Circuit Lab

Introduction
Circuit Lab is a laboratory 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. (It is generally ill advised to attempt this experiment. Not only will there be nothing to see, but short-circuiting a battery is potentially dangerous). 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.

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?

Just as where in mathematics subtracting a negative is equivalent to adding a negative, so also a flow of positive charges in one direction is the exact same current as a flow of negative charges in the opposite direction. As such in most applications, the choice of current direction is an arbitrary convention.

Conventional current flow, devised by Benjamin Franklin, views the current as a "flow" of positive charges. Therefore, this concept holds that current "flows" out of the positive end of the battery. Electron flow, on the other hand, deals with the ACTUAL route of the electrons (the primary carrier of electric charge in most circuits). Being negatively charged particles, electron currents moves out of the negative end of the battery.

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. The individual electrons generally move very slowly, but the electric current moves at the speed of light.

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)
To consider Amps pretend that you are the coach of a baseball team. You want to make your team the best that it can be. There are two ways you can do this, making your team score as much as possible and making the opposing team score as little as possible. Focusing on both would be impossible 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]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 its 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.

Voltage is technically electrical potential. While in many cases we treat it as an absolute, it is important to remember that in circuits we talk mostly about the difference in voltage, a potential difference, and that things like Ohm's laws only apply to potential differences not just electrical potential. However, in the context of circuits, Voltage is often used in reference to potential difference.

Resistance(Ω)
A resistor is just a piece of metal, and the piece in the center is what provides the resistance. A resistor limits the flow of electrical current. 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.

Other Analogy
The other way that these three are explained is using water as an example. Imagine the basic components of a circuit, a battery, wire, and say, a resistor. In the water analogy, this translates to a pump(because the battery pushes electrons around the circuit), some large pipe(wire), and a section of much smaller pipe(resistor). We know that in the water analogy, the flow rate of the pump is the same as the voltage of the battery, and the pressure in the tubing if the same as the current in the circuit. This is a pretty simple way to explain voltage/current/ and resistance. If we up the voltage, but keep the resistance(pipe size) the same, it logically takes more pressure, however if we keep the flow rate the same and put in large pipes, it takes a lot less pressure to so the same job. Conversely, if we drop the pressure, but keep the same pipe size, the flow rate goes down, and if we maintain constant pressure, but increase the pipe size, the flow rate goes up. And that's all there is to it. Thus we can see the relationships in Ohm's law. Here a fancy picture I didn't make myself.



Application of Ohm's law
This section doesn't teach any theory behind Ohm's law, but this is one of the easiest ways to apply the law(or the power law(P=IV), or any similar law). Basically, take a circle and divide into half, then divide one of the halfs in half again(so you have half a circle at the top, and two quarters at the bottom). Then you put the equation(any equation in the form a=bc), in the case of the power law, P would go into the half, and I and V would go into quarters. Now all you have to do to find a certain value is cover up what you're looking for(for example,finding I using P and V) and look at the 2 uncovered letters, in the example, P and V are uncovered, since P is on top of V, we know that I=P/V, if the letters are next to each other(i.e. finding P from I and V) then you simply multiply. Sure, the math behind it is very simple, but in a competition this method goes a lot quicker than rearranging equations.

This is the basic circle

Here's another very useful and much more detailed circle.

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



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:

By the way, the most common tolerance you will see is Gold, followed by Brown, but this doesn't rule out the other possibilities. 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 4 or more bands, all you do is read the first however many (normally 3) until you only have one color(not tolerance) left, and multiply by 10^last color band.

Resistor Networks
Networks of resistors between two points can be simplified into an equivalent single resistor, for which the resistance can be calculated according to the configuration and values of the resistors within the network.

Series Resistance
The resistance of a resistor is directly proportional to the length of the resistive material. As such, because placing resistors in series effectively adds the lengths, resistances add in series. Therefore, for a chain of resistors, the equivalent resistance is equal to the sum of individual resistors.

