Group4_8_ch21

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Lab: Multiple Capacitors
11/17/11 Allison Irwin, Bret Pontillo, Richie Johnson

Set up the following circuits using the above materials, adjusting the voltage of the power supply; record data. Setup #1: Setup #2: Setup #3: Setup #4:
 * Purpose**: How will voltage compare across capacitors set up in series and in parallel?
 * Hypothesis**: In series the sum of the voltage in the two capacitors will equal the voltage in the power supply. In parallel the voltage across each of the parallel branches will equal the voltage across the power supply.
 * Materials**: Power supply, connecting wires, capacitors, resistors, multimeter, Excel
 * Procedure**:

Analysis: We decided to graph total voltage of the circuit v. the charge through a capacitor to show how voltage compares in parallel and in series. Since Q=C*V and C is different in both capacitors, we are able to see when the voltage in the capacitor 1 is equal to the voltage in capacitor 2 from looking at the resulting value of Q. When Voltage is the same (in a circuit with only 2 capacitors) both capacitors the resulting charge will be different through both resistors. This would be an example of what happens when capacitors are in parallel as seen in our second graph. When the voltage is different (in a circuit with only 2 capacitors) the resulting Q will be nearly the same. This would be an example of what happens when Capacitors are in series as seen in our first graph. Sample Calculations:
 * Data:**
 * Graph:**

The voltages of the individual capacitors in series are smaller than the voltages when they are in parallel. In series the capacitors must add up to the voltage of the power supply and in parallel the capacitors must all be equivalent voltage when they are in different branches. When the same amount of voltage is in each circuit, the voltages in series will be smaller than the voltages in parallel. When the resistor is set up in the series circuit (Setup #3), there is very little voltage across it. When our power source is changed to three different settings, the voltages across the resistor are 0.00V, 0.01V, and 0.08V. Because there is such little voltage across the resistor, there is very little effect on the voltage across the two capacitors. In the parallel circuit (Setup #4) we added a second resistor in place of the capacitor 1. This had a significant effect of the voltage across capacitor 2. In setup #3 capacitor 2 had voltages of 2.00V, 3.01V, and 3.90V in our three tests. In setup #4 the voltage across capacitor 2 was 1.27V, 1.85V, 2.58V. This shows how the second resistor in parallel caused a significant drop in voltage across the capacitor. In the series circuit (setup 1) the voltage across the power source is equal to the sum of the voltage across the two capacitors. In setup 3, the voltage across the resistor must also be added. In the parallel circuit (setup 2) the voltage across the power source and across the capacitors are all equal. In setup 4, the voltage across the capacitor is equal to the voltage across resistor one. The sum of the voltage across the capacitor and the voltage across resistor 2 is equal to the voltage across the power source. The relationship between the voltage and the individual capacitance in each capacitor can be shown through the equation C=Q/V in which C is capacitance Q is charge and V is voltage. If the charge is set up to be constant the voltage will increase as the capacitance decreases and the capacitance will increase as the voltage decreases. This is can be seen when the equation is rewritten as Q=V*C. The two variable are being multiplied together so one had to decrease as the other increases. If the largest capacitor was switched out for one the was ten times as big as it the voltage that had been seen across the capacitor would decrease ten times. This is because charge is constant and Q=C*V. If capacitance was to increase ten times than the number that it was being multiplied by has to decrease by ten in order for the current to stay the same.
 * Discussion Questions:**
 * 1. How does the voltage on the individual capacitors in series compare to the voltage when they are in parallel?**
 * 2. What is the effect of the resistor on the voltage 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?**
 * 4. How is the amount of voltage on the individual capacitors related to the known capacitance?**
 * 5. Discuss the effect of switching out your bigger capacitor for one that is 10 times as big.**

Upon finishing our experiment, our group had come to a conclusion that our hypothesis was correct. In the experiment we set up four different types of circuits that tested a certain part of our hypothesis. For example we set up one circuit that had two capacitors in series as well as one that was in parallel. When we set up the circuit that had two capacitors in series that voltage across each capacitor added up to the voltage that was being sent out by the power source. The capacitor with the least capacitance also had the highest voltage. This occurred because the two capacitors were both being charged by the same power supply. The one with the least capacitance was able to have the higher voltage because the charge traveling the two capacitor was exactly the same and due to the equation to find capacitance, C=Q/V, having a smaller capacitance would yield a much larger voltage due to the fact that they had the same charge. When the circuit with two capacitors in parallel was set up the voltage through the capacitors was the same as the voltage being emitted by the power source. This occurs because the power source is directly connected to each capacitor, so they both end up having the same pressure difference. This is because the capacitor was able to fill until it achieved the same pressure difference as the power source. Although the results we obtained were exceptional there was still some slight error of about three percent throughout each experiment. This could have been caused by many different variables. One of these variables was the voltmeters that were used. They would fluctuate between a few numbers depending on how hard you pushed it down onto the wires. This could have been fixed by having access to very accurate voltmeters that would give very precise results. Another source of error was the power supplies. They would have a voltage shown on the display but when they were tested the voltmeters they gave a voltage that was slightly different than the number displayed. The final source of error was that we did not know how long it took to charge and discharge the capacitors. With out this knowledge it was possible that we took a reading prior to the capacitor being charged, which would have altered the results. Also, we could have set up the circuit prior to the capacitors being fully discharged causing the results to be slightly different. This error could have been eliminated if there was a way to see that the capacitor were completely charged and discharged.
 * Conclusion:**

