Circuit Lab

Introduction

Ciruit Lab is a labratory event which deals with the various components and properties of direct current (DC) circuits. Historically, the fields which have been tested in this event are DC circuit concepts and DC circuit analysis (both theory and practice).

What is a Circuit?

Let's take an example of a battery, for now. The battery has a positive (+) end, and a minus ( - ) end. When you touch a wire onto both ends of the battery at the same time, you have created a circuit. What just happened? Current flowed from one end of the battery to the other through your wire. Therefore, our definition of circuit can simply be a never-ending looped pathway for electrons (the battery counts as a pathway!).

The Requirement of a Closed Conducting Path

There are two requirements which must be met to establish an electric circuit. The first is clearly demonstrated by the above activity. There must be a closed conducting path which extends from the positive terminal to the negative terminal. It is not enough that there is a closed connecting loop; the loop itself must extend from the positive terminal to the negative terminal of the electrochemical cell. An electric circuit is like a water circuit at a water park. The flow of charge through the wires is similar to the flow of water through the pipes and along the slides of the water park. If a pipe gets plugged or broken such that water cannot make a complete path through the circuit, then the flow of water will soon cease. In an electric circuit, all connections must be made and made by conducting materials capable of carrying charge. Metallic materials are conductors and can be inserted into the circuit to successfully light the bulb. There must be a closed conducting loop from the positive to the negative terminal in order to establish a circuit and to have a current.

Basic Electrical DC Circuit Theory

Current Flow and Direction

"Conventional Current Flow" vs. "Electron Flow" - This has to do with how circuit diagrams are interpreted. Now, remember we said that electrons are 'flowing' in the wires? The question here deals with : Do they 'flow' from the positive end of the battery, or the negative end of the battery?

Conventional current flow, devised by Benjamin Franklin, has the moving particles (later called electrons) positively charged. Therefore, this concept holds that electrons flowed out of the positive end of the battery. Electron flow, on the other hand, deals with the ACTUAL route of the electrons - being negatively charged particles, they go through the negative end of the battery! They then flow around the whole circuit, la la la, and arrive back at the positive end. Capeesh?

Current

What is an "electron?" To put it simply, an electron is an atomic particle which carries a negative charge. These electrons spin around the nucleus of an atom, which has a positive charge, and is located in the very center of the atom. The concept of "electricity" has to do with these electrons and with their "electron flow." Do you remember the example of our battery? This battery takes these negatively charged electrons from a chemical reaction inside the battery, pushes them out of the negative end of the battery, and into the wire. These electrons will then bump electrons in the atoms of the wire over and over until finally electrons arrive back at the positive end of the battery. Elements which allow this process of "bumping" those electrons on over determines how conductive the element is. So, when there's a current, it's just electrons bumping each other from atom to atom and flowing on.

A circuit requires a loop for the electrons to travel on (think of "circle"). This means you can not simply attach a wire to one end of a battery and expect electrons to flow through it. As stated before, in our definition of the circuit, a continuous loop is required. But think about it scientifically: If you did attach the wire to only one end of the battery, where would the electrons go that got bumped to the opposite end of the wire? That is why there needs to be that continuous loop of wire: the electrons need somewhere to go.

Voltage, Resistance, and Amperes

For more in-depth information, see Episode 1

Amperes(Symbol I or rarely A)

So naturally, you're going to have to choose one area to focus on: say you want to score more runs; let's relate this to the concept of "amperes." The amount of runs you make is your score - the more you get the better your chance of winning. Similarly, amperes measure the amount of current you have flowing per second through an area: is it a lot, or a little bit? Now, if you want to win the game, you don't necessarily have to score a whole lot of runs, you just need to score more than your opponent. So, maybe your resistance to their scoring of runs will be high - and resistance to current flowing is also one of our important terms we need to know. Now, how do these concepts of amperes and resistance relate, straying from the daemons for now? If you multiply the resistance by the amperes, you have the voltage of a circuit (remember, we're always talking about in circuits here, not on a baseball field). This relationship was discovered by Georg Simon Ohm, and it says, simply, that:

[math]\displaystyle{ V = I \times R }[/math]

Or

Voltage = Current times Resistance

• Sometimes E is used in place of V, for electromotive force(EMF), it's the same thing, don't worry.

Voltage(V or sometimes E)

Imagine a battery as a super-soaker, and the water that comes out of it as voltage. The harder you pump that super-soaker, the harder that stream is going to be when it comes out of the gun. Voltage is the potential for that water to go very quickly out of the gun: the more you pumped, putting more "voltage" in, the faster that water will go: but sometimes you will have a "multi-functioning" nozzle which even allows you to adjust that water speed even further. You want the water to go out in a "wider" and "bigger" stream, you might change the nozzle to a bigger opening. What you've just done is changed the amount of space that the water is allowed to go through: the water is now given a much bigger space to flow through. The "voltage," or potential, of the water to go fast and give bruises is still high, but now you've taken away from it's hitting-power by spreading it out. Anyone know where I'm going next with this? The bigger your nozzle gets (think of it like the resistance), the smaller the hitting power (current (which is a speed in electricity too!)) is going to be.

Resistance(Ω)

A resistor is just a piece of metal, and the piece in the center there is what provides the resistance.

And as for what resistance is itself - it is the force against the flow of the electrons. They transform the electrical energy they absorb into heat energy.

Imagine our electrons - flowing along the wire, pushing new electrons to flow on, and so on. This wire is not very hard to flow in - it's made of a material that's very conductive. But what would happen if we placed something in the middle of the wire that was harder for the electrons to flow through? They're going to be bumping into all the atoms in the material, which will cause the atoms to vibrate. This, in turn, will cause nearby air molecules to take some energy. That energy is in the form of heat. Where did it come from again? From the electrons bumping into atoms inside the resistor.

