Kirchhoff came up with two laws. They pretty much say the same thing: Everything going out is matched by everything coming in. No exceptions.
Electricity is all about the movement of electrons. Electrons are part of atoms. Electrons move around the nucleus of the atom.
The simplistic model of the atom shows electrons moving around the nucleus like satellites move around a planet. That’s not entirely accurate. More sophisticated models show the electron inhabiting a sphere around the nucleus. They can suddenly show up at any point within this sphere from any other point within the sphere. This is not entirely accurate, but it is close enough for our purposes.
A chemist/physicist would say that that the electron inhabits an orbital around the nucleus, and that an orbital is not an orbit. That’s really important to them and it is accurate. See http://www.chemguide.co.uk/atoms/properties/orbitsorbitals.html if this interests you.
We’re going to think of electrons as living in a sphere around the nucleus, and generally hanging out on the outside edge of the sphere. If you like, you can think of the sphere defined by a satellite in a polar orbit around the Earth as being similar to this sphere.
Atoms have concentric spheres called energy levels. Electrons live in an energy level. Sometimes they move between energy levels, but mostly they don’t. Electrons in the outermost energy level, are somewhat loosely attached to their nucleus.
When you see a diagram of an atom, they usually show it like a little solar system. That’s OK, except you should remember that they’ve taken a 2-dimensional slice of something that’s 3D, and that instead of moving around in circles, electrons move around in spheres, and that they can suddenly move from one point in the sphere to another point, without any warning. Again, not entirely accurate from a physics standpoint, but close enough for our purposes.
If you look at a (diagram of a copper atom](http://en.wikipedia.org/wiki/Copper), you’ll see that it has 4 energy levels. The outermost energy level has a single electron in it. It turns out that this electron is pretty loosely attached to its copper atom. A copper atom is “willing” to give up this electron.
If you put a bunch of copper atoms in a line (as in a copper wire), and you push an extra electron onto the atom at one end of the wire, the original single electron will “feel crowded” and tend to move over to the next atom. (Or maybe it will be the new electron that will move over to the next electron. Electrons are somewhat flighty things.) The second atom will now have an excess of electrons, so one of them will “feel crowded” into moving to an adjacent atom.
If you keep pushing electrons into one end of a copper wire, electrons will keep coming out of the other end of the wire (if you let them). This is called “conducting” electricity. Copper is a conductor.
The periodic table groups atoms by the number of electrons they normally have. (Again, not entirely accurate from a physics standpoint, but close enough for our purposes.) You’ll notice that copper, silver, and gold all have a single electron in the outermost energy level. They’re all good conductors of electricity. They’re all “willing” to let their electrons get pushed from one end of a wire to another.
Atoms in other columns of the periodic table have different numbers of electrons in their outermost shell, and different numbers of shells. Some of them are very, very “unwilling” to let their electrons get pushed around. Materials that don’t conduct are called “insulators.”
I like to think of wires as being like a garden hose filled with marbles. The marbles are the electrons. If you push a marble into one end, another marble pops out of the other end. Again, not entirely accurate from a physics standpoint, but close enough for our purposes.
If you put a measuring device at one end of the hose, capping the end of the hose, and you push a marble into the other end, the scale at the closed end would measure how hard (with how much pressure) you’re pushing the new marble into the other end. We call this pressure “voltage” when the marble is an electron in a wire. Notice that we could push gently or push really hard, without the marbles actually going anywhere. The measuring device just measures how hard we’re pushing.
Suppose we take the measuring device away, and you stand at that end of the hose and count the marbles as they come out. If I put marbles into the other end slowly, they come out your end slowly. If I put marbles in fast, they come out fast. We call this speed “current” when the marble is an electron in a wire. Notice that we don’t care about how hard I pushed the marble into the hose – just the speed at which I push them in. Speed is different than pressure. Current is different than voltage.
We saw that an electron has \( 1.602 x 10^{-19} \) C (coulomb) of charge. We also saw that the speed at which electrons move is called current.
If you move a coulomb’s worth of electrons through a wire in one second, that current is called one ampere (or one amp, for short). Amperes are named after Mr. Ampere. They are abbreviated as A.
