The primary coil of a transformer contains 100 turns; the secondary has 200 turns. the primary coil is connected to a size-aa battery that supplies a constant voltage of 1.5 volts. what voltage would be measured across the secondary coil?

Transformers don't work with batteries. If you did this with a transformer, you would get nothing out of it but smoke. Transformers only work with AC. If you connect 1.5 volts AC to the primary of this transformer, you'll see 3 volts AC at the secondary.

Since transformers use laws that require time changing quantities (alternating current), the battery would produce no voltage on the secondary windings. In fact the primary winding would short out the battery to a large extent since the resistance of its copper windings would be very low.

In reality, as the battery was first connected to the primary, a very short blip of voltage would appear on the secondary as the magnetic field initially grew in the core (that would constitute a time-changing magnetic field required for the device to work). But it would immediately go away afterwards and that output cannot be determined without actually doing the experiment due to so many unknowns.

But this question isn't looking for that explanation. It's kind of a trick question.