2007 phy mc 44

The output and the input power is 4 times of that before altering from 6V to 12V provided that the number of secondary coil doubles.
If you double the no. of turns in the secondary coil (with the primary coil untouched), the output voltage will be doubled. Since power delivered at the output (i.e. secondary coil) is proportional to the "square of the output voltage", doubling the voltage will give 4 times the output power. Hence, by conservation of energy, the input power has to increase 4 times accordingly.
I double the coil turns just as above, but instead, i have the electricity supply constant, meaning that the input or output will not increase like the situation of this question, what will happen?
In the actual fact, the power output of a transformer is controlled by the "load resistance" connected to the secondary coil. Decreasing the load resistance will increase the secondary current, hence increasing the power delivered from the transformer. This, in turn, will increase the power drawn at the primary coil from the source because of conservation of energy. If your source could not provide as much as power as required (because you try to keep it at a constant value), the output power at the secondary, and hence the secondary current, will not increase. Ohm's Law no longer applies at the secondary circuit.
In other terms, my question is does the number of coil turns consequently increases with the supply and otherwise?
The number of turns in the primary and secondary (the turn-ratio) only affects the secondary voltage. It has nothing to do with the power. The power delivered by the transformer depends on the load resistance connected to the secondary coil.

2009-10-07 21:29:00 補充：
Q: If i 4x the supply without increasing the coil, what will in this case happen?
The output power will increase by 4 times because of the conservation of energy.

2009-10-07 21:29:18 補充：
...(cont'd) But be aware that the power delivered by the source is governed by the load resistance. You can't increase the power from the source without changing the value of the load resistance.