Recall from physics that work is force times distance moved. Push on something with a force of a pound and move it a foot, and you’ve accomplished one foot-pound of work. Work is seldom measured in foot-pounds by physicists. They like to use a unit known as the joule.
One joule = the energy expended (or work done) in applying a force of one newton through a distance of one meter (1 newton meter or N·m). This is the same amount of energy as passing an electric current of one ampere through a resistance of one ohm for one second. (It didn’t get that way by magic or by a property of reality – that’s how they defined amperes and resistance.) Joules are abbreviated J.
Measures of energy include:
We saw that the pressure of electrons is called voltage. Volts are joules divided by coulombs. i.e.
1V = \( \frac{1J}{1C} \)
Power is measured in Watts and are abbreviated as W. Watts can be calculated as (either):
Note: When generating, power is negative watts (i.e. Volts * Amps * -1) and conventional current arrow is drawn from negative to positive. When consuming, power is positive watts (i.e. Volts * Amps).
Positive means more of something and negative means less, right? So electricity must flow from plus to minus, right? Wrong!
Electricity is the flow of electrons. The negative end (terminal) of a battery supplies electrons. If you connect a wire between the negative and the positive ends of a battery, electrons will flow through the wire from the negative end to the positive end.
OK. Got it. Current flows from negative to positive, right? Well… not really. Although it is the electrons which actually move, we pretend like positive charge flows in the opposite direction. The protons don’t actually move, but in a relative sense there’s an excess of positive at the positive terminal and an excess of negative at the negative terminal. By convention, current is the flow of this mythical positiveness rather than the actual flow of electrons.
Why? Awhile back, before anyone actually knew about electrons, somebody observed that something had to be moving when electricity moved. He couldn’t observe what was actually moving. He had to guess which direction the something was moving. He guessed wrong and guessed that it was from positive to negative. But he guessed first, he established the convention, and we’re stuck with it (sorta like the layout of the computer keyboard).
If you see an arrow on a circuit diagram, indicating the flow of current, it indicates the flow of conventional current, and not the actual flow of electrons.
The arrows in semiconductor schematics show conventional flow and not electron flow. e.g. The arrow on a diode points from positive to negative, and it conducts when wired this way, but not the other.
The term ‘current’ (without a qualifier) typically refers to conventional current, and not electron flow. So the phrase, “Current flowing from A to B,” usually means, “electrons flowing from B to A.”
Formulae, constants, laws, etc.
| \[ \left | F \right | = k_{e}\frac{q_{1}q_{2}}{r^{2}} \] |
From plus, through to minus is forward (consuming power).
From minus, through to plus is backward (generating power).
For voltages, + connected to + is forward.
Resistors in parallel: \( \left ( \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} \right )^{-1} \) or use \( \frac{R_1 R_2}{R_1 + R_2} \)
Voltage divider (using resistors in series): \( v_1=\frac{R_1}{R_1+R_2}v \)
Current divider (using resistors in parallel): \( i_1=\frac{R_2}{R_1+R_2}i \)
Atoms have electrons, protons, and neutrons.
Electrons and protons have a property called “charge.” To quote Wikipedia’s entry on electric charge: Electric charge is the physical property of matter that causes it to experience a force when close to other electrically charged matter. There are two types of electric charges, called positive and negative. Positively charged substances are repelled from other positively charged substances, but attracted to negatively charged substances; negatively charged substances are repelled from negative and attracted to positive.
Electrons have negative charge. Protons have positive charge. Neutrons have no charge. This is one of the fundamental properties of matter. A physicist studying string theory and the nature of matter might take it to deeper levels, but for our purposes, electrons have a negative charge because that’s just how they are, and protons have a positive charge because that’s just how they are.
The amount of negative charge in an electron is equal and opposite the amount of positive charge in a proton. The amount of charge in a single electron or proton is called “the elementary charge” and is usually written as e.
