how many amps is 35 kva?

At 240 volts you could run 100 amps and at 120 volts you could run 200 amps. That assumes a perfect efficiency transformer, so it would be slightly less, but it's close enough that you could wire the box as if the transformer has no loss.

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RE:

how many amps is 35 kva?

I have a new transformer for my sub panel at work, and I was wondering how many amps would be available if I have 480 volts going in at 50 amps, and 240/120 volts coming out, with 35 kva. I'm not installing it myself, just wondering how many amps I would have available to work with in my sub...

if the current input would be 50 Amps:

if you use the 240 V output, current would be 100 amps.

if you use the 120 V output, current would be 200 amps.

this is computed where the transformer has 0 core and copper losses..but a good approximation for considering what wires and other accessories will be used..

35 Kva Transformer

Ampere measures how much current is going. Think of it as the weight of water flowing in from of you every second, to make an analogy. Kw is a measure of power. It is the product of the flow times the energy (or the speed). In electricity, this requires to know the voltage. If your power system is 110 volt, then 160 Amp would be 17600 w (or 17.6 kW or 17.6 kVA).

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35000VA/480V/SQRT(3) = 42A of 480. This implies 84A at 240 or 168A at 120.