These are the basic measurements used to design and engineer things electrical.
Volts measures how hard the electricity is pushing (Electrical Force)
Amps measures how fast the electricity is moving (Current)
Watts measures how much electricity is going through the circuit (Power)
Ohms measures how much resistance there is to electricity moving (Resistance)
$ - (Energy) How we purchase electricity can be a bit confusing. Electricity does things for us as it moves through some gadget that converts the moving electricity into something useful. This means that both the amount of electricity going through our circuits and the time period over which it was delivered are both important. The theoretical measure is the joule which is one full watt for one full second. What we also often see is the BTU which equates the energy used to how much and how fast it can heat water. The Kilowatt hour which means delivering a full thousand watts for a full hour is another common energy measure.
A typical type 27 auto battery can store about a kilowatt hour of energy. A 30# (7 gal) propane tank stores about 150 KwH. Effective costs are somewhere around 15 cents per KwH for the battery and 7 cents per KwH for the propane. For comparison, figure an average household may use about 50 KwH per day.
There are simple algebraic relationships between these measurements that can be used to help figure out what is going to happen when you wire things together. Most of the time we are not going to engineer anything but are more interested in making adjustments and accommodations for various conditions or repairs. This interest means that we don't need to worry about actual units or values but rather with how much things change relative to each other.
From these two equations, you can use common algebra to see how changing one measure will impact another. You can also re-arrange the terms and use substitution to solve for any one measure in terms of any two others. For instance, substitute amps time resistance for volts in the power equation to find that power is amps times amps times resistance. Similarly you can find that power is the square of voltage divided by resistance.
Wire gauge is a measure of its size. The AWG measure is what you will find most often used. In this measure, a change in three sizes changes the wire resistance per length by a factor of two. A convenient rule of thumb is that a ten gauge wire will cause a voltage drop of a millivolt for each amp going through it for each foot of wire (this is the definition of 10 AWG wire: 1 ohm resistance per thousand feet). In AWG terms, a change of three AWG will change resistance by two. Lower AWG means less resistance.
About wiring high power car stereo stuff: http://www.the12volt.com/info/recwirsz.asp
What size do I use? http://www.stu-offroad.com/misc/wire-1.htm
Stranded wire tends to be more flexible and less likely to break with flexing than solid wire.
The insulation around a wire not only protects the environment from the electricity inside the wire but also protects the wire from the environment. Make sure your wire has insulation properly rated for the environment where it will live.
The insulation around a wire and how you bundle it with other wires, and where you route it will all reduce how well it can dissipate heat. This means you may need larger sized wire than theory might otherwise suggest when you bundle wires together.
See How stuff works: http://www.howstuffworks.com/wfc1.htm
Soldering tends to create flex points that can break; screw down clamps can flatten wire which becomes loose and might even cause a resistance connection that will get hot or catch fire under load; stranded and solid wires don't twist together very well under wiring nuts ... make sure you use a connection method appropriate to your wire type, size, and environment.
Danger of fire - over stressed components and faulting connections can create conditions that generate heat and sparks that may lead to fire.
Danger from the effects of heat - Even when there is no fire, melted wiring and components may cause problems or generated heat may cause harm to things near the source of heat. When stuff cycles through power on and power off cycles, the heating and cooling may cause repeated expansion and contraction or parts that might contribute to early failure or fault.
Impedance is the term used when electricity in circuits does not behave by simple, algebraic rules. It becomes a significant when there are changes in the flow of electricity such as in alternating current or when direct current is turned on or off. If it is important, impedance considerations will usually be reflected in installation instructions which is one reason why those instructions should be carefully followed. For instance, impedance is an issue in the DC supply lines to some inverters and their instructions tell you to route both supply cables in parallel as much as possible.
Codes: nearly everything about wiring is covered in codes and standards that are often adopted as law. Make sure you follow the appropriate codes and standards!
