More turns = more voltage, as long as the load resistance is the same, and zero load current is a good thing.
Trying to calculate the sum of all impedances is a PIB. (Pain In Behind)
Measuring is so much easier!
Do not short a turn for more than a few seconds or you risk overheating the transformer.

Not to change the subject, but let's say if we had one turn through secondary, the secondary is already shorted...what if uninsulated wire was used and half the secondary loop was shorted with each other. The resistance will be half? Will all the currents double?

 

if we had one turn through secondary, the secondary is already shorted.

No it isn't. Making one turn around a core does not "short" the transformer. Connecting the ends of the wire which you used to make one turn is what shorts the turn, which is the secondary you just created.

What are the exquisite details of mistreating an unknown transformer? You're making me crazy!

 

No it isn't. Making one turn around a core does not "short" the transformer. Connecting the ends of the wire which you used to make one turn is what shorts the turn, which is the secondary you just created.

What are the exquisite details of mistreating an unknown transformer? You're making me crazy!

Hahaha. Just a curiosity question and something I dont intend in doing.
To summarize: to calculate

No it isn't. Making one turn around a core does not "short" the transformer. Connecting the ends of the wire which you used to make one turn is what shorts the turn, which is the secondary you just created.

What are the exquisite details of mistreating an unknown transformer? You're making me crazy!

Hahaha. Just a curiosity question and its something I dont intend in doing.

To summarize: to calculate the new V primary of a transformer with a shorted secondary:

-Measure secondary Open circuit Voltage (Vs open circuit)
-Measure Primary and Secondary Resistances.
-Therefore Secondary max current = Vs open circuit/(Rp+Rs)

 

Therefore Secondary max current = Vs open circuit/(Rp+Rs)

No.
You have to reflect the primary resistance into the secondary by the square of the turns ratio.

 

You say that you have an "educational" transformer. Post a picture of the transformer. Can you post a link to the web page of the manufacturer of the transformer?

Do you have specifications for it? Can you link to them? How many turns are on the primary? What is the maximum allowed primary current? What is the maximum allowed primary voltage? What wire size are you using on the secondary?

It would be easier to help you if you would post full information about the transformer and the actual value of measurements you have made. Instead of just saying that you have measured some voltage with 3 turns on the secondary and the value doesn't match up with your expectations, post the actual measurements you have made and show the calculations of the result you expect. Also give the values of all the measurements you have made, with the various number of turns you have placed on the secondary.

More information is always better when you're asking for help from people who haven't ever seen this particular transformer, and who can't look over your shoulder.