Parallel Resistance
In parallel, it is not the resistances that add, but the conductances. An analogy for this is to imagine a crowd of people trying to get through a door. A single door will allow so many people per minute, but if a second, adjacent, identical door is opened, the same number of people per minute will simultaneously move through that door. Therefore, twice the number of people will move through the doors per minute. Similarly, two identical resistors in parallel will conduct twice the current as a single one. Therefore the total conductance is equal to the sum of individual conductances in parallel. As conductance is the reciprocal of resistance, the usual formula is that 1/Rt=1/R1+1/R2+...+1/Rn for n resistors in parallel.

'Networks Containing Both Series and Parallel Many real circuits will contain a combination of both series and parallel components. To simplify these networks, one must find parts of the networks that are purely one or the other and simplify them according to the formulas above. One can repeat this process until the network is simplified into a single equivalent resistor.

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 schematic 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.



To understand this, think of a circuit with two resistors 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 in between 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 (remember 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 happens 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 derivation (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]V_G = ({R_x \over {R_3 + R_x}} - {R_2 \over {R_1 + R_2}})[/math]

Kirchhoff's Laws
Kirchhoff has two well-known laws of circuits: Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). They are simplifications of Maxwell's Laws of Electromagnetism that are valid for most practical circuits.

Kirchhoff's Current Law
A node is a junction in a circuit where two or more electrical components meet. Kirchhoff's Current Law states that sum of currents entering a node is equal to the sum of currents leaving the node. This is based on the assumption that charges cannot accumulate in a node of the circuit. Equivalently, if one designates the direction of the currents with a sign (eg all currents leaving the node are negative), the sum of currents at each node equals zero.

Node Method
The Node Method is a powerful tool of circuit analysis that is based upon Kirchhoff's Current Law. Basically, one writes the equation for every node in the circuit based upon unknown variables. Then from the resultant system of equations, one can calculate all the unknown variables and solve the circuit. It is often unnecessary for simple circuits, but becomes quite convenient for large circuits.

Detailed method: 1. Select a node to be your ground and assign it a voltage of zero. (N.B. The term "ground" in the context of circuit analysis does not necessarily mean that it is connected to the ground. Instead, it is a node designated at zero electrical potential from which all other voltages are measures.) 2. Assign every other node in the circuit a variable voltage. You may in certain cases be able to calculate a voltage for a few nodes (e.g. if the negative terminal of the battery is connected to the ground, the node connected to the positive terminal will have a known, positive voltage). 3. Write the KCL equation for every node in the equation. [Example soon]. 4. Solve the resulting system of equations for all the unknown variables. At this point, you know the voltage for every node in the circuit and should be able to easily calculate anything else.

Kirchhoff's Voltage Law
Kirchhoff's Voltage Law (KVL) states that for any closed loop in a circuit, the sum of voltages will be zero. One must be very careful with sign convention for this to work. For example, in a simple series circuit of resistors and voltage sources, one must choose either the voltage sources or the resistors to have negative voltages. This is based on the assumption that there is no changing magnetic field.

Mesh Method
The Mesh Method is another technique of circuit analysis based upon Kirchhoff's Voltage Law. Essentially, one designates a variable for a current circulating through every loop in the circuit, and then writes an equation for each of these in terms of KVL.

Equivalent circuits
Just as networks of individual resistors can be simplified into a single equivalent resistor, so also can more complicated networks. Any network containing resistors, current sources, and voltage sources can be transformed into a Thevenin or Norton equivalent. This is especially useful when analyzing circuits containing other components, as the entire rest of the circuit around the component may be a network which has an equivalent.

Thevenin equivalent
The Thevenin equivalent circuit between two points consists of a voltage source in series with a resistor. In order to find the Thevenin voltage, you must find the open-circuit voltage across the two points (ie when it is broken open). The resistance is found by removing all the power sources (replacing current sources with shorts and voltage sources with breaks) and finding the equivalent resistance of the resultant resistor network.

Norton equivalent
The network can also be represented by a Norton equivalent. It consists of a resistor in parallel with a current source. The Norton resistance is equal to the Thevenin resistance. The Norton equivalent current is equal to the current that passes between the two points if you short circuit them.

