Physics vs Electronics (Smartphone charger)

A transformer is not a charger. A transformer changes the voltage and current but it is of the same frequency, in the US 60Hz. An ac source cannot charge a battery because if in one half cycle of the 60Hz the source charges the battery then in the next half cycle when the polarity flips it will drain it. A battery charger needs a dc voltage: between the transformer and the battery there is a rectifier that is essentially a diode + a capacitor with a lot of other things. The transformer is there to change the input 110V (in the US) to a lower voltage that is "friendlier" to a diode and more importantly to a voltage near that of the battery to minimize losses in the rectification. When the primary is connected to an ac source but the secondary is open then the source sees an inductive load but it is still ac, so only an ac meter will work when you try to measure the current through it.

In an ideal transformer (which has no DC resistance), and which has no current flowing from the secondary coil, the primary current will be small and out of phase with the applied voltage. Average power in and out are both zero. When AC current flows from the secondary, it causes a shift in the phase and magnitude of the flux and in the primary current. I have a digital meter that shows what is being supplied by a wall plug. With my phone charger plugged in at 120 volts without the phone it's showing 0.09 amps, 1 watts and a power factor of 0.09. Plugged into the phone it shows 0.11 amps 3.5 watts and a PF of 0.27 . Note: Average power = (rms) amps x volts x PF (where the PF is the cosine of the phase difference).