Lab4-Capacitors

Capacitors NAME: ____Sehajpartap Gill_______________ Date: ____7/19/2021______ Lab Partner’s: _______(No Contact, Worked Solo)______________ Access the University of Colorado’s PhET simulation: Capacitor Lab OBJECTIVES :  To understand how capacitance varies with the separation between the plates  To understand how capacitance varies with the area of the plates  To understand how the dielectric affects the stored charge, energy, and voltage between the plates of the capacitor, when it is connected or disconnected from the battery BACKGROUND: When a capacitor is connected to an EMF ( E ), the plates attain charge from the terminals of the battery. The amount of charge is governed by the geometry of the capacitor. For a parallel plate capacitor, the capacitance is given by 0 A C K d   where A is the effective plate area (the area effectively overlapping, d is separation of the plates, o  is electric permittivity of free space, and K is the dielectric constant for the insulating material in the inner plate region. In this lab, you will investigate this relation. First you will keep the separation constant and vary the area. In this case, a plot of C vs A should be a straight line with the slope given by 0 1 K m d   Then, you will keep the area constant and vary the separation. Here, a plot of C vs 1 d should be a straight line with the slope given by 2 0 m K A   INSTRUCTIONS: Use Excel to plot the graphs and insert or attach all graphs, plots, and tables to this lab assignment. Convert values to SI units and show all your calculations. PROCEDURE: Open the simulator and select the middle tab: Dielectric .

PART I: Capacitance 1) Select “paper” from the choice of dielectrics in the menu on the right-hand side. Use the horizontal double-tip arrow to insert the dielectric completely inside the capacitor. Check “Capacitance” to see the capacitance meter. The battery could be either connected or disconnected for this part. NOTE : The exponent of the value shown below the capacitance meter should be negative. Common capacitor values are of the order of pF or m F. Use negative exponents to obtain the correct values. 2) Record the values of the plates’ area A 0 (initially, it should be the smallest possible), distance between the plates d 0 (initially, it should be the largest possible), and corresponding capacitance. 3) Use the diagonal double-tip arrow to slowly increase the plates’ area and measure the corresponding capacitance 4 more times. Record your results in the table, include units. It is recommended to use SI units for all measurements and calculations. 4) Use Excel to plot capacitance as dependent variable against the area. Then, use linear regression to draw the best-fit line (also called trendline) to approximate the data with the linear model. Insert a screenshot of your graph below. It should contain: 2 A C 0 100.0 mm^2 .89 x 10^-13 F 1 152.9 mm^2 2.39 x 10 ^-13 F 2 250.5 mm^2 5.48 x 10^-13 F 3 311.4 mm^2 7.54 x 10^-13 F 4 400 mm^2 10.62 x 10^-13F

5) Restore the area to initial value. Use the vertical double-tip arrow to slowly decrease the separation between the plates and measure the corresponding capacitance 4 more times. Record your results in the table below, along with the reciprocal of the separation. Include SI units. d 1 d C 0 10.0 mm .1 .89 x 10^-13 F 1 9.0 mm .111 .98 x 10^-13 F 2 8.0 mm .125 1.10 x 10^-13 F 3 7.0 mm .143 1.26 x 10^-13 F 4 5.0 mm .2 1.77 x 10^-13 F 6) Use Excel to plot capacitance as dependent variable against the reciprocal of the separation between the plates. Then, use linear regression to draw the best-fit line (also called trendline) to approximate the data with the linear model. Insert a screenshot of your graph below. It should contain the features outlined in step 4. 0.1 0.11 0.13 0.14 0.2 0.00E+00 2.00E-14 4.00E-14 6.00E-14 8.00E-14 1.00E-13 1.20E-13 1.40E-13 1.60E-13 1.80E-13 2.00E-13 f(x) = 0 x + 0 C vs. 1/d Plot 1/d (1/mm) Capacitance (F) 7) Summarize, based on your graphs , how the capacitance of a parallel plate 4

capacitor depends on area of the plates and the separation between the plates. The capacitance of a parallel plate is directly proportional to the area of the plates. The capacitance of a parallel plate capacitor depends on the distance between the plates, their area, and the dielectric constant of the medium between the plates. The m^2 of the smallest two plates is inversely proportional with the distance and the separation in meters between the two plates. 8) Use the slope of one of the graphs to calculate K , the dielectric constant of paper. Show your calculations below. Compare it with the value given by the simulator and find the percent error . Part 2: Effect of the Dielectric on the Capacitor 1) Revert the values of the plates’ area and the plate separation to the original and remove the dielectric entirely from the capacitor. Show the capacitance, charge, voltage, and energy meters by checking off appropriate boxes on the right side of the simulator. (You will have to “connect” the voltmeter – place the red electrode on the upper plate with the positive charge, and the black electrode on the lower plate with the negative charge.) NOTE : The exponent of the values shown below all the meters should be negative. Use negative exponents to obtain the correct values. 5

Queries: 1) If the battery is connected, is the energy of capacitor-battery system conserved throughout the process of inserting the dielectric? Explain the changes of energy, if any. In this case the capacitance will increase as the dielectric is being inserted while the battery is connected. The battery will stay at the same voltage, which causes the Q on the capacitor to increase, and the energy of the capacitor. However, the increasing energy of the capacitor will not exactly balance or decrease the energy of the battery because of the insertion of the dielectric. 2) If the battery is disconnected, does the energy stored in the capacitor remain constant as the dielectric is inserted? Explain the changes of energy, if any. When the battery gets disconnected, the charge on the capacitor gets stranded on the capacitor plates which means it remains constant. Moreover, capacitance increases after adding the dielectric. By observing the data and equation, the energy decreases. CONCLUSION In conclusion, there was a lot we were able to observe and see through out this experiment, one is that the charge and voltage depend on each other, so if one increases the other one will increase as well. Moreover, the capacitance of a parallel plate is directly proportional to the area of the plates; capacitance is dependent on distance and area because when we did the experiment we realized as the area, or the distance increased the capacitance also increased. However, not always will it affect the energy or change the energy; like when the battery was connected, as the energy increased for the capacitor, the energy of the battery remained the same, but when the battery was disconnected the energy decreased and dielectric was inserted as well. There were many points made and were observable through the data and graphs we collected to help us better understand the logic of this experiment. 7