Let me fill in a few gaps.
The reason that AC works better than DC in powering a city is that you can't "transform" DC--you can tamper with the voltage but always at a cost. Using a transformer, you can run a high voltage at low current through one side and get a low voltage with high current out the other, or do the opposite.
The reason this matters is because of line losses. When you force water through the pipe, you lose a little water through the leaks, as it were. The more water you're forcing through the pipe, the more it leaks. Now, it's tricky doing water-to-electricity analogies because there are three factors and they interact. Voltage is the equivalent of the force behind the water, current of the volume of water per minute, and resistance to the diameter of the pipe. Just as with water, the more force you've got the more volume you're going to move, but the narrower the pipes the less volume you're going to move. However, things which generate electricity usually have a "maximum output", defined in watts, which is voltage times current. That is, even if I have a thousand pounds of pressure per square inch and a thousand gallons of water, if I've got a pipe a mile in diameter and a mile long I'm not going to get more than that much water through it. In the same way, my battery will produce 12 volts of pressure, and the amount of current that will create is dependent in part on the diameter of the piple--the resistance of the circuit--but in part by the limits of the battery. If I connect the two ends of the battery directly to each other in a short, I'll get the maximum current from the battery, but I won't get 12V/0R=infinite current.
I feel like I'm drifting; I hope this is still helpful.
The more current you run through the wire, the more power you lose to line losses--electricity meeting resistance in the wire and so turning to heat. Thus if you use a very high voltage and a very low current you can send large quantities of electricity longer distances, where a high current at a lower voltage will be consumed by the resistance of the wires carrying it.
On the other hand, because Voltage divided by Resistance equals Current, if you have a super high voltage and enough power available, you can have some really serious accidents from it. John mentioned the Vandergraf Generator, making your hair stand up. If you get near enough to a high voltage line, you'll get the same effect--and if you get a bit nearer, you will become the shortest path to ground, and the current will spark across the gap to hit you. John did not mention that when you touch a Vandergraf Generator, you are always supposed to be standing on a thick sheet of insulation, so that you don't become a path to ground, and you're not to let go of the generator while it is running so there's no spark between it and you. High voltage looks for shortcuts to ground, and has the power to make its own. Current will spike, even if the generator can't support the power over a long term, drawing power from other points in the system. It can be fatal.
Thus power companies run alternating current (AC) in extremely high voltages at extremely low current in very large wires over long distances, and then run them through transformers to bring them down to safe voltages for home use.
High current is needed to heat a wire, and thus to operate such things as electric heaters, toasters, incandescent light bulbs, and even vacuum tubes and cathode ray tubes (television monitors before the recent flat screen models). High voltage is better for powerful motors and electromagnets, as it allows for higher wattage (total power) at a lower current level (and thus less heat).
As to production of power, what we call batteries are usually more properly called chemical power cells. The one in your car is a battery because it is a battery of six cells combined in one case. Chemical cells produce electricity by means of an ongoing chemical reaction; the reaction is impeded by the buildup of electrical charge in the system, but connecting the ends of the battery through something enables the electrical imbalance to balance itself, and thus allows the chemical reaction to continue. Most reactions known to us produce constant output at between about 1.2 and 2.5 volts.
If you connect batteries in series, that is, with the positive of one to the negative of the next, you add the voltage. That's why your car battery is 12 volts: it is composed of six "cells" with a standard output of 2V each, connected end to end. If you connect batteries in parallel, positive to positive and negative to negative and draw the power from all the positive ends to all the negative ends, you have the same voltage but increase the potential current available. Batteries can only produce direct current; you need a device to create alternating current from them.
Using a generator, what determines the power output is the number of strands of wire passing through the magnetic field, the strength of the magnetic field, and the speed at which they move. (You can pass the magnetic field through the wires, but most systems move the wire and keep the magnet stationary.) I believe that a stronger magnetic field creates higher voltage and a faster movement creates higher current, but I can't be certain of that. Generators naturally produce alternating current, because the wires pass through the magnetic field first in one direction and then the other; there is a trick to designing a direct current generator which essentially involves changing the polarity of the connection as the generator turns, but it makes for a more complicated generator. Even so, current from a generator pulses, rising from zero to maximum and falling again. Most generators produce voltage which changes following a sine wave; a complete pass of the full sine wave (from zero positive through zero negative and back to zero) is one wave, and the number of waves per second in the frequency, which used to be given in Cycles Per Second (CPS) but in the mid twentieth century was renamed for a famous scientist, Hertz (Hz).
