of 6 + Page Fit CAPACITORS AND DIELECTRICS I. OBJCTIVES In this lab you will explore the dependence of the capacitance C of a parallel plate capacitor on the plate separation d and the on the plate area A. You will also determine the permittivity of vacuum &, and the dielectric constant x of rubber. II. EQUIPMENT Parallel plate capacitor with adjustable gap, aluminum plates, multimeter, calipers, rubber sheets, ruler III. INTRODUCTION A parallel plate capacitor consists of two conduction plates of area A separated by a dielectric of thickness d. d Figure EC2-1. A parallel plate capacitor with a variable plate separation In Fig. EC2-1 we show a parallel plate capacitor with circular plates of radius R, separated by air. The capacitance of a parallel plate capacitor is given by the expression: C= AE. (EC2-1) d If we place a dielectric (insulating) material in the space between the two plates the electric field of the capacitor aligns the electric dipole moments of the dielectric molecules. The net result of this alignment is an increase in the capacitance which is now given by the equation: C= KAE. (EC2-2) d Here & is the dimensionless dielectric constant of the dielectric that separates the two conducting capacitor plates. IV. EXPERIMENTAL METHOD The capacitance in this experiment will be measured using a multimeter. In the first part of the experiment you will use a parallel plate capacitor with circular plates and measure the capacitance C as function of the separation d of the capacitor plates. From Eq. EC2-1 it follows that if we plot C versus (see fig.2) we will get a straight line that passes through the origin and has a slope S = AE (EC2-3)of 6 + Page Fit C 1/d Figure EC2-2 If the space between the plates is now filled with a dielectric of dielectric constant & the slope of the plot in fig.2 is given by the expression: S = KAE (EC2-4) In the second part of the experiment you will use a capacitor formed by the overlap of two rectangular conducting plates of dimensions L and b separated by a constant distance d. a =L - c Bottom plate Area of shaded region is the area of the capacitor. It is the region of overlap between the plates. Area = ab. Bottom plate Top plate Top plate Figure EC2-3. The arrangement of the 2 rectangular plates to achieve a capacitor of variable area. The two plates are shown in fig.3a. If we overlap the two plates along their long dimension by a length a and place one on top of the other, the effective area A of the resulting capacitor is equal to the product ab. The area A is indicated in fig.3b in gray- Equation 1 becomes: d (EC2-4) If we plot C versus a (see fig.4) we get a straight line that passes through the origin and has a slope s given by the equation: S = -beo (EC2-5) V. PROCEDURE 2of 6 Page Fit V-1: Use the parallel plate capacitor with circular plates. Using a ruler and basic geometry, measure and record the area of one of the plates Using the graduations on the base of the capacitor, set the plate separation to be 4 mm and record the capacitance. Move the sliding plate away from the fixed plate 5 to 10 cm and then reset the distance to be 4 mm. Again record the capacitance. Do this to record a total of 5 values of C for 4 mm. Using this same procedure, measure the capacitance 5 times at the following plate separations: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15 mm. See fig EC2-4 Figure EC2-4 V-2: Use the provided dielectric material to fill the gap between the plates on the circular capacitor. You should use two or three sheets of material (your choice). Make sure the sliding plate is snug against the dielectric. Move the sliding plate a few cm away from the fixed plate and then push it back against the dielectric material. Record the capacitance and the plate separation 5 times. See fig EC2-5 34 of 6 + Page Fit EXTRCH Figure EC2-5 V-3: Use the two rectangular aluminum plates to form a capacitor as shown in fig.EC2-3. The lower plate should be resting on a book or a notebook so that the clip used to connect the wire does not cause the plates to sit crooked. Use four small cardboard separators or plastics disks (as provided in lab) to keep the two plates at a distance d. See fig EC2-6. Record the value of d and estimate the uncertainty in d. Measure the dimension b and L using the ruler. Figure EC2-6of 6 Page Fit Set the distance c equal to 2 cm. Use the multimeter in the to measure C. Record the values of C; c and a. You should remove and replace the top plate and again set c = 2 cm. Record the capacitance You should record the value of C a total of 5 times at each value of c, removing and replacing the top plate each time. Repeat the measurement using c = 3 cm through 12 cm in steps of approximately 1 cm. 0 146- Figure EC2-7 VI. FOR THE REPORT VI-1. Tabulate the data recorded in V-1. Your table should include columns for C, d, and 1/d. values of C and d recorded in sections V-1. Plot C versus - . Use linest to determine the slope s and its uncertainty Os. From the slope and eqs EC2-3 determine the permittivity of free space and its uncertainty. Report your answer as to + Oso. Compare this to the accepted value. You may take the uncertainty in the area of the plates to be negligible. VI-2. Using the average values of C and d from section V-2 and your experimentally determined value of So + Oso: determine the dielectric constant x of the inserted material. Hint: use eq EC2-2. Report your answer as XI Ox. You may use the standard deviation of the mean of the values of C and d for the uncertainty in these parameters (remember to show the work for these calculations as well). You may take the uncertainty in the area of the plates to be negligible. VI-3. Tabulate the values of C, c and a recorded in section V-3. Plot C versus a. Use the least squares method to determine the slope s and its uncertainty. From these and eqs EC2-5, calculate the effective separation d and its uncertainty. Use your experimental value and its uncertainty of a in your calculations. Report your result as d + Ca. Compare this to your measured value. Do they agree within the range of uncertainties