The elementary charge (the amount of charge on a single electron/proton) is very, very small. If you put \( 6.241509745 * 10^{18} \) electrons or protons in a pile, we call that amount of charge a coulomb. (Coulombs are named after Mr. Coulomb.) The other way of looking at it says that an electron/proton has \( 1.602 x 10^{-19} \) coulomb of charge. Coulombs show up in formulae as C.
Protons attract electrons (and vice versa). If you put a pile of protons and a pile of electrons near one another, they’d try to get together, in much the same way that the south pole of a magnet pulls on the north pole of another magnet.
Coulomb’s Law tells us just how hard they’ll try to get together (the attraction of the Electromagnetic Force):
| \[ \left | F \right | = k_{e}\frac{q_{1}q_{2}}{r^{2}} \] |
where
\( k_{e}=8.988 \ast 10^{9} \frac{Nm^2}{C^2} \)
You may recall from physics that a newton is the amount of force needed to accelerate 1 kilogram of mass at the rate of 1 meter per second squared. In other words, if you push on something that weighs a kilogram with a force of one newton for one second, at the end of that second the mass will be moving at a speed of 1 meter per second. Newtons are abbreviated N.
Here’s an example:
20 cm = 0.2 m
| \( \left | F \right | = k_{e}\frac{q_{1}q_{2}}{r^{2}} \) becomes \( \left | F \right | = k_{e}\frac{10^{-6}*10^{-6}}{0.2^{2}} \) |
| and that becomes \( \left | F \right | = k_{e}\frac{10^{-12}}{4*10^{-2}} \) which is 0.2247 newtons |
Here’s another example:
20 cm = 0.2 m
| \( \left | F \right | = k_{e}\frac{q_{1}q_{2}}{r^{2}} \) becomes \( \left | F \right | = k_{e}\frac{3 * 10^{-6} * 5 * 10^{-6}}{0.2^{2}} \) |
| \( =\left | F \right | = k_{e}\frac{15 * 10^{-12}}{4 * 10^{-2}} \) |
\( =3.3705 N \)
Easy enough, but mostly useful for trivia contests.
I want to try PSK31 with my KX3. It looks like a panadapter (waterfall display) will be really handy for that. Here’s my story of how I got the panadpter going.
I decided on NaP3 because it seems to be relatively popular, it focuses on display (as opposed to rig control or contest logging), and it is available for multiple operating systems, in case I change my mind about which PC I’m going to use to run it. Other people seem to setup NaP3 on top of a layer of com-port virtualization software, in order to permit multiple programs to talk to their KX3 at the same time. I might do that later, but I’m going to start without it, on the basis that debugging one package at a time is complicated enough!
I’ve got an unused PC with no OS. First, pick an OS. I could run OS X, Linux, or Windows. I’m comfortable with any of them. I chose Windows 7 as the most “mainstream,” to give me access to the same software that the average ham is using.
* Menu: RX I/Q = On
* Note: Your radio will consume batteries a little faster when this is enabled, so you might want to disable it before you go portable (if you're not using your panadapter when portable). ## Configuring Sound
* Windows used to have a nice little sound recorder which would show you the input level as you recorded. Win7 has a simplified recorder which shows you nothing. Download and install http://audacity.sourceforge.net. It shows you the input audio levels. This can be handy for debugging things, if they don't work.
* Start / Control Panel / Sound / Recording / Line-in / Properties / Advanced
* Set the sampling rate to 2 channel, 24-bit, 48kHz. Later, you might want to try higher. At first, you want to use this rate because you can count on it actually being supported by your card.
* Turn on the radio, tune it to 15.0, and turn down the volume.
* Start NaP3
* Configure / Audio. Set sample rate to 48 kHz. OK.
* Configure / Rig. KX3, COM3, 38400. OK.
* Choose the "Run" menu. You should see a waterfall. You should hear WWV on your computer speakers.
See my trip planning guide at: SOTA Guide: W4G/NG-041, Gooch Mountain
Commentary:
I hit the trail at 8:30. It was the darkest 8:30 I can recall. Heavy overcast, mild fog, and heavily wooded.
