Work in Progress Therese Peffer c. 1993 Therese Peffer Trains and orchestras need conductors to guide their way, and well, electrons need them too! I'm still putting together a small system for the trailer I live in. I figured out my loads, bought a 60 Watt photovoltaic (PV) panel to produce electricity, and have a car battery to store it in (discussed in last issue, HP #32). Now what? I need to connect the two and plug in! What is a conductor? I have a very basic understanding of electricity. I know that there are negatively charged particles called electrons revolving around the nucleus of all atoms. Some materials are made up of atoms that let their electrons wander around, moving from atom to atom. If we can induce a current, that is, a continuous movement or flow of these electrons in a material, we call that material a conductor. For example, metal is a good conductor of electricity Ä copper in particular, but also aluminum. Metal wires are typically used conductors. If you look around your home, you may see many cords, for the telephone, for lights, for a radio, extension cords, or maybe battery jumper cables. Essentially all the cords are doing the same thing: conducting electricity, but in different ways. One size does not fit all One difference is the size of the wire. Sometimes I think of wires as freeways for electrons. A small wire, say #20 AWG (American Wire Gauge), could be a single lane road, but a larger wire such as #10 AWG would be a one way 4 lane road, and #0000 AWG is an Los Angeles interchange of 7 lanes and more stacked up!! Lower numbers correspond to larger diameter wire. The bigger the cross section of the wire, the more capacity the wire has to carry these electrons. It is called ampacity; electrical current is measured in Amperes. There are no affordable perfect conductors. Wire conducts pretty well, but even copper wire has a certain resistance. If a wire is too small for the amount of current it's carrying, then it will heat up! I think of a traffic jam Ä too many electrons trying to move at the same time. Part of figuring out how to hook up my photovoltaic panel to the battery was figuring out the size of wire to use! My PV panel produces about 3 Amperes of electrical current at about 17 Volts. I think of the voltage as the force that causes the electrons to move. Time to do a little math! A fellow named Ohm discovered a relationship between voltage, current and resistance which can be expressed as Resistance = Voltage divided by Current, or R = E/I. If you have current flowing through a bit of wire, you can measure the voltage drop across it, and figure out the resistance! Reducing the heat The amount of power (in watts) is equal to the voltage times the current. Low voltage systems such as my 12 Volt system, carry a lot of current compared to 117 volts ac from the utility for the same amount of power. If you look at the cords around the house you'll notice that your cords for appliances are much smaller than the battery jumper cables. If I used a small wire for my 12 Volt system, some of the power that the panel is producing turns into heat in the wire instead of reaching the battery. More math here: Power (lost to heat) equals the voltage loss times current, P= EI. (Aside: Voltage loss equals current times wire resistance, so substitute RI for E, and Power equals current squared times resistance, P=I2R. For a constant resistance (a piece of wire), if you double the amount of current, you quadruple the power lost to heat!) The resistance of the wire should be as low as possible so the voltage loss will be as low as possible. The PV panel may produce 17 Volts, or on a sweltering summer day, the panel may only produce 15 Volts. For the panel to charge the battery, the voltage produced by the panel has to be larger than the voltage of the battery. This wasn't obvious to me when I first started my system, but it makes sense! The electrons flowing from the panel have a hard job; jump-started by the sun, they have to have enough force (voltage) behind them to overcome the resistance of the connections, the wire, the regulator, and finally, the internal resistance of the battery. If the voltage of the current when it reaches the battery is only 12 Volts, then the battery won't get charged. So the idea is to find wire with low resistance. The total resistance of the wire depends on the type of metal, the diameter, and also the length. Wire tables list the resistance per 1000 feet of wire for different diameters and types of wire. The voltage difference (or loss) from what the panel is producing and what the battery is receiving should be about 2.5 to 5%. My system is a 12 Volt system, and I decided a 2.5% loss of voltage is okay. So 2.5% of 12 Volts is a 0.3 Volt drop; a 0.3 Volt loss is acceptable along the total length of wire between my PV panel and my battery. How long a wire? And what is meant by "total length of wire"? This confused me at first. After all, when you look at the cords all over the house, these are just single wires, aren't they? Nope. It turns out that if you cut a cord you'll see two or three insulated conductors (the third is for ground). Why two? Basically one conductor carries the electrons coming to your appliance and the other conductor carries the electrons going back into the outlet. For electrical current to flow in a circuit, there must a loop. Electricity comes from a utility, travels through lines to your home, travels on one conductor from the outlet through your toaster oven and then returns via the second conductor back to the outlet and to the utility. I understand DC (Direct Current) a lot better than ac (alternating current)! The way I visualize this electrical path is as a grooved path for say, an endless line of marbles, all touching each other. But the trick is that they can't leave the grooved path: if the grooved path (or wire) is cut, the marbles (or electrons) don't fall out, they just stop. If there is a complete loop for the marbles, once they are put into motion, all the marbles in the loop move at the same time and at the same speed. I picture marbles put into motion by the PV panel traveling to the battery and back again. So basically, I need two conductors from the panel to the battery, one to the loads and one from the loads. Positive and negative are terms used to differentiate them. The positive lead from the panel is connected to the positive post of the battery, and the negative lead to the negative post. (This wasn't obvious to me either until I thought about the panel's voltage overcoming the battery voltage.) In chemistry classes I learned that electrons flow from negative to positive; physics classes taught that current flows from positive to negative. It means the same thing; this is all just notation. At any rate, the convention is to label the positive wire with red electrical tape and the negative with black tape. (My ac extension cord has the conductors labeled white for neutral (common), black for line (hot), and green for ground. Go figure Ä maybe they'll get it together someday.) Right now I have a car battery that sits under a seat in the trailer. I measured the distance between the panel and the battery as about 25 feet; so I need 50 feet of wire total. I need to choose a wire size that will carry 3.5 Amps (the maximum that my panel produces) over this length with only 0.3 Volts loss. Math Continued... I know the voltage loss I will accept along my length of wire. If I can figure out how this translates to resistance, than I can look it up on the wire tables to choose the right size wire. It works like this: R = 1000E/ L(I). R is equal to the Resistance per 1000 feet of wire. E is the voltage loss acceptable. I equals the maximum current that will pass through the wire. And L is the total Length (round trip path) of the conductor. In my case, Resistance = the voltage drop that I will accept (2.5% or E = 0.3 Volts) times 1000, divided by the amount of current (I = 3.5 A) times the length of the round trip (L = 50 feet). R = 0.3 Volts (1000) / (50 feet) 3.5 Amps = 1.714 ê per 1000 feet. The most resistance I will accept is 1.714 per 1000 feet. I look at the wire table under the Ohms per 1000 feet column for a resistance less than this amount. Twelve gauge wire has a resistance of 1.59 ê per 1000 feet, so I can use #12 wire or larger (i.e., #10, #8...) from my panel to the battery. I may add another panel in future so I decided to use #10 gauge wire. I got to know this equation very well in the process of wiring my system! My next step is to wire the 12 Volt outlets so I can finally unplug from Home Power Office and Power, and turn on my lights and music on my own power! I haven't finished with these equations yet! Access Therese Peffer, c/o Home Power, POB 520, Ashland, OR 97520 ù 916-475-3179