Lab report ASAP PLEASE.
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Lab report ASAP PLEASE.
Lab report ASAP PLEASE.
77 Capacitance 77 – Page 1 of 7 Written by Chuck Hunt Capacitance Equipment 1 Basic Electrometer ES -9078 1 Basic Variable Capacitor ES -9079 1 Electrostatics Voltage Source ES -9077 1 Short Patch Cords (set of 8) SE -7123 Required but not included: 1 850 Universal Interface UI -5000 1 PASCO Capstone Paper Introduction The purpose of this experiment is to investigate how the capacitance of a parallel -plate capacitor varies when the plate separation is changed and to qualitatively see the effect of introducing a dielectric material between the plates. A computer model of the system will be developed and the student will observe some of the power of computer modeling. Theory A capacitor is used to store charge. A capacitor can be made with any two conductors kept insulated from each other. If the conductors are connected to a potential difference, V, as in for example the opposite terminals of a battery, then the two conductors are charged with equal but opposite amount of charge Q, which is then referred to as the “charge in the capacitor.” The actual net charge on the ca pacitor is zero. The capacitance of the device is defined as the amount of charge Q stored in each conductor after a potential difference V is applied: C = Q/V Rearranging gives: V = Q/C (1) The simplest form of a capacitor consists of two parallel conducting plates, each with area , separated by a distance d. The charge is uniformly distributed on the surface of the plates. The capacitance of the parallel -plate capacitor is given by: C = κ εo A/d Where κ is the dielectric constant of the insulati ng material between the plates ( κ = 1 for a vacuum; other values are measured experimentally and can be found in tables), and εo is the A 77 Capacitance 77 – Page 2 of 7 Written by Chuck Hunt permittivity constant, of universal value εo = 8.85 x 10 -12 F/m. The SI unit of capacitance is the Farad (F). The system we use is more complex. In addition to the two moveable parallel plates, the connecting wires and the electrometer also have some capacitance. This capacitance is roughly equal to the capacitan ce of the moveable plates when the plates are 1 cm apart and cannot be ignored. Including this gives: C = κ εo A/d + C sys (2) where C sys is the capacitance of the rest of the system. Substitution of Equation 2 into Equation 1 yields: V = Q/( κ εo A/d + C sys ) (3) Any material placed between the plates of a capacitor will increase its capacitance by a factor κ called the dielectric constant where: C = κCo (4) with C o being the capacitance when there is a vacuum between the plates of the capacitor. Dielectric materials are non -conductive. Any dielectric material can be used to keep the plates in a capacitor insulated from each other (preventing them from touching and d ischarging). To three significant figures, κ = 1.00 for air. For all materials, κ > 1. If the charge on a capacitor is kept constant while a dielectric is inserted between the plates, Equations 1 & 4 yield: Q = CV = C oVo = C/ (κ εo Vo) so V = V o/ κ Where V 0 is the voltage before inserting the dielectric and V is the voltage after insertion. Since κ > 1 always, we have V < V o (5) . 77 Capacitance 77 - Page 3 of 7 Written by Chuck Hunt Setup Figure 1: Setup Figure 2: Indicator Foot 1. Move the Variable Capacitor plates so they are about 2 mm apart. Use the adjustment screws on the back of the moveable plate to make the plates parallel. Easiest way to do this is to look directly down from above the plates and adjust the horizontal adjust until the gap looks uniform, then look at the gap from the side and even with the center of the plates and adjust the vertical screw. May need to repeat the process a few times. 2. Position the movable plate so the leading edge of the indicator foot (see Fig. 3) is at the 0.2 cm position. The gap betwee n the two plates should be 0.2 mm all the way around. Check it with a ruler. If the gap varies repeat step 1. If the gap is not 0.2 mm, release the holding screw on the non -moving plate and move it until the gap is 0.2 mm and then tighten the screw back do wn. 3. Attach the twin lead (red & black) connector to the Signal Input jack on the Basic Electrometer. Route the wires as far away from where your hand and your body will be as possible. The charges in this experiment all small so static discharge will foul things up. Also, people are conducting plates and have a significant amount of capacitance. You can foul things up just by being close . It is best to make the fixed plate ground by attaching the black wire’s spade lug to it. Attach the red spade lug t o the terminal on the moving plate. The wire must be free to move when the plate moves. 