Group1_8_ch21

AP Physics - Period 8toc

Ross Dember, Erica Levine, & Rebecca Rabin

Lab: Multiple Capacitors
Date: 11/17/2011 OBJECTIVE The purpose of this activity is to compare the voltage of capacitors in series to those in parallel.

HYPOTHESIS W/ RATIONALE The voltages in the series circuit will be split up amongst the capacitors. The voltage of the capacitors should add up to the voltage of the power source. This is due to the capacitance equation Ceq = C1 + C2. The voltages in the parallel circuit will all equal each other due to the capacitance equation Ceq = C1 = C2.

MATERIALS 1. 2 Capacitors of known value 2. DC voltage source 3. Voltmeter 4. Lead wires 5. 2 resistors

PROCEDURE NOTE: Make sure all capacitors are uncharged before connecting them. (Use a short wire to momentarily short each one.) 1. Create closed loop using lead wires to connect DC voltage source with 2 capacitors in a series circuit 2. Using a voltmeter, calculate the voltage of each capacitor 3. Create closed loop using lead wires to connect DC voltage source with 2 capacitors in a parallel circuit 4. Using a voltmeter, calculate the voltage of each capacitor 5. Create a closed loop using lead wires to connect DC voltage source with 2 capacitors and a resistor in a parallel circuit 6. Using a voltmeter, calculate the voltage of each capacitor and the resistor 7. Create a closed loop using lead wires to connect DC voltage source with a capacitor and 2 resistors in a parallel circuit 8. Using a voltmeter, calculate the voltage of the capacitor and each resistor 9. Using the given values, calculate the voltage in each capacitor and resistor for each circuit
 * Refer to schematic diagrams and pictures below

DATA

CALCULATIONS







DISCUSSION QUESTIONS 1. How does the voltage on the individual capacitors in series compare to the voltage when they are in parallel? The voltages of the individual capacitors in the series circuit are smaller than the voltages when they are in a parallel circuit. In a series circuit the capacitors must add up to equal the voltage of the power supply and in a parallel circuit the capacitors must all be equivalent to the voltage of the power supply. Therefore when using the same amount of voltage in each circuit, the voltages in the series will be smaller than the voltages in the parallel. Our results in the series circuit were C1 = 1.41V, C2 = 3.52V. When you add up these two values the voltage is very close to 5. Our results in the series circuit were C1 = 5.03V, C2 = 5.02V. Both these voltages are very close to 5. 2. What is the effect of the resistor on the voltage of the capacitors? When there is only one resistor in the parallel circuit the resistor has a minimal effect on the voltages of the capacitors. In the original parallel circuit C1 = 5.03V and C2 = 5.02V. With the addition of the resistor the voltages each drop to 4.89V. The voltage of the resistor then has the remaining voltage from the power supple which we recorded as .19V. When there was only one capacitor and 2 resistors in the parallel circuits the resistors has a great effect on the voltages of the capacitors. In the original parallel circuit C2 = 5.02 V. This capacitor now has a voltage of .06V. The majority of the power supply went to resistor 1 which was recorded as 5.03V and the remaining went to the second resistor which was recorded as .06V. This makes sense because the second resistor was in parallel with the capacitor, so they should have the same voltages of the capacitors. 3. How does the potential difference of the capacitors in series compare to the voltage of the source? What about when they are in parallel? The potential difference of the capacitors in the series circuit add up to the voltage of the source. The potential difference of the capacitors in the parallel circuit are equivalent to each other as well as the voltage of source. However, when resistors are added into the parallel the circuit there is an influence on the voltage. 4. How is the amount of voltage on the individual capacitors related to the known capacitance? The equation that relates capacitance and voltage is C=Q/V. Therefore, when charge is constant, the larger the capacitance, the smaller the voltage across the capacitor. 5. Discuss the effect of switching out your bigger capacitor for one that is 10 times as big. If we switched out our larger capacitor for one that was 10 times as large, the voltage across this capacitor would decrease by a factor of 10. Therefore, the voltages of other objects in the series circuit would increase, so that the total voltage adds up to the voltage across the power supply.

