is there any power loss?(compare to step up transformer,actually I see
there is some thin and thick copper wire binding in the transformer.
Will this affect the power loss?
Primary and secondary share the same core so, the main thing to consider is whether the core saturates more when driven backwards. Here's a sort of worked example: -
If the primary winding is 10 henries inductance, on 240V AC supply the current will be: -
\$\dfrac{240V}{2\pi f L}\$ = 76 mA.
Let's say the transformer had 1000 turns on the primary so ampere turns are 76.
The 12V secondary has one twentieth of the primary turns i.e. 50 and its inductance will be \$20^2\$ times smaller at 25 mH. Now, if you applied 12V AC to the secondary you'd get a magnetization current of: -
\$\dfrac{12V}{2\pi f L}\$ = 1528 mA.
Ampere turns are 50 x 1.528 = 76 (i.e. just the same)
This answer explains that for an unloaded secondary, the natural phase relationship between primary voltage and secondary voltage is is zero degrees.
It therefore follows that if there is a secondary load current (due to a resistive load), the current in the primary due to that secondary resistive load must be 180 degrees out of phase with the secondary load current i.e. as current flows into the primary, current flows out from the secondary.
This of course is for an ideal transformer and a resistive load.
If you ignore the leakages and magnetization inductance of the transformer, and the load is reactive, then there will be a 90 degrees phase shift.
Bringing in leakage inductance and DC coil resistance will/can muddy the waters. Bringing in magnetization inductance muddies the water a bit more.
The low frequency transformer equivalent circuit is this: -

As you should be able to see, if you considered all the leakages, magnetization inductance and losses and then added a semi-reactive load, the phase angle is quite complex to calculate.
However I do-not know, in which-way Lenz's law acts in transformer;
because the law states the induced current will try to hinder the
cause.
Strictly speaking, it is voltage that is induced and any current that flows is subject to the that voltage, the load and the leakage inductance.
but when the secondary circuit of a step-up transformer turned On
(closed) , so-far I've know , the current in primary-coil goes-up
In normal usage, for a voltage transformer it is non-ideal to consider the secondary being short circuited. However, it makes no difference to the phase angle providing you obey the rules inherent to the model.
Best Answer
In a step-down transformer, the primary winding will have a higher resistance. The resistance will be low, but there should be a noticable difference unless you've got a really big transformer.
If you're trying to identify what a winding is, then here are some notes:
Transformer windings have a phase relationship, but it's typically not important for power supplies. Unless one of the wires has continuity to the transformer core, the polarity doesn't matter.
A relatively safe way to test transformers is to hook up a small AC voltage (1-5VAC) and measure the voltages across the other windings.