When you send an alternating current through the primary coil of wire in a transformer, that current produces a magnetic field in the transformer. Because the current in the primary coil is changing with time—it's an alternating current—this magnetic field is changing and changing magnetic fields are accompanied by electric fields. In the transformer, this electric field pushes electric charges around the secondary coil of wire in the transformer. Since these electric charges are pushed in the direction they are traveling, work is being done on them and their energies are increasing. However, in the transformer you mention, the secondary coil of wire has fewer turns in it that the primary coil of wire. As a result, the charges don't receive as much energy per charge (as much voltage) as the charges in the primary coil are giving up. This type of transformer, in which the secondary coil has fewer turns of wire than the primary coil, is called a step-down transformer and reduces the voltage of an alternating current.
An electric welder sends an electric current through an ionized gas, forming a pattern of current flow through the gas that is known as an arc. The ionized gases in this arc consist of electrons that are negatively charged and atoms or molecules that have lost electrons to become positively charged. The electrons flow toward the positively charged metal at one end of the arc while the positively charged ion flow toward the negatively charged metal at the other end of the arc. As these charged particles move, they collide frequently with one another and with gas atoms or molecules along their paths, and they convert some of their electric energies into thermal energy. These collisions also produce additional ions. The enormous amounts of thermal energy produced by collisions as the charged particles flow through the arc melts the metals at the ends of the arc so that these metals can be fused together.
If an appliance receiving power from an AC power source behaves as an electric resistor—meaning that the current passing through it is proportional to the voltage drop across it—then it's easy to calculate the power being consumed by this appliance. You simply multiply the voltage drop across the appliance (measured in volts) by the current passing through the appliance (measured in amperes) to obtain the power (measured in watts). The voltage drop across the appliance indicates how much energy the appliance extracts from each unit of charge pass through it and the current passing through the appliance is the measure of how many units of charge are passing through the appliance each second. Thus the product of voltage drop times current gives the energy that the appliance extracts from the current each second, which is the power extracted by the appliance. On the other hand, if the appliance behaves like an inductor or capacitor—meaning that the current passing through it isn't proportional to the voltage drop across it—it's much harder to calculate the power that the appliance is consuming.
The frequency characteristics of a transformer are determined principally by the materials in the transformer's core. Power flows from the primary circuit to the secondary circuit by way of the magnetization of the transformer's core. With each half-cycle of the alternating current in the primary circuit, the transformer's core must magnetize and demagnetize. A transformer core's ability to magnetize and demagnetize properly depends on the frequency of the alternating current in the transformer's coils. If that frequency is too low, the core may saturate—reach its maximum possible magnetization—during the half-cycle. In that case, the core will not be able to transfer the requisite amount of energy to the secondary coil and the power transferred between the two coils will be inadequate. That's why low frequency transformers often contain huge iron cores—cores that avoid saturation by spreading out the magnetization and stored energy over large volumes of iron.
On the other hand, if the frequency of current in the primary is too high, the core may be unable to magnetize and demagnetize fast enough to keep up with it and the power transfer will again be inadequate. The core may also become hot due to friction-like losses in the core material. That's why high frequency transformers use special core materials such as ferrite powders or even air. Although air (or really empty space) can't store large amounts of energy in small volumes when it magnetizes, it can respond extremely quickly. Air-core transformers operate well at extremely high frequencies.
Generating heat from a battery is relatively easy. All you need is a material that conducts electricity only moderately well and you're in business. If you allow current to flow through that material from the battery's positive terminal to its negative terminal, the current will lose energy as it struggles to get through the material and the current's lost energy will become thermal energy in the material. The only difficult part of this task is in choosing the right material so that it doesn't produce too much or too little heat. In short, the electric resistance of the finished material has to be in the right range. For a solid system that you can cut and tailor, that's not much of a problem. But for a paint, it could be tricky. To make an inexpensive paint, it would probably need to use carbon powder as the electric conductor. A thin layer of carbon granules held in place by a plastic of some sort would probably provide a suitable conducting surface that would become warm when you allowed current to flow through it from a battery. There are copper and silver conducting paints that might also work, but these are rather expensive and I'm not sure how they behave at elevated temperatures.
A transformer only works with ac current because it relies on changes in a magnetic field. It is the changing magnetic field around the transformer's primary coil of wire that produces the electric field that actually propels current through the transformer's secondary coil of wire.
When dc current passes through the primary coil of wire, the coil does have a magnetic field around it, but it doesn't have an electric field around it. The electric field is what pushes electric charges through the secondary coil to transfer power from the primary coil to the secondary coil. In contrast, when ac current passes through that primary coil of wire, the magnetic field around the coil flips back and forth in direction and this changing magnetic field gives rise to an electric field around the coil. It is this electric field that pushes on electrically charged particles—typically electrons—in the secondary coil of wire. These electrons pick up speed and energy as they move around the secondary coil's turns. The more turns these charged particles go through, the more energy they pick up. That's why doubling the turns in a transformer's secondary coil doubles the voltage of the current leaving the secondary coil.
Your hot water heater is powered by 240 volt electric power through the two black wires. Each black wire is hot, meaning that its voltage fluctuates up and down significantly with respect to ground. In fact, each black wire is effectively 120 volts away from ground on average, so that if you connected a normal light bulb between either black wire and ground, it would light up normally. However, the two wires fluctuate in opposite directions around ground potential and are said to be "180° out of phase" with one another. Thus when one wire is at +100 volts, the other wire is at -100 volts. As a result of their out of phase relationship, they are always twice as far apart from one another as they are from ground. That's why the two wires are effectively 240 volts apart on average.
Most homes in the United States receive 240 volt power in the form of two hot wires that are 180° out of phase, in addition to a neutral wire. 120-volt lights and appliances are powered by one of the hot wires and the neutral wire, with half the home depending on each of the two hot wires. 240-volt appliances use both hot wires.
When you complete a circuit by plugging an appliance into an electrical outlet, current flows out one wire to the appliance and returns to the electric company through the other wire. With alternating current, the roles of the two wires reverse rapidly, so that at one moment current flows out the black wire to the appliance and moments later current flows out the white wire to the appliance. But the power company drives this current through the wires by treating the black wire specially—it alternately raises and lowers the electrostatic potential or voltage of the black wire while leaving the voltage of the white wire unchanged with respect to ground. When the voltage of the black wire is high, current is pushed through the black wire toward the appliance and returns through the white wire. When the voltage of the black wire is low, current is pulled through the black wire from the appliance and is replaced by current flowing out through the white wire.
The white wire is rather passive in this process because its voltage is always essentially zero. It never has a net charge on it. But the black wire is alternately positively charged and then negatively charged. That's what makes its voltage rise and fall. Since the black wire is capable of pushing or pulling charge from the ground instead of from the white wire, you don't want to touch the black wire while you're grounded. You'll get a shock.
Your body is similar to salt water and is thus a reasonably good conductor of electricity. Once current penetrates your skin (which is insulating), it flows easily through you. At high currents, this electricity can deposit enough energy in you to cause heating and thermal damage. But at lower currents, it can interfere with normal electrochemical and neural process so that your muscles and nerves don't work right. It takes about 0.030 amperes of current to cause serious problems for your heart, so that currents of that size can be fatal.
The bulb in a battery doesn't care which way current flows through it. The metal has no asymmetry that would treat left-moving charges differently from right-moving charges. That's not true of the transistors in a walkman or gameboy. They contain specialized pieces of semiconductor that will only allow positive charges to move in one direction, not the other. When you put the batteries in backward and try to propel current backward through its parts, the current won't flow and nothing happens.
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