Experiment B AP: DC Circuit Introduction
First, find your name in the data table below. The experiment doesn’t begin until page 3. The table below assigns you a power supply voltage and what is called a resistance value (in ohms) for 4 resistors to use in the computer simulation for Experiment 5. It looks like you are being assigned 5 resistance values, but when you read the directions, you will see why it is only 4.
Name / Power Supply Voltage / R0 / R1, R3, and R4 / R2(V) / (Ohms) / (Ohms) / (Ohms)
Bottlik-Pierry / 70 / 25 / 25 / 12.5
Burda / 60 / 25 / 25 / 12.5
Chon / 50 / 25 / 25 / 12.5
Davis / 70 / 50 / 50 / 25
Doub / 50 / 2.5 / 2.5 / 1.25
Frazier / 60 / 2.5 / 2.5 / 1.25
Fukuyama / 70 / 2.5 / 2.5 / 1.25
Glaser / 50 / 7.5 / 7.5 / 3.75
Irish / 40 / 25 / 25 / 12.5
Isozaki / 60 / 7.5 / 7.5 / 3.75
Kao / 70 / 10 / 10 / 5
Kim / 80 / 8 / 8 / 4
Lauro / 70 / 5 / 5 / 2.5
Lucas / 80 / 4 / 4 / 2
Millman / 80 / 40 / 40 / 20
Munoz / 60 / 6 / 6 / 3
Patel / 50 / 5 / 5 / 2.5
Shiao / 80 / 2 / 2 / 1
Sun / 70 / 5 / 5 / 2.5
Tahbaz / 50 / 25 / 25 / 12.5
Tsai / 60 / 5 / 5 / 2.5
Usui / 80 / 5 / 5 / 2.5
Wang, A / 80 / 25 / 25 / 12.5
Wang, W / 80 / 20 / 20 / 10
Wyrwitzke / 100 / 25 / 25 / 12.5
Zhang / 100 / 20 / 20 / 10
Note: Perhaps I introduced the idea of ΔV = RI in class to you. (Some of you tend to be absent so it’s hard to keep track.) R would be resistance in ohms, and I would be current in Amperes. You’ll need those facts.
Introductory DC Circuit Measuring
Open the following PhET simulator on the Interwebs:
http://phet.colorado.edu/en/simulation/circuit-construction-kit-ac
Either by making it yourself on the program or by selecting Load and using the Circuit Diagram File that you downloaded from Edline, construct the circuit in the picture below on the Circuit Construction Kit.
When you are ready to go, this is what your screen needs to look like:
If “Load” didn’t work and you made it yourself, you will probably want to click it on “Schematic” instead of “Lifelike” so it looks like the diagram. Also, if you made it yourself, click on “Show” near the bottom, and choose to hide the electrons. You are not ready to go unless you have the measuring tools ready: Under “tools” you must check all the boxes except for stopwatch. You’ll mostly use the voltmeter and the non-contact ammeter. The non-contact ammeter is the one that says “Move over a wire to read current” on it. Your screen must have the voltmeter and the non-contact ammeter near the circuit just like the diagram above shows.
If you are having any trouble making the circuit, the Appendix at the end of this assignment packet could clear some things up.
You have been assigned a resistance value R0 in ohms. Three of your resistors will be given the value R0, and one will be given the value ½ R0. To find out which, keep reading. The four resistors will each be given a subscript, and please look at the diagram below to see how these subscripts are assigned. Give R1, R3, and R4 the assigned ohm value constant (R0) that is attached to your name, and give R2 an ohm value that is one-half of that constant ( ½ R0). For example, if Tony Cho’s assigned R0 is 10 ohms, then the resistances he programs on the screen will be 10 ohms for three resistors and 5 ohms for the fourth. Right click on each of your resistors and give it the assigned ohm value. Similarly, right click on the battery and give it the assigned voltage value that is also attached to your name. For people whose voltage is greater than 100 Volts, just click the box that says “More Volts” after you right-click. We shall now define 6 locations in the circuit as points A, B, C, D, E, and F as you see in the diagram below. Also, “PS” will refer to power supply.
