Parallel Plate Capacitor and Dielectrics
Different materials were placed in between the plates of a parallel plate capacitor and the change in capacitance for each of the materials was tested using a galvanometer. The results were studied to determine the dielectric constant for each of the dielectric materials and to determine the permittivity of air.
By its self, results show that the parallel plate capacitor's capacitance is inversely proportional to the distance between the plates. This relationship was plotted on a graph. The slope of this graph determined the permittivity of air to be 2.04E-10 F/m
For each material the capacitance increased by a constant factor, under a constant voltage. This is known as the material's dielectric constant. The relationship between Capacitance versus the change in thickness of a certain type of paper was inversely proportional. This relationship was graphed and using its slope, the dielectric constant for the paper was calculated to be . The dielectric constant was also calculated for both plastic and wood to be and respectively.
This experiment concludes that the capacitance increases when the materials are placed in between the plates of the parallel plate capacitor.
ichael Faraday first conducted experimentation of Dielectrics . The SI unit the Farad, to denote 1 Coulomb per Volt (C/V), was named after this scientist. Through his experiments on capacitors, he found that by filling the inner plates of a capacitor with different kinds of materials, it increases the capacitance by a constant factor, the dielectric constant. Each material used in between the plates (including air) has a dielectric constant. Faraday also discovered that dielectrics effect the "break down" voltage, the maximum potential difference that can be applied between the capacitor plates before the dielectric breaks down and forms a conducting path. . This experiment tries to conduct an experiment similar to Faraday's on the properties of dielectrics pertaining only to changes in capacitance.
To calculate some of information needed from the results, the experiment involved the following theory. The Capacitance (C) of the parallel plate capacitor can be calculated given by the area of the plates, the separation (d) between the plates and the permittivity of the material () between the plates:
C = A / d equation 1
The dielectric constant (k) can be calculated, given the permittivity constant of the dielectric () and the permittivity of a vacuum (0).
k = / 0 equation 2
The dielectric constant can also be found given the measured capacitance (C) of the dielectric material with the capacitance of a vacuum (C0), by combining equations 1 and 2:
k = C / C0 equation 3
The Capacitance (C) can be determined given the a charge in Coulombs, and Voltage from the power supply:
C = q / V equation 4
Figure 1 describes how the apparatus for the experiment was set up. This involved a voltmeter, to measure the voltage being provided by the power supply with a double-pole-double throw switch. The load in the circuit was a resistor with the resistance of 1 Mega Ohm. The amount of charge in coulombs was measured using a galvanometer. There were also two capacitors used, one of known capacitance of 0.00948F to calculate the sensitivity of the galvanometer, and a parallel plate capacitor with a vernier scale used in experimenting with dielectrics.
EXPERIMENTAL METHOD, OBSERVATIONS & RESULTS
Determining Galvanometer Sensitivity
In order to convert the measured deflection from the galvanometer into coulombs, the sensitivity of the galvanometer needed to be determined. This is done using the capacitor of a known capacitance, it being 0.00948 F. The power being supplied is around 83V. After allowing some time for the capacitor to charge, the throw switch turned off the power, causing the capacitor to discharge. When this happens, the amount of deflection shows on the galvanometer and is recorded. This is repeated about three times to get an average deflection of 4.9mm. Using equation 4, from the Capacitance and the known voltage, the amount of charge in coulombs is determined and is then divided by the amount of deflection recorded. The sensitivity of the galvanometer calculated is 0.16x10-5 C/m The capacitor then is replaced with the parallel plate capacitor and is ready to conduct the following experiments.
Determining permittivity of Air
By finding the slope on a graph of the Capacitance versus the change in the inverse linear distance between the parallel plates, and by determining the area of the plates, the permittivity of the material between the plates can be calculated using equation 1.
A standard metric ruler is used to measure the diameter of the plates. The radius is then plugged into the area of a circle formula A=2r2. The radius of the plate is 12.5cm and the area of the plates calculated is 981.7cm2 or 9.81E-2m2
Knowing the sensitivity of the galvanometer, it is now possible to use it to measure charge. At a potential difference of 202 volts, the amount of deflection caused by the capacitor discharge read on the galvanometer is recorded at gradually increasing separations, shown on the vernier scale. This is initiated by throwing the switch to the power supply off after allowing the capacitor a moment to build up charge. Table 1 shows the observed results of the experiment. The amount of discharge from the capacitor at each separation is then calculated by multiplying the deflection by the sensitivity of the galvanometer.
It appears that the relationship between the amount of capacitance and the separation distance is inversely proportional. Graph 1 is based on this relationship where the amount of capacitance is against the inverse of the separation.
Using this slope and equation 1, the determined air permittivity is 2.04x10-4 F/m.
Determining dielectric constant for Paper.
Finding the dielectric constant for paper involves finding the permittivity of the paper, and then calculating the dielectric constant using equation 2. The procedure is identical to the previous, except sheets of paper occupy the space between the plates. The thickness of each sheet of paper measures to be about 7m or 7 x 10-3 mm. The amount of discharge was measured for every additional sheet placed in between the capacitor plates until 6 sheets. The separation distance between the plates equals the thickness of the paper stack. Table 2 shows the observed results from this experiment, including the calculated discharge. The relationship of the discharge versus the inverse of the thickness of the stack (or separation) is plotted on graph 2.
Using the slope of this graph in equation 1 determines the paper's permittivity to be . Using the paper's permittivity and the permittivity of air (for this experiment's purpose, the permittivity of air is close enough to a vacuum's) in equation 3, the dielectric constant for paper is calculated to be .
Dielectric constants of other materials
A dielectric constant for a certain material can be determined by finding the ratio of its capacitance to the capacitance of the capacitor without the material, but at the same separation.
The thickness of each material was measured, and the amount that felt sufficient to conduct the test is recorded as the plate separation. For each material, the voltage is kept at a constant 100V. The amount of discharge through the material is recorded, then again without the material at the same separation distance. The observed results and calculated charge is shown in table 3. Using equation 4, the capacitance for each instance of the material is calculated. Then by using the capacitance of each material in equation 3, the dielectric constant is calculated.
AREAS OF EXPERIMENTAL ERROR
By far the most erroneous of all the procedures necessary in all of the experiments above is the reading of the galvanometer. Having little experience with this device, it is difficult to determine the maximum swing on the meter, given only an instant to capture the reading with the naked eye.
This error explained above shows through out the experiment because most of the data depends on the galvanometer readings. It is not possible to determine a certain percent of error in this respect.
The calculated permittivity of air is also very incorrect. This experiment determined that the permittivity of air was 2.04x10-10 and the accepted value is around 8.85x10-12 , which is actually the permittivity of a vacuum but close to that of air. It is obvious that this is a huge error of 2205% of from the accepted value! Sources of error may point again to the reading of the galvanometer, but the error is more likely the cause of a computational error.
Also a noteworthy area of error is in the separations made. The separations may be too far than they should be made. Note that in finding the permittivity of air, which the separation distance jumped from 0.3 and 0.5 to 1.0 and 2.0. Perhaps a more accurate reading could have been made using closer separations
Despite the poor accuracy of this experiment, it has yielded some sound conclusions. From the apparent increase in capacitance as the separation between the plates increased. This means that Capacitance is inversely proportional to the separation distance. This experiment also concludes that by occupying the space between the plates with some material, the capacitance increases. Also that each kind of material increases the capacitance of the capacitor by a constant factor. This is known as the dielectric constant.