= =

Lab: Magnetic Field 11/22/11
Bret Pontillo, Allison Irwin, Richie Johnson

Purpose: To find the relationship between magnetic field strength and distance from the source

Hypothesis: There is going to be an inverse relationship between distance and magnetic field strength, as distance increases the magnetic field strength will decrease. Since in the equation there are a multiple constants, the equation is basically one constant times magnetic moment divided by distance cubed. As the distance in the equation increases it will increase the denominator and decrease the resulting Magnetic Field Strength.

Procedure: Materials: Magnetic Field Sensor, Data Studio and Science Workshop Interface, index card, Meterstick, neodymium magnet. Data: 0.015 m

Data Table:

Graph:



Analysis:

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 b) What exponent do you get for d? How well does this agree with the ideal expression? c) From the above comparison, does your magnet show the magnetic field pattern of a dipole. 3. Use your value of A to determine the magnetic moment //m// of your magnet.  m = 0.4 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.   5. Discuss the precision of your data, referencing the correlation coefficient to support your conclusion.  Our R^2 value was .99542 which is very close to 1. Our error was at 16.9% which is not so high for this lab. We were expecting to get an exponent of -3, but our data produced -2.493.

Conclusion:

Based on our results, we concluded that our hypothesis was correct. There is an inverse cube relationship between the magnetic field strength and the distance from the source. We showed this is the above graph, where the relationship is showed by the exponent of -2.493. While this is not exactly the -3 exponent that we were looking for, there are many sources of error in this lab that would explain the 16.9% error. In the equation there are many variables. An error in any one of them could significantly alter our results. For example, if our magnetic field sensor was not correct, then our B value could have been off. We do not entirely know if our sensor was zeroed. If there was any magnetized material in the area this could have effected our results. While we tried to keep these things away, the presence of things like our computers from across a table could have effected our results. We also do not know how the Earth's magnetic field effected our results. We were also dealing with such small measurements. There was likely to be some human error when measuring the distance (d). In order to improve this lab we would need more accurate ways of gathering measurements for both B and d.

Lab: Magnetic Force on a Current Carrying Wire
12/1/11 Allison Irwin, Bret Pontillo, Richie Johnson Set Up:

__**Data:**__
 * Part 1: Force vs. Current (Data Collection By: Rebecca Rabin, Erica Levine, Ross Dember)**
 * This graph shows the direct relationship between magnetic force and current. The slope of this line is 0.00174 represents F/I.


 * Part 2: Force vs. Length (Data Collection By: Allison Irwin, Bret Pontillo, Richie Johnson)**
 * This graph shows the direct relationship between magnetic force and the length of the conductor. The slope of this line is 0.157 and represents F/L.


 * Part 3: Force vs. Number of Magnets (Data Collection By: Chris Hallowell, Ryan Listro, Eric Solomon)**
 * This graph shows the direct relationship between magnetic force and the number of magnets. The slope of this line is 0.0006 and represents F/N.


 * Part 4: Force vs. Sin(theta) (Data Collection By: Phil Litmanov, Steven Thorwarth, Sam Fihma)**
 * This graph shows the direct relationship between magnetic force and the sin of the angle (theta). The slope of this line is 0.0063 and represents F/sin(theta).

__Percent Difference:__

Analysis: > > n each of the four graphs, there was a direct relationship between FB and each of the other variables, which were similar. We see a very small % difference when solving for B in the slope of each graph. > Yes, the experimental relationships shown the graphs prove that Current, Length, and sin thata all have the same direct relationship with the Magnetic Force. The slope is determined by the other values in the equation. > No because the Magnetic Force increases as the amount of magnets increase. When the number of magnets is included in the equation F=nBILsin(thata), it has a relationship with magnetic field strength one that would be indirect. As the number of magnets increase, the magnetic field strength would decrease as a result.
 * __Sample Calculations:__**
 * 1) Using the equation of the trendline from the graph of Force vs. Current, find the magnitude of the magnetic field. Show your work.
 * 1) Discuss the relationship of the quantities shown in the graphs. How do they agree with the theoretical relationships?
 * 1) 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.
 * 1) Is it reasonable to assume that the strength of the magnetic field is directly proportional to the number of magnets? Why or why not?