Capacitors
Capacitors are, in DC at least, a device that stores a charge. When capacitors are in a circuit, they are said to resist change in voltage(i.e. if the voltage in a circuit goes up, the capacitor charges, taking away the excess voltage. If the voltage drops, the capacitor discharges, adding back to the circuit to make up the difference. There are many types of capacitors(Mylar, polystyrene, electrolytic, etc), but they all do the same basic job. At the most basic level, a capacitor is comprised of two plates separated by a dielectric(insulting material) that stores a charge, there's a few basic concepts it may be helpful to know. First off, look at the charging circuit below, the capacitor is uncharged in the beginning, but when the switch is closed, it begins to charge, as it starts to charge, the resistance across it is small(thus a current flows through the circuit, charging the capacitor), however as the voltage of the capacitor reaches [math]V_0[/math], the current decays exponentially, because the voltage is smaller, less current flows(remember?). This can also be shown by trying to measure the resistance of a capacitor(see below, because the meter puts out a small current, that charges the capacitor). Its useful to in some cases calculate the voltage for a capacitor as it is charging or discharging, for which 2 formulas are incredibly helpful. For a charging capacitor in an RC circuit Vc = Vo(1-e^(-t/(RC))) and for a discharging one, Vc = Vo(e^(-t/(RC))).

Other Analogy

In the water analogy, a capacitor is simulated as a piece of rubber blocking the pipe. Using this example, we can see that a DC current would flow for a time, but when the rubber reached it's elastic limit, it would stop, the same as the capacitor charge curve discussed above. However, an AC current(imagine the water moving back and forth very fast) would simply move the rubber back and forth, never stopping the rubber on the other side from flowing(this is true for electricity, but in an effort to not drone on to long, it's not in there).

Inductors
An inductor is basically an electromagnet, however it exhibits special characteristics in a circuit. In the most simple terms, it's the opposite of a capacitor, however this is slightly misleading. An inductor has an ability to store a charge in a magnetic field(whereas a capacitor stores it in an electric field) and has the ability to maintain a constant current in a circuit(whereas a capacitor can maintain a constant voltage). This means that an inductor can easily conduct DC(whereas a capacitor can easily conduct AC), however if AC is put through an inductor, the magnetic field will grow and collapse with the rise and fall of current, which tends to oppose the flow of AC through an inductor.

Other Analogy In the water analogy, an inductor is a waterwheel, with a constant flow of water through it, the waterwheel spins, and all is fine, however with an alternating flow, the water wheel is continuously trying to turn back and forth, limiting the flow of water.

Diodes
Don't let anything in here scare you, you probably only really need to know that a diode conducts only in one way, but hey, it never hurts to know more, right? This is a topic that's not covered very deeply in the rules, so I will only go over the basics in here. A diode is a semiconductor made of a junction of P-type and N-type silicon(don't worry to much about the details), it's special in that it only conducts in one direction. There are a lot of different types of diodes(schottky, zener, light emmitting diodes) they all vary in a few charecteristics, mainly, their forward voltage drop(how much voltage is lost while conducting), and avalanche voltage(point at which they coduct in reverse), for example, schottky diodes are used in power supplies when you need to combine two power supplies of the same voltage(so one doesn't backfeed the other) because of their charecteristcally low forward voltage drop, whereas zener diodes are used in applications where one needs to detect when a voltage is above a certain point becuase of their low avalanche voltage(put on in backwards and you'll only get a voltage on the other side of it when it crosses a certain point), light emmitting diodes are used... well... you should be able to figure that one out. The arrow on the symbol of a diode points the direction of the conventional (positive) current through the diode.

Other Analogy In the water analogy, the diode is simply a check-valve(one way valve). That's it, nothing more to it.

Circuit Analysis with Ideal Diodes
Ideal diodes can generally be approximated by either a short or a break in the circuit. Generally to analyze a circuit with an ideal diode, one will make an educated guess on whether or not the diode will conduct. Once one finds a solution for this hypothesized circuit, one much check whether it makes sense. If you assumed the diode would conduct, you must make sure it is conducting current in the correct direction. If you assumed it does not conduct, you must check to make sure the voltage across the hypothetically non-conducting diode is such that it would not conduct. If this is not the case, you must switch your assumption and recalculate the circuit.