CONCLUSION: Our hypothesis was correct, as our results show in the multiple setups. For the first one, the capacitors' voltages add up to the same as the power supply. Likewise, in all the other circuits, considering the loops as separate form each other, each loop would equal the voltage of the battery. This is shown in our last two experiments. Likewise, in terms of parallel resistors/capacitors, whichever ones were parallel would equal each other. Shown in the second experiment, the two capacitors had the same voltage as the source, which means they were also equal to each other. In the latter two experiments, the capacitors/resistors in parallel to each other were equal to each other in voltage, so those experiments reaffirmed the first two ones. Although there was minimal error (it was never greater than 1.5%), there were a few factors that led to our results being off by a little. This could stem from inaccurate voltmeters, as they can skew the numbers by a little bit. Also, the power supplies could have similar problems and may not have accurately displayed the voltage they were showing by a one-hundredths of a volt. Furthermore, the final question came to how accurate the capacitors were and if they were in fact charged all the way during the measurements. If they were not, the voltages would be higher than expected since they are inversely related to each other. To fix the error in this lab, more accurate equipment could have been used. Also, we could have tested out the capacitors before to see how long it actually took them to charge and discharge. Furthermore, this lab has real-life implications since capacitors are found in many situations. For example, capacitors are put in cars, and if the designer wants more voltage for each capacitor, he would have them be parallel to the battery. However, if he was forced to line them up in series, he would have to take into account the capacitance because, as shown in the first part of the experiment, the lower capacitance will yield a higher voltage, meaning that whichever needs more voltage should get that capacitor.

Lab: Magnetic Field Strength
Date: 11/22/2011 OBJECTIVE What is the relationship between magnetic field strength and distance from the source?

HYPOTHESIS W/ RATIONALE The magnetic field strength should be inversely cubed related to the distance of the source based on the equation given in the pre-lab assignment and the similarities towards action-at-a-distance forces such as electrostatic force, where distance and force are also inversely related. Since force and magnetic field are directly related, we came to this hypothesis.

MATERIALS 1. Magnetic Field Sensor 2. Data Studio and Science Workshop Interface 3. Index card 4. Meterstick 5. Neodymium magnet

PROCEDURE 1. Tape the measuring tape or meter stick to the table, and tape the Magnetic Field Sensor to a convenient location. The sensor should be perpendicular to the stick, with the white spot inside the rod facing along the meter stick in the direction of increasing distance. Carefully measure the location of the sensor on the meter stick. This will be your origin for all distance measurements. 2. As a convenient way to measure to the center of the magnet, and to ease handling of the small magnets, allow the two magnets to attract one another through an index card, about 0.5-cm from either edge near the corner. The magnets should stay in place on the card. The card itself will serve to mark the center of the magnet pair. 3. Connect the Magnetic Field Sensor to Channel A of the interface. Set the switch on the sensor to //1x//. 4. Open Data Studio and choose “Create Activity”. Click on “Setup” and add a Magnetic Force Sensor to the icon of the interface. For a display, click on “314 Digits”, which will show the magnetic field strength in Gauss. 5. Zero the sensor when the magnets are far away from the sensor in order to remove the effect of the Earth’s magnetic field and any local magnetism. The sensor will be zeroed only for this location, so instead of moving the sensor in later steps, you will move the magnets. a) Move the magnets far away from the sensor. b) When the reading in the meter window is stable, click “Tare” on the sensor. 6. Now you are ready to collect magnetic field data as a function of distance. a) Click “Start”to begin data collection. b) Place the card with the magnets against the meter stick, 2.0 cm from the Magnetic Field Sensor, so the card is perpendicular to the meter stick. Measure from the card to the center of the Magnetic Field Sensor. c) The current magnetic field measurement is shown in the meter window. If necessary, reverse the magnets so the reading is positive, and reposition the card 2.0 cm from the sensor. d) Carefully measure the distance of the card to the sensor. e) Record your data in a table. 7. Continue taking readings every 0.5 cm until you get no more change in Magnetic Field Strength.

DATA

GRAPH

SAMPLE CALCULATIONS
 * Data taken from Sam, Steve, and Phil

DISCUSSION QUESTIONS 1. On Excel, create a graph of magnetic field //vs.// the distance from the magnet. Produce a best fit line using a “Power” function. 2. Compare your data to the ideal inverse-cube model: a) What value do you get from the constant, A, or [( // m // 0 2 // m // ) / (4 p )]? How well does this agree with the value that the rest of the class measured? 1*10^(-7) b) What exponent do you get for d? How well does this agree with the ideal expression? 3.047, the ideal expression is 3-flat, so were were pretty close. c) From the above comparison, does your magnet show the magnetic field pattern of a dipole. Yes. Exemplified by the inverse cubic relationship. 3. Use your value of A to determine the magnetic moment //m// of your magnet. A= 1E-7=1E-7*2µ (4π's cancel out) µ=.5 A//m//^2 4. The units of //m// may suggest a relationship of a magnetic moment to an electrical current. In fact, a current flowing in a closed loop is a magnetic dipole. A current //I// flowing around a loop of area p // r // 2 has a magnetic moment of //m = I// p // r // 2 //.// If a single current loop had the same radius as your permanent magnet, what current would be required to create the same magnetic field. m=Iπr^2 .5=Iπr^2 I=.5/(πr^2)... Half of the inverse area.