Photocells work more like batteries because they produce a constant chemical reaction induced by sunlight; sound and pressure generation devices work more like generators, because they are dependent on being compressed and released and so create wave forms positive and negative which match the wave form of the compression. If you compressed most of these and held them constant they would cease producing power until they were released, although some function under constant pressure to produce constant voltage (and I don't know how).
Capacitors are used in particular for what is called a stroboscopic circuit. A capacitor is in essence a large plate that holds electrons but doesn't let them go anywhere. The strobe on a camera uses a capacitor to store power equal to the voltage of the battery, but when the low-resistance bulb is dropped into the circuit it release that power at a very high current (which the battery could not match) into the bulb, causing the bulb to light brightly but using up the full power quickly so that it immediately goes out again. (Connecting the bulb to the battery would cause it to illumine more slowly and not as brightly but stay lit longer.)
An inductor is a coil of wire which uses the magnetic field created by moving electrons to induce more moving electrons. The spark system in a car uses the combination of a capacitor and in inductor. The battery stores power in the capacitor; when the points close allowing the power to go to the spark plug, it passes through the inductor which, if I've got it correctly, converts part of the power into a magnetic field and then back into electricity (I can explain how that works, but it's probably already too technical) so that the pulse lasts a bit longer. Not being an automotive engineer, I'm not at all certain why that's a good thing.
Capacitors and inductors are also used together to create tuned circuits. These are much more common in electronics, but they have the use in electricity of stabilizing electrical power at a desired frequency in alternating current. In essence, the impedance of a capacitor decreases with frequency, and the impedance of an inductor increases with frequency, and there is for any pair of capacitor and inductor a specific frequency at which the impedance of the capacitor equals that of the inductor. You can design a circuit based on that which will allow electricity of that frequency to pass and block electricity which is significantly off that frequency. Actually, someone can--I can't, although I've tuned such circuits in an old electronic keyboard once. (I should dig out that keyboard and see if I can fix it. It might be useful to me now.)
So let me hit the curve question head on:
- 9@9 eliminates the 9@10 static power used by the Daleks in the first episode of Dr. Who; you can't have usable electricity without a return path.
- 9@8 eliminates the 9@9 broadcast power used in Gamma World to power robots, and the theoretical transmission of electrical power via microwave from orbiting solar satelites to earth-based receiving stations.
- 9@7 eliminates the 9@8 use of crystal radio sets (not modern electronic ones) and Marconi sets and of solar energy power generator farms and rooftop solar-electric panels.
- 9@6 eliminates 9@7 systems which generate power from heat or which directly control resistance based on heat; this mostly affects industrial heating controls.
- 9@5 eliminates 9@6 frequency generators (capable of producing alternating current at different frequencies or of altering the frequency of alternating current), electrical filters (as described, using an inductor and a capacitor to eliminate AC outside a specific frequency, or to block either all AC or all DC current in a circult), and thermostats (simple devices designed to activate a switch at a specified temperature).
- 9@4 eliminates 9@5 transformers, capacitors, and inductors, in essence limiting power grids to a single voltage throughout and so keeping them small-scale.
- 9@3 eliminates 9@4 sound and pressure systems and electric motors.
- 9@2 eliminates 9@3 light bulbs, resistors (which have a specific constant resistance), circuit breakers (relay systems designed to open a switch when current reaches a critical level and then lock it open), and meters (coil systems which measure electrical values by the magnetic field produced).
- 9@1 eliminates 9@2 skills including generators (described above), electric heat, and fuses (wires designed to burn up when the current running through them exceeds a specific level).
I think that's the list. I hope it helps.
--M. J. Young