If current times voltage equals power, this makes it seem that high current time…

If current times voltage equals power, this makes it seem that high current times low voltage would equal low current times high voltage; but this is not true because of resistance. How is resistance taken into account in the current times voltage equal power equation?

Your first observation, that high current times low voltage would equal low current times high voltage is true; it means that electricity can deliver the same power in two different ways: as a large current of low energy charges or as a small current of high energy charges. That result is critical to the electrical power distribution system. The resistance problem is a side issue: it makes the delivery of power as a large current of low energy charges difficult. If you could get this current to peoples’ houses without wasting its power, there would be no problem, but that delivery isn’t easy. The wires waste lots of power when you try to deliver these large currents. So the electric power distribution system uses small currents of high-energy charges instead.

What is the purpose of the iron core in a transformer?

What is the purpose of the iron core in a transformer?

The iron core of a transformer stores energy as power is being transferred from the primary circuit to the secondary circuit. This energy is stored as the magnetization of that iron. The transformer needs to store that energy for roughly one half cycle of the alternating current or about 1/120th of a second. The more iron there is in the transformer, the more energy it can store and the more power the transformer can transfer from the primary circuit to the secondary circuit. Without any iron, the energy must be stored directly in empty space, again as a magnetization. But space isn’t as good at storing magnetic energy as iron is so the iron increases the power-handling capacity of a transformer. Without the iron, the transformer must operate at much higher frequencies of alternating current in order to transfer reasonable amounts of power.

In what circumstances is a step-down transformer more advantageous than a step-u…

In what circumstances is a step-down transformer more advantageous than a step-up transformer and vice versa?

The transformer moves power from the primary circuit to the secondary circuit, almost without waste. The main reason for using a transformer is to change the relationship between voltage and current. Whenever you need a large current of low energy, low voltage charges, you probably want a step-down transformer. Whenever you need a small current of high energy, high voltage charges, you probably want a step-up transformer. I have already described the issues in power distribution, but transformers are used in many other devices. Step-down transformers are used to power small electronic devices instead of batteries (those little black boxes you plug into the wall socket contain transformers and some electronics to convert the resulting low voltage AC into low voltage DC). Step-up transformers are used in neon signs and bug-zappers.