4. If you have a black banana/banana wire (not included) attach it as shown from the common (com) terminal on the Electrostatic Voltage Source to the ground terminal on t he Electrometer. Alternately, use the provided banana/spade wire and connect the spade lead to the terminal on the fixed plate where the other ground lead is already attached. Attach the red banana/spade lead to the +30V terminal and leave the spade end fr ee. Plug in the transformer and apply power to the Electrostatic Voltage Source. Shift the switch on the back to the On position. The green Power On light should glow. 5. Use the supplied adaptor cable to attach from the Signal Output on the Electrometer to the A Analog Input on the 850 Universal Interface. It is important that it be the A input! 77 Capacitance 77 - Page 4 of 7 Written by Chuck Hunt 6. In PASCO Capstone, create a table and create a user -entered data set called Separation with units of cm . Enter the values shown in Table I. Select the Voltage measurement in the second column. Table I: Air Gap Capacitor Separation (cm) Voltage (V) 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.5 1.0 0.5 0.3 7. Create a graph of Voltage vs. Separation. Procedure A: The Effect of the Plate Separation 1. Set the capacitor plates 0.3 cm apart by setting the movable plate so leading edge of its indicator foot is at the 0.3 cm mark. 2. Turn on the electrometer and set the range button to the 100 V scale. 3. Remove any charge from the capacitor by momentarily touching both plates at the same time with your hand. 4. Zero the electrometer by pressing the ‘ZERO’ button until the needle goes to zero. 5. Momentari ly connect a cable from the +30 V outlet in the voltage source to the stud on the back of the mov able capacitor plate. This will charge the capacitor. Remove the charging cable. 6. Read the following steps. They need to be performed quickly since the charge will slowly escape from the electrometer, especially if the humidity is high. One person should r un the computer while one moves the capacitor plate. Everyone else should stay back. Everyone should try to be in the same position for each reading. Anybody who is close is a significant part of the system and can make the readings chang e. 77 Capacitance 77 - Page 5 of 7 Written by Chuck Hunt 7. Slide the mo vable plate so it is at 8.0 cm (leading edge of the indicator foot). Once the plate is in position, the person moving the plate should move away 50 cm or so and try to be in the same position for each measurement. 8. In Capstone, c lick the PREVIEW button at the lower left to begin collecting data. Colored numbers will appear in first row of the table. The person doing the computer should click the Keep Sample (red checkmark in the lower left) button. The number in the first row will turn black and the colore d number will move to the second row. The person at the computer should read the next separation (7 cm) out loud and wait. 9. Move the plate to 7.0 cm and repeat the process until 0.3 cm. 10. Click the STOP button to end the data collection. 11. Examine the graph . If it looks like a smooth curve, you are done. If not, repeat the process until you get a nice looking run. Analysis A V = Q/( κ εo A/d + C sys ) (3) Examination of Equation 3 from Theory A show that if C sys = 0, then V is directly proportional to d and the Voltage vs. Separation graph on the Data page should be a straight line. This is clearly not the case. To verify Equation 3 for the case where C sys is not zero, we need to know Q and C sys . We determine these by fitting the math model (Equation 3) to the data. First we note that κ εo A = (1.00)*( 8.85 x 10 -12 F/m)( 2.46 x 10 -2 m2) = 2.18x10 -13Fm = 2.18x10 -11F cm. So the parallel plate capacitance when d = 1 cm is C 1.0 = 2.18x10 -11 F. Note that this value is entered in line 2 of the Calculator. When d is small (0.3 cm) the first term in the denominator dominates and Q ~ V 0.3 (κ εo A)/d = (30 V)*(2.18x10 -11F cm )/(0 .3 cm) = 2.2x10 -9 C. This value is entered as an initial guess for the value of Q in line 1 of the calculator. Q is constant so when d becomes large, C sys dominates in the denominator and we have: Csys ~ Q/V 8 ~ 2.2x10 -9 C/80 V = 2.7x10 -11 F Where V 8 is the voltage when d = 8 cm. This is taken as the initial guess for C sys (=C 1) on line 3 of the calculator. 77 Capacitance 77 - Page 6 of 7 Written by Chuck Hunt Note that C sys is about equal to C 1.0 at 1.0 cm. At 0.3 cm, C 0.3 = 7x10 -11 F so C 0.3 ~ 3 C sys and the approximation above is decent but not great. At 8 cm C 8 = 2.7x10 -12 F = C sys /10, so the approximation is good, but not perfect. 1. In the Calculator, create the following calculations: Q = 3.0*10^( -9) Units of C κε₀A = 2.18*10^ -11 Units of (F cm) C₁ = 3.6*10^ -11 Units of F V model = [Q ]/([κε ₀A]/[Separation]+[C ₁]) Units of V 2. Use the Data Display button ( ) to select your best run. 3. Adjust the values for Q on line 1 of the Calculator and for C 1 on line 2 to make the model match the experimental curve as well as possible. 