5. Discuss the precision of your data, referencing the correlation coefficient to support your conclusion. Our data was very precise. For evidence, our R value of .99792 was very close to 1, and our percent error for our exponent was only 1.56%, showing that besides being accurate, our results correlated well with each other.

CONCLUSION Based on our results, we conclude that our hypothesis was correct. We found the relationship between magnetic field strength and distance to be an inverse cube. As the distance from the magnet increased, the magnetic field strength decreased in a cubic fashion. This claim is validated by the equation shown on the graph we formed using our collected data. The exponent (-3.047) indicates an inverse cube correlation between the two variables. Theoretically, the exponent should have been (-3.0) based on the equation, where B is magnetic field strength, and d is distance. We know our results were fairly accurate, because the percent error for the value of the exponent was 1.56%. Although we had accurate results, there are many sources of possible error for the small amount of error we did see. Once possible source of error was the accuracy of the sensor. The values were constantly fluctuating, and it was hard to extract accurate data from its reading. Another possible source of error is human error. It is possible that when we read the distances between the sensor and the magnet, we were off by a little. This would cause inaccuracies in our data. For more accurate data in the future, we think it is important to use a more accurate device to read the magnetic field strength.

Lab: Magnetic Force on a Wire
PRE-LAB 1. The objective is stated as a question. What is your hypothesis? (Attempt to answer the question, to the best of your knowledge.) For a conductor placed in a magnetic field, the magnetic force is directly related to the magnetic field strength, the length of the conductor, the current, and the angle between the field and the current. a) Include the rationale for your hypothesis (Provide detailed reasoning here. This may take the form of a list of what you already know about the topics, with a summary at the end.) Each of the variables tested are those included on the right side of the equation Magnetic Force = Current*Magnetic Field Strength*Length of Conductor*SIN(Theta). In this equation all the variables are multiplied by each other to reach the resulting magnetic force. Therefore, if any of the variables being tested are increased, the magnetic force should increase. Alike, if any of the variable being tested are decreased, the magnetic force should decrease. Thus creating a direct relationship. b) How do you think you might test this hypothesis? (What might you measure and how?) In order to test the hypothesis, it is essential to keep all variables constant while influencing only one variable and observing the influence on the resulting magnetic force. For example, to test the relationship between the current and the magnetic force, using some sort of device, keep the length of the conductor, the strength of the magnetic force, and the angle completely the same and change the current to variations values. Observing the resulting magnetic field should prove our hypothesis correct. 2. Read the entire procedure through. 3. Design __data table(s)__ in order to record your observations __and__ calculations. Do this in Excel (preferable), and post a copy on your wiki. 4. Answer the following questions: a) How is the direction of the magnetic force oriented with respect to the directions of magnetic field and current which produced it? Using the right hand rule one can determine the direction of the magnetic force with respect to the directions of the magnetic field and current. To use the right hand rule properly, align your thumb with the direction of the current and align the remaining fingers with the direction of the magnetic field. The direction in which your palm is facing is the direction of the magnetic force. b) How do changes in the angle between the current and the magnetic field affect the force acting between them? Changes in the angle between the current and the magnetic field have a direct affect on the force acting between them. As the angel increases the force acting between them increase as well. This is due to the equation Magnetic Force = Current*Magnetic Field Strength*Length of Conductor*SIN(Theta). c) What angle between the current and the magnetic field produces the greatest force? 90 degrees d) What angle between the current and the magnetic field produces the least force? 0 and 180 degrees e) How is the magnitude of the force of magnetism related to the magnitude of the length of the wire carrying the current? The magnitude of the force of magnetism has a direct relationship with the magnitude of the length of the wire carrying the current. As the magnitude of the length of the wire carrying the current increases, the magnitude of the force of magnetism increases as well. This is due to the equation Magnetic Force = Current*Magnetic Field Strength*Length of Conductor*SIN(Theta). f) A graph of force vs. current has a trendline with an equation of y = 0.00559x. What is the theoretical magnetic field strength of the magnet used in this experiment if the loop is 4.2-cm long? Show your work. g) Find the magnetic force on the conducting loop described above, when the current is 0.352-A. Date: 12/01/2011 OBJECTIVE For a conductor placed in a magnetic field, what are the relationships between the magnetic force, magnetic field strength, length of the conductor, current, and angle between the field and the current?

