So according to Ohm's law, the secondary current of a transformer can be found from dividing the secondary voltage by the resistance of the load (Is = Es/Rl). According to this formula, as the secondary voltage decreases, the secondary current should also decrease (assuming that resistance stays constant.)

Well today in class I learned that a short in the secondary of a transformer causes voltage to go down, since a short basically lowers the number of windings of the coil. But according to my reading a short in the secondary of a transformer causes current to increase. This also makes sense, since shorts normally increase current.

So the math doesn't seem to add up. If a secondary short in a transformer causes voltage to decrease and current to increase, then how can Is=Es/Rl? I know a short will decrease the resistance of the transformer itself, but the resistance of the transformer isn't that significant is it?

 

If you are referring to an internal short between turns in a transformer secondary winding, depending on where the short occurs this is equivalent to connecting all or part of the winding to a negligibly small resistance. In this situation you no longer have a neat single external load Rl, but a combination of an external load (if the short does not reduce the output to zero) and the internal shorted turns.

You will indeed expect to see the output voltage reduced, and at the same time an excessive current will flow in all or part of the secondary. There is no contradiction here, it is just that you no longer have the simple circuit described by Is = Es/Rl

The current will be limited only by the winding's own resistance, perhaps leakage inductance, and the primary resistance and the feeding supply impedance. Typically a power transformer in this situation will draw such a large current that it will quickly overheat and burn out, unless some kind of fault protection is used.

 

What Adjuster said is correct.

Additionally, you should not assume a transformer's own resistance is negligible. This resistance has many names (DCR being one for Direct Current Resistance, where no inductance effects are considered).

Back in the day I did switch mode power supplies we jumped thru hoops to design a transformer with an acceptable amount of DCR, it was never neglected.