Problem Description
The aim of the laboratory project is to measure the capacitance of the experimental setup made with the copper sheets and the dielectric material placed between the sheets. Distilled water and cooking oil were used as dielectric materials. The calculations of dielectric constant for distilled water and cooking oil were performed. The sources of errors were assessed. The experimental dielectric measurements are supposed to comply with the dielectric constant of the copper.
Design
The copper sheets were cut into different sizes, namely 4”X6”, 4”X5”, 4”X4”, and 4”X3”. Two equal copper sheets were used for the experimental setup. It was assembled so that the copper sheets faced each other; they were placed on a white foam board base. The dielectric, in a zipped plastic bag, was placed between the two copper plates. The first set of experiments was performed with distilled water, and the second set with cooking oil. The measurements of capacitance were performed with the multi-meter and recorded. The next set of experiments was performed with the other sheets (sheets of different sizes). The exemplified measurements are illustrated in Figures 1 and 2.
Theoretical Results
Despite of the methodological difficulties with base set up and copper sheet cutting, the operations were performed accurately. The calculations section is presented in Table 1 and 2. The distilled water is observed to amplify the capacitance of the capacitor, and this is a significant property. The same pattern is observed for the experiment with cooking oil; the only difference observed is about values.
Calculations
The capacitance C (nanoFarad) calculates as:
C=ε0kA d, (1)
where ε0 is constant permittivity of free space, ε0 = 8.8541∙10-12 F/m ; A – the area of the copper sheet (m2); d - the distance between the two capacitances in parallel (m), k - relative permittivity of the dielectric material between the plates (dimensionless).
Basing on the expression (1), the relative permittivity of the dielectric material k:
k= dCε0A (2)
The calculations are presented in Tables 1 and 2.
The Calculations of the Dielectric Constant for the Distilled Water
The Calculations of the Dielectric Constant for the Cooking Oil
Conclusions
The experiment of capacitance measurements with the copper plates and two materials between the plates: water and oil have been performed. The experimental set up has been thoroughly assembled, and the experiments performed strictly according to methodology. Therefore, the experimental measurements do not have the systematic error; only the random errors are present. The random errors are present in all the experiments, irrespective of the researcher’s skills and experience. The margin of error is caused by errors at measurement, which are caused by the device, and assessed as 5% for the distilled water measurements, and 10% for oil measurements.
Basing on the capacitance measurements, the permittivities of water and cooking oil have been calculated by formula (2). The permittivity value increases with the decrease of the copper plates area for both dielectrics tested. The permittivity of water is about 100 times greater than the permittivity of oil. Therefore, oil reveals stronger dielectric properties.
The experiment can be improved, if the capacitance measurements are performed several times to assess the error for the experiment.