Base and Derived Units
SI base units are the base quantities that are independent. There is a total of seven units, but the ones important to this event are meters (m, length), kilograms (kg, mass), amperes (A, electric current), and seconds (s, time). Derived units are units that come from a combination of the base units. The ones important to this event are newtons, joules, watts, coulombs, volts, farads, siemens, and ohms. The table below shows how each of the units is related.

Another important derived quantity that does not have a special unit name is the electric field strength, measured in V/m. One coulomb is also equal to the charge of 6.24 x 1018 electrons.

Meters


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). Never put a meter set up to measure current in parallel with part of the circuit. You might blow a fuse in the meter or worse.

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. Generally, one must first disconnect a component from the circuit before measuring the resistance. Never put an external voltage across a meter in resistance mode, as this could damage the meter.

AC Power
For more info, see this page.

Up until now, the entire discussion(minus a mention when talking about capacitors) has dealt with DC, or direct current. In a DC circuit, current flows from the positive to the negative terminals of a battery or other source, that it(electrons flow the opposite, see above). However, the power in your house is AC, not DC(unless you live in a very strange house), AC, or alternating current, is a much more complicated beast. Basically, the direction of the current flow change, if you plotted voltage vs time, instead of a line, for DC, you would get a sine wave. This yields many advantages, namely, the use of transformers for voltage step-up/step-down.

Transformers

Transformers are basically 2 electromagnets that are put together, most of the time sharing a common core of iron. Transformers work because the AC generates a constantly changing magnetic field in the primary coil, which can induce a charge in the secondary coil. It isn't possible to build a DC transformer because the magnetic field would be constant, remember that stable magnetic fields(stationary) can't induce a charge.(a changing field acts the same as a moving one). The ratio of the turns of the primary winding to the turns of the secondary is equal to the ratio of the primary voltage to the secondary(i.e. 2 turns on the primary and 1 on the secondary will half the primary voltage)

Digital Logic
In digital logic in circuits, a current corresponds to a "true" or "1", and no or very little current corresponds to a "false" or "0". A logic gate will take 1 or more of these signals, perform a logical operation on it, and then either send a true or a false on its way.

A simple example of a logic gate is a transistor. If it receives very little current (false/0), then it does not allow current to pass through it (false/0). If it receives a current (true/1), then it allows current to pass through it (true/1).

Here is a list of logic gates: Truth Table: Boolean Algebra: [math]A \cdot B[/math] or [math]A[/math] & [math]B[/math].
 * AND AND must have two trues in order for current to pass through it.

Distinctive Shape:

Rectangular Shape:

Truth Table: Boolean Algebra: [math]A+B[/math].
 * OR OR will allow current to pass through it if any true is given to it.

Distinctive Shape:

Rectangular Shape:

Truth Table: Boolean Algebra: [math]\overline A[/math] or ~[math]A[/math].
 * NOT NOT turns trues into falses and falses into trues.  The NOT gate is commonly called an inverter.

Distinctive Shape:

Rectangular Shape:

Truth Table: Boolean Algebra: [math]\overline {A \cdot B}[/math] or [math]A | B[/math].
 * NAND NAND blocks current only when two trues are given to it.

Distinctive Shape:

Rectangular Shape:

Truth Table: Boolean Algebra: [math]\overline {A + B}[/math] or [math]A - B[/math].
 * NOR NOR only allows current to pass through it when it is given two falses.

Distinctive Shape:

Rectangular Shape:

Truth Table: Boolean Algebra: [math]A \oplus B[/math].
 * XOR XOR only allows current to pass through it when the two signals it is sent are not the same.

Distinctive Shape:

Rectangular Shape:

Truth Table: Boolean Algebra: [math]\overline {A \oplus B}[/math] or [math]A \odot B[/math].
 * XNOR XNOR only allows current to pass through it when the two signals it is sent are the same.

Distinctive Shape:

Rectangular Shape:

Information Source

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

[[Media:SCIENCE OLYMPIAD CIRCUTE LAB MARCH 7TH.pdf| Circuit Lab Notes]]