #10 wire was originally used to supply a load that required pure DC, meaning low ripple, at about 12 V and some load current within the wire rating, and you now want to now supply that load from a power supply derived from the 120 VAC, then you need to also ask the question what min-max DC voltage is allowable at the load.
If the regulation does not need to be very good, then an isolation transformer, about 10 V secondary, a bridge rectifier, and filter cpacitor should work. 10*1.414 = 14.1, subtract 1.8 for the bridge, and you get 12.3. This is only a rough calculation. If you assume a 95 to 135 posssible input variation, then that is a +12 to -21% variation relative to 120 V nominal. This pecentage variation will directly map to the secondary. To this you add maybe 10% variation due to load changes.
If you need good reglation relative to load and line, then you need a regulated power supply.
If the ouput load regulation is satisfactory with the unregulated transformer, rectifier, capacitor supply, but the line variation is a problem, then you could consider a Sola type line regulator.
You have not mentioned current or power levels.
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