C D
R0 R1 R2 ½ R0
B R3 E
R4
A F
Here is how we must visualize the direction of current flow. The long side of the PS is positive. This means that positive current (which we call conventional current) will be pushed by electric repulsion to the left in the wire toward A. This means that the current flow in the circuit shown above will generally be clockwise. This means it will be up from B to C and to the right from B to E and to the right from C to D and down from D to E, and finally, the branch from E through R4 back to the negative of the PS will be consistent with this clockwise idea. Some people put directional arrows on the branches.
Before you begin, take a guess about how the current that leads from point B to R1 will compare to the current that leads from point C to R2, and how these will compare to the current that leads from R2 to point E. Write down your guess.
Data:
If your simulation circuit has the right shape…and the right R values…and the right PS voltage…and you know where A, B, C, D, E, and F are… and you have the meters ready…and you can visualize current flow correctly, record the following, realizing that you are not supposed to know a lot and the fake experiment walks you through things in a step-by-step way. It will probably take you an hour, but all results are checkable:
Use the non-contact Ammeter for the following Currents:
Between PS and A: ______(units please)
Between A and B: ______
Between B and R1: ______
Between R1 and C: ______
Between C and D: ______
Between D and R2: ______
Between R2 and E: ______
Between E and R4: ______
Between R4 and PS: ______
Between B and R3: ______
Between R3 and E: ______
Points B and E are called Junctions, but points A, C, D, and F are not junctions. USE YOUR DATA, and be as specific as possible to come up with a mathematical law for the current values that enter and leave a junction point such as B (or E). Write in the space I gave you below. If you can’t find this law from your data, ask about it first thing in class. The law you write below uses phrases such as “the sum of currents coming into a junction” and “the sum of currents exiting a junction. This is law is called Kirchoff’s 1st Law, and will be applied from now on.
Note: If you choose “Show Electrons”, it might help you to understand the physical meaning of Kirchoff’s Current Flow rule above, but you must realize that the direction of the electron flow is opposite to the direction that we record as the current direction. This is because electrons are negative and when we say the word “current”, we pretend that it is positive charge that is moving. Mathematically, nothing is in error.
Law:
Data Set II:
Use the voltmeter for the following voltages:
DV across R1: ______
DV across R2: ______
DV across R3: ______
DV across R4: ______
DV across PS: ______
DV with the red on point B and the black on point E: ______
Simple patterns/calculations using the data above:
- Sum of DV across R1 plus DV across R2 = ______
- The Loop Rule (which you already know) is called Kirchoff’s 2nd Law. Consider the loop that is defined by the following circuit path (a circuit path means that you start and finish at the same point; the word “circuit” is not at all defined by electricity. Bicycle races can be circuits.) The circuit path in question is defined by A→B→E→F→A. Run your finger around this path. For this path AND ONLY THIS PATH, show that your voltage numbers above satisfy the loop rule. (You will not pick out all the measured voltages to prove this. Your job here is to identify which of the six are relevant.) Show numerically with units below.
- Consider the loop that is defined by circuit path A→C→D→F→A. Run your finger around this path. For this path AND ONLY THIS PATH, show below that your voltage numbers above satisfy the loop rule. (You will not pick out all the measured voltages to prove this. Your job here is to identify which of the six are relevant.)
- Calculate the following products:
A. (Sum of Resistances R1 and R2)(Current through these resistors)
= ( ohms)( A) = _____ ohm×A = _____ Volts
B. (Resistance R3)(Current through R3)
= ( ohms)( A) = _____ ohm×A = _____ Volts
Realizing that the simulation cuts off some of the significant digits, check the overall consistency of what you are getting for the last four exercises. Only power calculations remain! These will give another chance to check for consistency.