There are three sorts of issues that cause problems with electrical power. One is whether you are getting the right power, a second is whether it is 'clean' power, and the third is proper connections. RV house battery power should be direct current with the proper polarity between 12 and 14 volts. Line power in the U.S. needs to be 60 Hertz sine wave (smoothly transitioning back and forth sixty times a second) with an averaged voltage rating (known as RMS) between 105 and 130 volts (or double that for 240 v circuits). Proper connections means that the circuits have the proper size wiring for their intended use, are fused appropriately, have appropriate isolation, and are properly wired.
The biggest problem with the right power is usually when it gets too low due to a battery running out of charge or a supply line too long for the load. This is the 'brownout' condition and can be hard on motors, especially.
Another problem is connecting to the wrong power source or getting the connection backwards. This is dangerous and can create very impressive equipment failure. Always check your wiring first, then delivered energy (voltage and polarity) second.
Over voltage can occur in house battery circuits when a battery charger is getting overly ambitious but it more likely in line power situations where there is some fault in the supply. Mild over voltage is usually not catastrophic but can shorten the life of light bulbs and other devices.
Electrical power can pick up dirt on its way from one place to another. From the RV house battery, common sources of dirt in the power include battery charging devices, abrupt load changes, poor connections, faulty equipment, or induced dirt such as from wires too near non-DC electricity or lightening strikes. Dirty AC line power can come from similar sources and these are aggravated because the source is usually much farther away than in battery supplied power systems. More distance to travel means more opportunity to collect dirt.
Power cleaning devices are readily available as surge suppressers for AC devices. There are also filters that can be used in DC situations if dirty DC becomes a problem.
Proper connections has two areas to consider. One is the physical connection between conductors and the other is making connections in the right places. There are usually three conducting paths to worry about. The ground is the safe one as it is supposed to be at the same electrical status as everything around you. The neutral is the electrical return line and is usually at the same electrical status as the ground - and the ground may even be used for a neutral, especially for DC circuits. The hot conductor is the one that is of opposite electrical status to the neutral and is the most dangerous.
240 volt AC service, such as used in 50 Amp RV connections has two hot conductors. They are put together in such a way that they will have opposite voltages when referenced to the neutral line. A 240 volt appliance will be wired between the hot conductors. 110 volt gear is connected between one hot and the neutral. The 240 volt service essentially provides one 240 volt or two 110 volt circuits.
Telephone service is a current limited 48 volt battery system with 90 volt AC added to ring the bells. It uses 24 AWG pairs with a 600 ohm characteristic impedance.
There are three voltage considerations to plug into these equations for typical RV needs. We either use battery voltage (12 volts), line voltage (120 volts) or we are concerned with the voltage drop in wiring due to the resistance of the wires. Typical household wiring is usually 14 AWG for 15 amps at 100 feet or 12 AWG for 20 amps at 100 feet.
Battery voltage circuits need larger wires than household circuits with line voltage. The RV house battery is at one tenth the voltage of typical power lines so battery wires have to carry more current to provide equivalent power. There are two issues that complicate the matter. One is that a twelve volt drop in a 120 v line isn't too bad, such a drop in a twelve volt line would be very bad. So we need to consider the voltage drop in the wire as a matter of percentages - in this case 10% or 12 volt for 120 volt service or 1.2 volts for 12 volt service. The second issue is one that helps a bit. Power is proportional to the square of voltage or current. This means changing the voltage by a factor of ten will only require a change in wire resistance by a bit more than three to compensate (three squared is close to ten, isn't it?).
A foot of ten gauge makes a convenient shunt for measuring current with a cheap digital voltmeter. This size wire is also very common for the thirty amp service lines on RV's.
Thirty amps through a hundred foot 10 AWG cord would mean that the total drop would be 6 volts (3 volts out and three more on the return) and that means the cord would be consuming nearly 200 watts (6 volts times 30 amps) of energy just to get electricity where you want it.. This 200 watts of heat to dissipate is why you shouldn't leave in-use supply cords stashed in a confined space. The 200 watts loss in the line also counts towards the total load on the circuit breaker.