HYPOTHESIS W/ RATIONALE Magnetic Field Strength, Current, Length, and SIN Theta will all have linear relationships with Magnetic Force. We hypothesize that this will happen based on the equation Fmag=BILsin(theta). As Each of these variables increases, the Magnetic force will increase.

MATERIALS 1. Power source 2. Ring stand 3. Circuit loop 4. Magnets

SETUP/PROCEDURE 1. Put the magnet on the scale and zero the scale. 2. Line the magnet up with the loop. 3. Adjust the current on the power source. 5. Record the current and the resulting scale reading. 6. Repeat to find multiple data points. 7. Repeat steps 5-7 for magnetic field strength, length, and theda.

DATA AND GRAPHS Force versus Current Analysis: This graph shows that current and magnetic force have a linear relationship thus proving our hypothesis correct. In our experiment, every time we increased the current, the magnetic force increased as well.

Force versus Length Analysis: This graph, which includes data taken from Allison, Brett, and Richie, shows that length and magnetic force have a linear relationship thus proving our hypothesis correct. In their experiment, every time they increased the length, the magnetic force increased as well.

Force versus Number of Magnets Analysis: This graph, which includes data taken from Chris, Eric, and Ryan, shows that strength and magnetic force have a linear relationship thus proving our hypothesis correct. In their experiment, every time they increased the number of magnets, the magnetic force increased as well.

Force versus sin theta

Analysis: This graph, which includes data taken from Phil, Sam, and Stephen, shows that the angle and magnetic force have a linear relationship thus proving our hypothesis correct. In their experiment, every time they increased the angle, the magnetic force increased as well.

SAMPLE CALCULATIONS __Current__ __Length__ __Magnets__ __Sine of Angle__ .0063=B(3)(1.7)(.11) B= .0112 T

__Average__ __Percent Difference__ Current Length Magnets Sine of Angle

ANALYSIS QUESTIONS

1. Using the equation of the trendline from the graph of Force vs. Current, find the magnitude of the magnetic field. Show your work. The equation of the trendline on the Force vs. Current graph was y=.0174x. Y represents the magnetic force, and x represents the current. We can manipulate the equation F=B*I*lsinø to find the magnitude of the magnetic field. The slope of the graph must be equal to the product of the other three variables, so .0174=B(.0232)(6)(sin90). After solving for this equation, we found that the magnetic field was .125 T. Work is shown above in calculations. 2. Discuss the relationship of the quantities shown in the graphs. How do they agree with the theoretical relationships? All four variables tested have a linear relationship with magnetic force. When we graphed one of the variables vs. magnetic force, it formed a straight line, with a slope composed of the product of the other three variables. When we solved for B based on the slopes of each graph, there was little percent difference, indicating that all four variables share an identical relationship with magnetic force. As any of the four variables increases, so does the magnetic force. 3. Do the experimental relationships shown in the 4 graphs validate the theoretical relationships? Explain your reasoning using specific evidence from the lab to support your answer. Yes, the experimental relationships found in the four graphs all validate the theoretical relationships. Current, angle, length, and number of magnets all have a linear relationship with magnetic force, and the slope on each graph is comprised of the remaining variables. 4. Is it reasonable to assume that the strength of the magnetic field is directly proportional to the number of magnets? Why or why not? No, as the magnetic force increases the amount of magnets will also increase. However, as the number of magnets increases, the magnetic field strength will decrease as a result to keep the equation F=n*B*I*l*sintheta linear.

CONCLUSION Based on the information we collected and analyzed, our original hypothesis was correct. The number of magnets, current, length, and sin of theta all shared a linear relationship with magnetic force. As one or more of these variables increased, so did the magnetic force. This relationship can be demonstrated by the equation F=B(I)(//l//)(sin θ). In order to collect our data, we collected data and made for graphs. Each graph had one of the four variables on the x axis, and magnetic force on the y axis. The slope on the graphs were composed of the product of the other three variables. For example, we graphed data for Length vs. Magnetic Force. The slope of this graph was .1569. Since the slope is comprised of the other three variables in the equation, we concluded that (n)BIsin θ was equal to .1569. We performed the same procedure for the other variables. In order to determine the accuracy of the experiment we solved for the value of B in each graph. The low percent difference between the different magnetic field values from the various graphs indicates that our results were fairly accurate. We were able to solve for B by setting the slope equal to the other three variables. For example, we calculated B off of the angle graph by setting the slope equal to nBIL. The number of magnets, current, and length were known, so we were able to solve for B, and got .112 T. Even though our results were fairly accurate, there were still some possible sources of error in the design of the experiment. There may have been some inconsistency in the procedure considering four different groups participated in the data collection. The scale could have been zeroed differently, the distance between the scale and the magnet could have been slightly different, among many other details. This lab has many real life applications. These relationships are vital in the manipulation and creation of generators and motors.

