The wire size you are looking for is #1 copper with an insulation factor of 90 degrees C. This wire is rated at 140 amp but with a voltage drop correction it will give you 100 amps at the load. The wire for transformer feeders at 125% is included in the sizing.
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A control transformer marked 240V - 24Vac would have a control voltage of 24 volts.
If a load were only 240 volt on a single phase 240v system with a center tapped transformer the neutral conductor would carry no current.
With a transformer.
It would be better if you got a transformer and stepped up the voltage.
3
Ohms law says that watts are equal to volts times amps. 240v X 13.5a = 3240 va VA / 1000 = Kva So, your load requires 3.24 Kva. The transformer should have a rating greater than this as a safety factor, so you would choose the next larger size, in this case probably a 5 Kva transformer with a 480v primary and a 240v secondary. Your local electrical codes may require a larger safety factor, so you would want to consult them before buying the transformer!
That could only happen if the neutral wire (white) becomes disconnected at either the panel, the meter base or the transformer.
No. The neon sign is fed by a step-up transformer. Primary side 120V, secondary side 7500V. If you applied 240 to the primary side you would get 15000 volts on the neon tube. A flash over and then nothing. If you can find a transformer from 120V to 240V or 240V to 120V then you are good to go. Connect 240V to 240V side and you will get 120V out the other, connect the 120V side to the neon sign and you should have light. Transformer should be at least 100va. This will give you an output of .83 amps at 120V
If they are both using the same watt globes the 240v is slightly more efficient due to small losses in the transformer.
Since this transformer has a ratio of 1:2 the load current on the 480V side just has to be doubled. 85 x 2 = 170A on the primary. 40.8 KVA transformer. To prove this just find the KVA of both sides and they should be equal.
No
Sounds like the wrong size fuse protection was used. The transformer should be protected to its kva capacity.