Conclusion: Our hypothesis that, the magnetic force will be directly proportional to the strength of the magnetic field, the current, the length of the conductor, and the angle between the current and the magnetic field. When the magnetic force increases, the other variable will have increased as well, because of the equation, F=B(I)(//l//)(sin θ) was proven to be correct. The current vs. force graph shows the direct relationship between magnetic force and current. The slope of this line is 0.0174 represents F/I. The Length vs. force graph shows the direct relationship between magnetic force and the length of the conductor. The slope of this line is 0.157 and represents F/L. The number of magnets vs. Force graph shows the direct relationship between magnetic force and the number of magnets. The slope of this line is 0.0006 and represents F/N. The sin of theta vs. Force graph shows the direct relationship between magnetic force and the sin of the angle (theta). The slope of this line is 0.0063 and represents F/sin(theta). We calculated percent difference to find how much error occurred. Our percent difference remained around 10% and below for a majority of our data. There was one outlier that was at 33.06%. Some of the error could have been from not setting up the scale with the loop the same way. The loop could have been a bit further a way or closer the magnets which were on the scale. Since distance away from the magnets could affect the force, this could have contributed to our slight error. Also the scale might not have been zeroed at the right spots for each part, considering 4 different groups worked with scales. This would not have contributed a large amount of error but it could have created a slight difference in the force read on the scale. The information discovered in this lab can be applied to real life situations. The information could be applied to loops in motors as we have previously worked with also, when we created one on our own. The info learned can also can be applied to electric generators used to generate voltage.

Lab: What is the Magnetic Field Strength of a solenoid?
12/8/11

Pre- Lab 12/8/11
>> The solenoid will be the strongest at the center, and as the sensor moves further out of the sensor from the center, the field will lose strength. Distance affects the magnetic field, which is why the field gains and loses strength when a sensor will moved in and out of the solenoid. >> We could connect a solenoid to a power supply, and move a magnetic field sensor in and out of the solenoid in increments to determine magnetic field strength at specific distances. > a) How does the strength of the magnetic field inside a solenoid relate to the position inside? As the position gets closer to the center of the solenoid, the magnetic field strength will get stronger. As the position gets closer to leaving the solenoid the magnetic field strength will become weaker. b) Is the magnetic field the same strength at every location within the solenoid? No magnetic field strength is different throughout a solenoid. The magnetic field strength depends on the distance into or leaving the solenoid. c) What is the magnitude of the magnetic field inside a very long solenoid? where n=number of loops and L=length. d) What is the relationship of the magnetic field strength and radius of the coil? Magnetic field strength does not depend on the radius of the coil exhibited by the equation in the previous question. They do have a relationship in magnetic flux where the radius will affect the area and if the flux stays constant, the radius and field strength would have an indirect relationship, otherwise there is none. Purpose: To find the magnetic field strength of a solenoid.
 * 1) The objective is stated in the title. What is your hypothesis? (Attempt to answer the question, to the best of your knowledge.)
 * 2) 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.)
 * 1) How do you think you might test this hypothesis? (What might you measure and how?)
 * 1) Read the entire procedure through.
 * 2) Design __data table(s)__ in order to record your observations __and__ calculations. You can do this by hand (acceptable) or in Excel (preferable).
 * 1) Answer the following questions:

Hypothesis: The solenoid will be the strongest at the center, and as the sensor moves further out of the sensor from the center, the field will lose strength. Distance affects the magnetic field, which is why the field gains and loses strength when a sensor will moved in and out of the solenoid.

Materials:

In this lab there are only a few materials needed to test the hypothesis. First we need a solenoid, then we need a magnetic field sensor to measure the strength inside the solenoid as well as a power supply to run a current through the solenoid. The last material is a meter stick that will be used to measer the distance in which the sensor is inside the solenoid.

Procedure: Data: Analysis: We only graphed one side of our data because a graph with the full set of data did not yield a graph which properly represented our data. The max going in from the left of the solenoid and the max going in from the right of the solenoid were not equivalent. One was .0003 T more than the other. The graph is a negatively shaped parabola where the maximum will be the field strength maximum at the area in the center of the solenoid.

Calculations: Theoretical Magnetic Field Strength (Max) n=number of coils divided by the length of the solenoid



Conclusion: Our hypothesis that the the magnetic field strength of the solenoid would be the strongest at the center was correct. The solenoid was 15cm long, and at 7.5cm we measured the magnetic field to be 32.45 gauss or 0.003245T. We calculated the theoretical maximum magnetic field strength of the solenoid to be 0.003225T. We calculated our percent error to be 0.61%. This value shows that we had negligible error. This error could be the result of our field strength sensor not measuring 100% accurately. We had no quantitative way to make sure that the sensor was correct. It could also be from human error in taking measurements. We were using a wooden meter stick. The cylinder shape of the solenoid and the rounded front of the sensor made measuring slightly difficult. In order to fix this error we would need more accurate measuring equipment than a meter stick. Something that held the sensor in place at a certain length would be desirable. We would also need some way to zero the magnetic field sensor in order to make sure that this was measuring accurately. Solenoids are used in everyday items such as pinball machines, fuel injectors, disk drives, and automobile starters. An understanding of the magnetic field strength within a solenoid is necessary in making these products function.