. 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.
. 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.
. Is it true that if you double the current through a wire then you double the voltage loss and if you halve the current then you halve the voltage loss?
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).
. What are the relationships between Joules, Coulombs, Amperes, Volts, and Watts?
A Joule is a unit of energy; the capacity to do work. A Coulomb is a quantity of electric charge; equal to about 6,250,000,000,000,000,000 elementary charges. An Ampere is a measure of current; equal to the passage of 1 Coulomb of charge each second. A Volt is a measure of the energy carried by each charge; equal to 1 Joule of energy per Coulomb of charge. A Watt is a measure of power; equal to 1 Joule per second. A current of 1 Ampere at a voltage of 1 Volt carries a power of 1 Watt. That is because each Coulomb of charge carries 1 Joule of energy (1 Volt) and there is 1 Coulomb of charge moving by each second (1 Ampere). That makes for 1 Joule of energy flowing each second (1 Watt).
. What causes large electric resistances?
Thin wires or wires made of poor conductors. Some metals are simply better at carrying current without wasting energy than other metals. It has to do with how often a charge bounces off of a metal atom and loses energy. Copper, Silver, and Aluminum are good conductors while stainless steel and lead are pour conductors. Metals tend to become better conductors as you cool them and worse as you heat them. Semiconductors such as carbon (graphite) are poor conductors but have the reverse temperature effect. At low temperature they are poor conductors but become good conductors at high temperature.
. What does voltage rise mean?
When current flows through a battery or the secondary of a transformer, its receives power. Each charge leaves the battery with more energy than it had when it arrived. Since the energy of each charge has increased, the voltage (energy per charge) of the current has increased. Thus the current passing through the battery experiences a rise in voltage or a "voltage rise".
Resistance is the measure of how much an object impedes the flow of electricity. The higher an object's resistance, the less current will flow through it when you expose it to a particular voltage drop. To use the water analogy, resistance resembles a constriction in a pipe. The narrower the pipe (higher the resistance), the harder it is to push water through that pipe. If you keep the water pressure constant (constant voltage drop) as you narrow the pipes (increase the resistance), then less water will flow (the current will drop).
. What is the difference between current and voltage?
Current is the measure of how many charges are flowing through a wire each second. A 1-ampere current involves the movement of 1 Coulomb of charge (6,250,000,000,000,000,000 elementary charges) per second. Voltage is the measure of how much energy each charge has. A 1-volt charge carries 1 Joule of energy per Coulomb of charge. To use water in a pipe as an analogy, current measures the amount of water flowing through the pipe and voltage measures the pressure (or energy per liter) of that water.
. What is the difference between single-phase and three-phase electric power?
In single-phase power, current flows to and from a device through a pair of wires. The direction of the current flow changes with time, reversing smoothly 120 times a second in the US or 100 times a second in Europe (60 or 50 full cycles of reversal, over and back, each second respectively). In its simplest form, one of the two wires is called "neutral" and its voltage is always close to 0 volts (meaning that it has essentially no net electric charge on it). The other wire is called "power" and its voltage fluctuates from positive to negative to positive many times a second (meaning that its net electric charge varies from positive to negative to positive). The difference in voltage between "neutral" and "power" propels current through the device.
In three-phase power, current flows to and from a device through a group of three wires. These three wires are often called "X", "Y", and "Z", and each one is a power wire with a voltage that fluctuates from positive to negative to positive many times a second. (A fourth wire, "neutral", with a voltage of approximately 0 volts, may also be used.) But while the voltages of the three power wires fluctuate up and down the same number of times each second, they do not reach their maximum or minimum voltages at the same time. They reach their peaks one after the next in an equally spaced sequence: first "X", then "Y", then "Z", and then "X" again and so on. Because these three wires or "phases" rarely have the same voltages, currents can and do flow between any pair of them. It is such current flows that power the devices that use three-phase electric power. The natural sequencing of the three phases is particularly useful for devices that perform rhythmic tasks. For example, three-phase electric motors often turn in near synchrony with the rising and falling voltages of the phases.
Another advantage of three-phase electric power is that there is never a time when all three phases are at the same voltage. In single-phase power, whenever the two phases have the same voltage there is temporarily no electric power available. That's why single-phase electric devices must store energy to carry them over those dry spells. However, in three-phase power, a device can always obtain power from at least one pair of phases.
. What is the difference, if any, between appliances with a 2 prong plug and a 3 prong plug?
In the 2 prong system, current travels to the appliance through one prong and leaves through the other prong. The roles of the two prongs interchange every 120th of a second. In the 3-prong system, there is one extra prong and that connects the frame of the appliance to the ground (the earth). This extra connection is a safety feature. If a wire comes loose inside the appliance and touches the frame, the frame can deliver charge and current to you through your hand and you can deliver it to the ground through your feet or your other hand. The earth is very large and a large amount of charge can flow into it without repelling further charge. Moreover most electrical systems are actually connected to the ground at some point. So if current can travel out of the circuit feeding power to the appliance and travel through you and into the ground, it will. You'll get a shock. The ground connection (the extra prong) allows this extra current to flow to ground so easily that a huge current is drawn out of the power source, causing the fuse or circuit breaker in that power source to break the connection. When that power connection is broken, no power can flow to the appliance at all and you can't get a shock from it. Plastic appliances often omit the extra prong because they have nothing dangerous to touch on their exteriors.