Lab: Magnetic Field in a Solenoid
Date: 12/9/2011 PRE-LAB QUESTIONS 1. The objective is stated in the title. What is your hypothesis? (Attempt to answer the question, to the best of your knowledge) a) Include the rationale for your hypothesis (Provide detailed reasoning here. This may take the form of a list of what you already know about the topics, with a summary at the end.) b) How do you think you might test this hypothesis? (What might you measure and hot?) 2. Read the entire procedure through. 3. Design __data table(s)__ in order to record your observations __and__ calculations. You can do this by hand (acceptable) or in Excel (Preferable). Field (T) || Current(A) || Number of Coils || Theoretical Field (T) || Percent Error (%) ||
 * The solenoid will have the greatest magnetic field strength in the center of the solenoid, and it will equal the number of coils per length times the permeability constant times the current in the wire.**
 * The equation B=NµI leads us to believe that the magnetic field strength will be equivalent to the product of the previously mentioned variables. The field will be the strongest in the center of the solenoid, because the field gets disturbed the closer the distance gets to the edge of the solenoid.**
 * We can measure the magnetic field inside the solenoid at different distances from one end of the solenoid. When we graph distance vs. field strength, we will be able to find the maximum field strength and compare it to the theoretical value, based on the equation B=NµI.**
 * Length(m) || Experimental

4.Answer the following questions: a) How does the strength of the magnetic field inside a solenoid relate to the position inside? b) Is the magnetic field the same strength at every location within the solenoid? c) What is the magnitude of the magnetic field inside a very long solenoid? d) What is the relationship of the magnetic field strength and radius of the coil?
 * The closer the position is to the center of the solenoid, the greater the magnitude of the magnetic field.**
 * No, the location inside the solenoid will affect the magnitude of the magnetic force.**
 * B=NµI. The magnetic field equals the product of the number of coils divided by the length, times the permeability constant, times the current in the wire.**
 * There is no relationship between the magnetic field strength and the radius of the coil.**

OBJECTIVE What is the magnetic field strength of a solenoid?

HYPOTHESIS The center of the solenoid will have the strongest magnetic field strength. As the magnetic field gets farther from the center, it will gradually become weaker forming a parabolic shaped graph.

MATERIALS Magnetic field sensor, power supply, meter stick, patch cord, solenoid, ruler

PROCEDURE 1. Connect power supply to solenoid. 2. Plug magnetic field sensor into computer and open EZScreen. 3. Lie meter stick next to solenoid. 4. Using magnetic field sensor test various spots inside the solenoid. 5. Be sure to record distance used. 6. Record data. DATA
 * Trend line max is .04676 T

CALCULATIONS DISCUSSION QUESTIONS 1. Did the axial reading change when the sensor was moved radially outward from the center toward the windings on the coil? Yes, as the sensor moved radially outward from the center toward the windings on the coil the axial reading gradually became weaker. 2. Was the axial reading different from the reading in the middle of the coil when the sensor was inside but near the ends of the coil? Why? The axial reading in the middle of the coil was very strong reading. As we moved the sensor near the ends of the coil the axial reading became much weaker. This is because as the sensor moves farther away from the center of the solenoid, the magnetic field becomes much weaker. 3. By comparing the axial and radial readings, what can you conclude about the direction of the magnetic field lines inside of a solenoid? There are the greatest amount of magnetic field lines in the center of the solenoid which has the greatest magnetic strength. The remanding lines wrap around the solenoid going from one end to the other and have a weaker field than the center. 4. At what position in the solenoid should you get the greatest magnetic field strength? In the center of the solenoid. 5. How does the theoretical value compare to the value at this position? Our theoretical value was extremely close to our experimental value.

CONCLUSION Our hypothesis proved to be correct, shown by our table and graph. Since we measured on both sides, it is clear to see that the middle had a larger magnetic field. This comes from the middle the middle of our trend line, which is our theoretical maximum at .0432 T.

Our error came out to be 8.24% percent, as the experimental maximum was .04676. This error probably came from our method of measuring. Since the magnetic field detector was not long enough, we had to measure half from the left and half from the right, and it is clear to see which numbers were measured on each side. This could be fixed by a longer field measurer. Also, we assumed that the solenoid's coils were evenly distributed, and if this was not the case, then our numbers make more sense. The lab has many uses, as solenoids are found in car starters and disc drives, so understanding where the magnetic field is strongest can be very important as they can help jumpstart electricity.