Surprise - The trail has been rerouted and no longer goes near the summit. This is common with the Appalachian Trail. Things got busy at work and I didn’t take the time to cross-check the topo with other sources for accuracy. I was looking at a bushwhack up the side of the mountain. I don’t mind a bushwhack in fall/winter/early spring, but lush vegetation makes for a miserable climb. Navigating to the peak is easy (just go up), but without a shadow I sometimes wander off route when returning to the trail. I decided to come back and get it on a clear winter day.
See my trip planning guide at: SOTA Guide: W4G/NG-041, Gooch Mountain
Commentary:
This was my second attempt to activate Gooch. Last time, in July, I learned that I’d have a non-trivial bushwhack, regardless of my approach. Bushwhacking is much easier when cold weather has killed off the vegetation so I came back to try again in November.
Instead of trying to get close on the Appalachian Trail, I parked by the side of the road, bushwhacked up the side of the ridge which runs south from the summit, and followed the ridge line to the summit. The climb was short and steep. I was able to move pretty quickly along the ridge line, so I arrived early.
This was my second expedition with my new 36’ carbon mast. Instead of lying it flat, attaching my antenna wire, and raising it to vertical, I went straight up with it. I attached the wire as I extended it up (using zip ties), leaning it on my shoulder. Once it was fully extended, I leaned it against a tree, and then I guyed it out, to prevent a stray breeze from toppling it. It went up in about 5 minutes, so now I was running way ahead of schedule.
I’ve found a sweet spot with my equipment. I’m very happy with:
I can switch from 20m to 40m in about 2 minutes. Most of that time is spent in untangling from my earphones and standing up! The only thing I plan to add is an iambic paddle, once my CW is ready for prime time.
I was nervous about propagation. Before leaving home in the morning, the forecast was for poor propagation on 40 and fair on 20, with high noise and geomagnetic activity. G4ILO’s widget was predicting blackouts. When I activated, it might have been a little noisy, but it wasn’t bad. I made fewer QSOs than recent weekends, but since I called CQ at about 9:40 Eastern, that’s early for chasers to the west.
This hill will combine nicely with Sassafras Mountain (NG-040). I drove to that trailhead after activating Gooch, and it is only about 15 minutes away. I’d activated it earlier this year, so no double-header today. Some Forest Service roads in Georgia get gated from January to mid-March, but I saw no gates, so I’ll try and come back for the double-header in January/February.
See my trip planning guide at: SOTA Guide: W4G/NG-040, Sassafras Mountain
Commentary:
After hiking up, I found a flat spot off the trail and, with the weather dark and ominous, I set up my ‘easy’ antenna quickly. (There was about a minute of light rain, and I almost packed up.) There was lots of thunderstorm QRN, but 14 chasers were patient enough to work through the noise despite my sub-optimal antenna.
As I was packing up, I heard crashing in the bushes. I once spent an unpleasant night getting harassed by 3 bears while solo backpacking in the Smokies, so any time I hear unexplained crashing in the bushes my pulse quickens. I called a loud hello several times with no answer, so I was getting pretty antsy. It turned out to be a troop of Army Rangers in camo and green face paint. (When I got home I told my kid it was like being invaded by green plastic army men.) In setting up off the trail, I had intended to avoid traffic through my site, but since they were on a training mission, they were going summit-to-summit, disdaining the trail.
Ironically, the trainer and another leader had scouted ahead of the rest of the troops, because they were concerned that I might be a bear. Reassured that I posed no threat to the troops, they called, “Rangers, move out!” and the troops were off.
See my trip planning guide at: SOTA Guide: W4G/NG-023, Big Cedar Mountain
Commentary:
Woody Gap is on GA-60, and easy to find. Lots of parking, but lots of hikers/bikers/picnickers on weekends.
If you go there, watch out! There’s lots of poison ivy on that summit. I went off trail, to activate from the true high point. There was lots of thunderstorm QRN, but a good number of chasers persisted through the noise and my weak signal.
Given the poison ivy and the fact that the high point of the trail is within the activation zone, I’ll operate from the side of the trail when I go back. I was observed by a doe for part of my activation, so that was unusual.