Yes. If you use higher voltages, you can transfer the same amount of power with a small current of charged particles. The energy lost in the transmission through wires increases as the square of the amount of current through those wires so reducing that current is very important.
These devices use diodes, which are one-way devices for current. They only allow the current to flow a certain direction and block its flow the other way. With the help of some charge storage devices called capacitors, these diodes can stop the reversals of AC and turn it into DC. Those little black battery eliminators that you use for household electronic devices contain a transformer, a few diodes and a capacitor or two.
A step-up transformer has a secondary coil with many, many turns. As the current in the primary circuit flows back and forth, it creates a reversing electric field around the iron core of the transformer. This electric field pushes charges through the secondary coil so that it travels around and around the core. Each charge goes around many times, picking up more energy with each passage. By the time the charge leaves the transformer, it has lots of energy so its voltage is very high.
A transformer involves two completely separate circuits: a primary circuit and a secondary circuit. Charges circulate within each circuit, but do not move from one circuit to the other. If the primary circuit of a transformer has a small current flowing through it and that current experiences a large voltage drop as it flows through the transformer’s primary coil, then the primary circuit current is transferring power to the transformer and that power is equal to the product of the primary circuit current times the voltage drop. The transformer transfers this power to the current flowing in the secondary circuit, which is an entirely separate current. That current may be quite large, in which case each charge only receives a modest amount of energy as it passes through the secondary coil. As a result, the voltage rise across the secondary coil is relatively small. The power the transformer is transferring to the secondary circuit current is equal to the product of the secondary circuit current times the voltage rise.
Usually with alternating current generators, which we will discuss next. It can also be made by electronic alternators, such as those found in the uninterruptible power supplies that provide backups for computers.
The reversal of the current in an alternating current (AC) circuit occurs everywhere in the circuit at once. The whole current gradually slows to a stop and then heads backward. At the moment it comes to a complete stop, the electric power company isn’t supplying any power at all and the circuit isn’t consuming any. Because the power delivery pulses on and off in this manner, devices that operate on AC power are designed to store energy between reversals. Motors store their energy as rotational motion. Stereos store energy as separated electric charge in devices called capacitors, or as magnetic fields in devices called inductors.
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.
Your body is a relatively good conductor of electricity and it is easily damaged by currents flowing through it. Your body uses electricity to control its functions and an unexpected current of as little as a few hundredths of an ampere can interrupt those functions. In particular, your heart can stop beating properly. Fortunately, your skin is a pretty good insulator so it is hard to get any current to flow through you. But high voltages can push current so hard that it punctures your skin and begins to flow through you. While the current is actually what injures you, the high voltage is what breaks down your protective skin and allows that current to flow through you.
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.
Only electromagnets can change back and forth and then only when they are connected to a supply of alternating current. A permanent magnet, such as that used to hold notes to a refrigerator, has permanent poles that do not change. But an AC powered electromagnet, such as that found in a transformer, does have poles that change back and forth.
Yes. When you try to push current through a wire, the voltage drop across that wire (i.e. the energy lost by each charge passing through that wire) is proportional to the number of charges flowing through that wire each second (i.e. the current through the wire). If you double the number of charges flowing through the wire each second, then each charge will lose twice as much energy (the voltage drop across the wire will double). If you halve the number of charges flowing through the wire each second, then each charge will lose half as much energy (the voltage drop across the wire will halve).