Power
Imagine the power supply. Suppose it provides something called “20 Volts”. This really means that it would do 20 Joules of work to separate 1 Coulomb of + and – charge from each other. But you can’t say the PS does 20 Joules of work, because it is not always pumping exactly 1 Coulomb of charge around the circuit. So imagine that it is pumping 2 Coulombs around the circuit in 1 second. This means that the power supply is doing 40 Joules (20 J/C times 2 C) in one second. This means that it is doing work at the rate of 40 Joules per second. This quantity is defined as 40 Watts, where 1 W = 1 J/s. So if it pumped 3 C/s (a current of 3 A), the power would be (20 J/C)(3C/s) and the Coulombs cancel, leaving us with 60 J/s = 60 W. Therefore, another way of saying this is that the power is current through a certain region times the voltage across that region. And it is usually written as P = VI. So…
- Calculate the total power given by your power supply:
PPS = (Voltage across PS)(current running through PS from F to A)
= get these numbers from the data
= ( V)( A) = ______W
Before #2, realize that the power number calculated at any resistance represents the rate at which heat is being dissipated by that resistor. So while PPS was seen as an energy given INTO the circuit, the power at the resistors will be seen as energy leaving the circuit as heat. Those resistors can burn your fingers sometimes.
- Calculate the power associated with each of your resistors individually.
PR1 = (Voltage across R1 only)(current running through R1 only)
= ( V)( A) = ______W
Finish the rest of the powers, and check it for consistency.
PR2 = (Voltage across R2 only)(current running through R2 only)
= ( V)( A) = ______W
PR3 = (Voltage across R3 only)(current running through R3 only)
= ( V)( A) = ______W
PR4 = (Voltage across R4 only)(current running through R4 only)
= ( V)( A) = ______W
- Make sure (taking into consideration the significant figures of this) that all the total power given off as heat by the sum of the resistors is equal to the power given to the circuit by the power supply, because your circuit must exhibit energy conservation. (Notice that there is no physical reason whatsoever to expect power to obey a loop rule. This is an important distinction.) If your circuit does not conserve energy, your answers are wrong, either by measurement or by calculation. You must show written evidence below that you have actively done this last power-checking exercise, #3.
Appendix: Trouble-shooting the Circuit Simulator
Before beginning, a word on using “Load” to load a pre-existing circuit file, like the “Experiment 5” I sent you. When you hit “Load”, you will then look on your desktop to find the file, and it might not appear. Don’t forget to tell the computer to search for All Files rather than just for files of a certain type. Now onto manipulating the circuit simulator.
Suppose I successfully load the Experiment 5 file, and I am overwhelmed by what I see in the following window:
I am overwhelmed because of the fire, the warning at the bottom, the lack of measuring devices, the way it doesn’t look like a circuit diagram like in the assignment sheet, the fact that the resistances and battery voltage are all what I haven’t been assigned. The purpose of this document is to show you how that is all easily fixable.
First, the fire: don’t worry about it; it doesn’t change the measured values. It’s just for fun, because sometimes the current will be so high that things will get too hot. As soon as you change the display from Lifelike to Schematic, the fire will disappear. How to change to Schematic? See the diagram on the next page. See in the upper right how “Schematic” is now selected?
Some other things in the diagram above: Notice that the voltmeter, ammeter, and non-contact ammeter are all checked now to the right. You can see the voltmeter on the screen measuring the voltage across R2, and the value is 16 Volts. (Pay close attention to where the red and the black leads are.) Above R2, notice that the non-contact ammeter is measuring 5.33 Amps of current in that particular line of the circuit. The non-contact ammeter is extremely artificial. It is acting like Superman with X-ray vision pretending that it can see through the wire’s insulation and can see the rate of charge flow inside there. Real ammeters do not work this way so don’t think this simulation is giving you a complete experimental experience!