Resistors

Of course, you didn't think that was all there was to resistors, right? Of course not.

This is a basic ¼ watt resistor, the actual resistor is the part in between the two silver leads

So what can you do with that... Lots, actually. The color bands around the resistor tell you what the resistance is, and what the tolerance is(how accurate it is). The color codes are:

Resistor Color Codes

Color	Value
Black	0
Brown	1
Red	2
Orange	3
Yellow	4
Green	5
Blue	6
Purple(Indigo)	7
Gray	8
White	9
Gold	.1
Silver	.01

Example Table

Color	Percent
Silver	10%
Gold	5%
Red	2%
Brown	1%

By the way, the most common tolerance you will see is Gold, followed by Brown, but this doesn't rule out the possibility. To convert the color codes into resistance values(on a resistor with 3 bands and a tolerance band) read the first two bands off in order(in the picture it would be green, then blue, thus 56) and then multiply that by 10^(color of third band), so the picture would be 56x10^0 which is 56 ohms. If the resistor has more than 4 bands, all you do is read the first howevermany(normally 3) until you only have one color(not tolerance) left, and multiply by 10^last color band.

Series and Parallel - *note: add basics above* Finding resistance in series and parallel is pretty simple. If the resistors are in series, you can simply sum them up, and you're done. If they're in parallel, sum up the reciprocals of resistance(conductance, which, by the way, is measured in siemens) and take the reciprocal of the sum.

For resistors in series
[math]\displaystyle{ R_t = R_1 + R_2 + ... + R_n }[/math]
\over In parallel
[math]\displaystyle{ {1 \over R_t} = {1 \over R_1} + {1 \over R_2} + ... + {1 \over R_n} }[/math]

Wheatstone Bridge

A wheatstone bridge is used to measure an unknown resistance value to a high degree of accuracy. It uses 4 resistors set up in a diamond fashion(shown below) and a voltmeter. In the schmatic below, Rx is the unkown resistance, R1 and R3 are fixed resistance values(generally the same, but they don't have to be the same, also generally >1% tolerance, but again, not always) and R2 is a variable resistor(potentiometer, this is not always the case, see below). By adjusting R2 until the voltmeter reads 0 volts, you know that the ratio between the R1/R2 and R3/Rx is equal.

Wheatstone Bridge Schematic(Courtesy Wikipedia)

To understand this, think of a circuit with two resistorsr of equal value in series, connected to a +5v source, becuase the resistances are equal, the voltage droop is equal, this kind of circuit is called a voltage divider, becuase the voltage inbetween the two resistors is 1/2 the input voltage. Again, imagine a circuit with 2 resistors in series connected to a +5v source, however this time, the resistors are 50 ohms and 25 ohms, becuase the total resistence(rememer series resistance?) is 75 ohms, at 5v, we can calculate the current, and from there calculate the voltage drop from each resistor, you should have gotten 3.33 volts across the first, and 1.66 for the second one(I tried to pick better numbers, honest!)well the voltage happen to be in the same ratio as the resistance values, now that we've proved that, we can apply it to the wheatstone bridge.

With that in mind, we now know that the ratio of the resistors is what controls the voltage at the midpoint, so if two sets of resistors have the same ratio, then they would have the same voltage, see where I'm going? When the voltage across the bridge is 0, the sets of resistors(R1/R2 and R3/Rx) have the same voltage, and thus the same ratio of resistance values! Since we know the ratio of the first leg(R1/R2, remember we set R2 to a known value to balance the bridge...) and we know R3, it's fairly simple to solve for Rx.

Now here's the fun part... What if you don't want to have to change R2? Well then, you can, using the same principle, take the voltage across the bridge, and calculate Rx from that... I'll leave out the derrivation(Hey, it'd make good practice!), but basically, by applying all the concepts discussed here(Kirchhoff's laws, Ohm's law, etc) you end up at the equation
[math]\displaystyle{ V_G = ({R_x \over {R_3 + R_x}} - {R_2 \over {R_1 + R_2}}) }[/math]

Other Topics

Meters

File:Meter.JPG

This is a fairly complex Fluke 287 multimeter, note the separate jacks for measuring current.

During the event, the test may require you to measure certain values in a circuit, for this you can use either a multimeter or probes(whatever the ES gives you), but you have to know how to hook it up, or you could get yourself dq'd(I've seen this happen). Basically, there are three things that you could be asked to measure, voltage, current, or resistance.

Voltage is fairly straightforward, you put the said device in voltage mode(make sure the probes are hooked up in the right place!) and put them across whatever you want to measure and it reads off a voltage(the difference in potential between the probes, the meter has a high enough resistance(called impedance) that it won't cause any significant amount of current to flow(most meters are around 11 million ohms!)).

Current is another one you might be asked to measure, think of current as the flow-rate in the water analogy, to measure the flow, you have to 'get into' the circuit, this is why meters have a separate jack for current, there's a fuse in between the current jack and the common, and a low value(<5 ohms), by connecting the leads to the circuit, you allow current to flow with minimal resistance. The resistor in the circuit is called a shunt(that's just a big term for a resistor used to measure current) and by measuring the voltage across it, you can calculate the current(because the resistor has a constant value)

Resistance is a little trickier, it can help to understand how the meter's going to measure it, basically, it puts out a small voltage(~2-3v) and measures the current that flows in the circuit, and calculates the resistance. This means that you can't measure resistance with power on the circuit, and you have to account for all the possible paths, not just the most direct route.

Resources

The rest of the "episodes" on ciruitry, as well as circuit worksheets, can be found here. The rules for a trial event form on Ciruit Lab can be found here