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.