4. Answer the first four questions on the conclusions page. Procedure B: The Effect of a Dielectric between the Plates 1. In PASCO Capstone, create a table and create a user -entered data set called Paper Position with no units. Enter the values shown in Table II. Select the Voltage measurement in the second column. Table II: Paper Diele ctric Paper Position Voltage (V) 1 out 2 in 3 out 4 in 5 out 6 in 7 out 8 in 9 out 2. You will use paper as the dielectric to be inserted between the plates. Get a stack of paper about 1 cm thick. 3. Position the movable plate of the capacitor at 8 cm. 4. Turn on the electrometer and set the range button to the 100 V scale. 5. Remove any charge from the capacitor by momentarily touching both plates at the same time with your hand. 77 Capacitance 77 - Page 7 of 7 Written by Chuck Hunt 6. Zero the electrometer by pressing the ‘ZERO’ button. The n eedle must be at zero. 7. Momentari ly connect a cable from the +30 V outlet in the voltage source to the stud on the back of the movable capacitor plate. This will charge the capacitor. Remove the charging cable. 8. Cl ick on the PREVIEW button. 9. One student hol ds the stack of paper directly above the gap between the capacitor plates so that the long side of the paper is vertical. Hold the paper with one hand and keep the other hand on the metal connector attached to the signal input of the Electrometer so that t here is no static charge on the student holding the paper. Press the Keep Sample button to record the voltage when the paper is not between the plates. 10. Lower the paper between the two plates until it touches the base. Do not let the paper touch either pla te! Keep your hand as far above the plates as possible. Press the Keep Sample button to record the voltage when the paper is between the plates. 11. Pull the paper back above the plates and repeat steps 8 and 9 several times. 12. Click the STOP button to stop mo nitoring the data. 13. If the final voltage with the paper out is much different from the initial paper out value, you probably touched the plates and should repeat the experiment. Conclusions 1. What happened to the voltage as the plates got closer together ( decreasing)? 2. What were your best fit values for the charge Q and C sys ? 3. How well did your model fit the data? Try to explain any discrepancy. Hint: W hat approximations are made when deriving the parallel plate capacitance (C = κ εo A/d) from Gauss’ Law? 4. Briefly discuss the value of computer modeling. 5. Examine Table II . Does the data agree with Equation 5 ? What does a dielectric do? d Lab report ASAP PLEASE. Physics 2320 Lab Title: Your Name Due Date: Lab reports must be typed. For equations, you can use the equation editor in Microsoft. Abstract: In the Abstract, you summarize your findings from the experiment in a short paragraph. You will briefly state the results and what you learned from the experiment. Introduction Summarize the introduction found in the in the lab write-up. For example, in the Capacitance lab, one objective is to investigate how capacitance varies with separation etc. . Theory Summarize the theory behind the experiment. For example, in the Capacitance lab, show how the equation is derived from equating the electric field of a charge distribution with gradient of the potential, or, Then show the governing equation for the problem you are trying to address in the lab which is how to us a model to find the charge in the capacitor and the system capacitance, Data Present in this section your data. This should include the raw data and any data obtained from the raw data. In this section, present the graphs plotted from the data. For example, in the Capacitance lab, I expect to see your table of Voltage versus Separation of plates, as well as table 2 in the lab. Results, Data Analysis and Sample Calculations In this section, you need to present any data analysis done on the obtained data in order to draw your conclusions. If you have done repetitive calculations, you need to show one sample from each calculation. For instance, in the capacitance lab, show the plot that shows best agreement with the data and the best fit model with the charge and system capacitance like, With a caption describing what is plotted. In this section you report on the Model and the values of Q and Csyst you obtained. Also you report on your investigation with the dielectric materials. Conclusions In this section, you will answer questions posed in the lab write-up. In the Capacitance lab, you need to answer questions posed in the Conclusion section of the lab instructions that you downloaded from BB. If the lab instructions do not have any questions on the performed lab, then you draw your own conclusions and your findings. References If any…
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