Experiment FT1: Measurement of Dielectric Constant


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1 Experiment FT1: Measurement of Dielectric Constant Name: ID: 1. Objective: (i) To measure the dielectric constant of paper and plastic film. (ii) To examine the energy storage capacity of a practical capacitor. 2. Apparatus/components: DC power supply Digital multimeter with capacitance measurement function A4 papers and plastic films (transparency), 10 sheets each Micrometer (to measure thickness of papers and plastic films) Electrolytic capacitors, 50V 1000 µf and 2200 µf Resistor, 10 kω 3. Theory: Capacitor, also known as an electrical condenser, is a device that can store electric charge or energy. It can also be used in various types of circuit functions involving: i) Oscillator (alternate charging and discharging of the capacitor); ii) Blocking the flow of direct current; iii) Filter (varying impedance with respect to frequency). In its simplest form, a capacitor consists of two metallic plates (conductors) separated by a nonconductive layer called the dielectric. The dielectric is a good insulator (incapable of passing electrical current, but is capable of passing electrical flux). When a voltage is applied across a capacitor, one plate becomes positively charged, the other negatively charged, with the corresponding electric field directed from the positive to the negative. The capacity of a capacitor is represented by its capacitance, the amount of electric charge it can hold per volt, or C = Q / V. The charge stored in a capacitor is given by Q = CV (1) Page 1 of 7
2 where Q = quantity of electrical charge on one plate C = capacitance of the capacitor V = voltage drop across the capacitor The capacitance of a capacitor is dependent on the size of the plates, the spacing between them, and the kind of dielectric medium used as the insulator. For a parallelplate configuration, the relationship is expressed as follow: where A 0 A C = = r d d C = Capacitance in farads, F A = overlapping area of the plates in square meters, m 2 d = separation distance between plates in meters, m ε = dielectric constant of the dielectric medium ε o = free space dielectric constant (8.854 x F/m) ε r = relative dielectric constant of the dielectric medium (2) The above equation indicates that the capacitance is directly proportional to the surface area of the plates and the dielectric property of the dielectric medium. The capacitance is inversely proportional to the spacing between the plates. For example, doubling the surface area of the plates doubles the capacitance, and reducing the thickness of the dielectric by onehalf also doubles the capacitance of a capacitor. A capacitor can be formed with air (where ε r = 1) as the insulator between the metal plates. When air space is replaced with a plastic film, it would be found that the capacitance will increase. This increase in capacitance shows that plastic has a higher dielectric constant than air. If C is measured and plotted against 1/d, a straight line will be obtained, the slope of which will be 0 r A. Knowing 0 and A, the value of can be calculated. When a battery is connected to the two metal plates, the capacitor will be charged up to the voltage of the battery. When the battery is removed, the charges stored in the capacitor will remain on the metal plates. Hence, the voltage across the capacitor will stay even though the battery has been removed. This phenomenon shows that the capacitor is able to store electric charge or energy. When a light bulb is connected to the capacitor terminals, it will light up. The light intensity will decay as the capacitor discharges through the light bulb. The charge quantity decreases as the capacitor release the stored energy to the light bulb. Practical capacitors use thin dielectric media with high dielectric constant to reduce the physical size of capacitor for the desired capacitance. The common types of dielectric media include aluminum oxide (electrolytic capacitor), mica, glass, ceramic, and plastic films (polyethylene, polypropylene, polystyrene, and polycarbonate). r Page 2 of 7
3 4. Procedure: (i) Measurement of Dielectric Constant 1. Measure the overlapping area of the parallel plates, A. Plate 1 Overlapping area, A Plate 2 2. A sheet of A4 size paper is to be inserted between the two plates. A fixed pressure is to be applied between the two plates. 3. Measure the capacitance using a multimeter. 4. Repeat step 3 by progressively adding the number of papers between the two plates (up to 10 sheets). 5. Using a micrometer, measure the thickness for 10 sheets of papers. Assuming the thickness for every sheet is the same, calculate the thickness for 1 sheet of paper. 6. Plot the graph of C versus 1/d and determine the relative dielectric constant (ε r ) of the paper. 7. Repeat steps 2 6 with plastic sheets. (ii) Energy Storage Capacity 1. Set the voltage of the dc power supply to 12V. 2. Connect the negative terminal of the 1000µF electrolytic capacitor to the negative terminal of the dc power supply. Connect the other terminal of the capacitor to the positive terminal of the dc power supply. 3. Measure the voltage across the capacitor, V Without switching off the dc power supply, remove the wire connected to the capacitor. 5. Measure the voltage across the capacitor, V Connect a 10kΩ resistor to the terminals of the capacitor. Record the discharging time or time duration for the capacitor voltage to decay to 1 volt. 7. Repeat steps 1 6 with the 2200µF electrolytic capacitor. 5. Precautions: Make sure that the two plates are pressed well with a fixed weight placed flat on the plates. This will avoid air gaps between various layers. Make sure that the two plates are not shorted during the experiment. Page 3 of 7
4 6. Measurement Results: (i) Dielectric Constants of Paper and Plastic Overlapping Area of Parallel Plates, A = m 2 Thickness for 10 sheets of paper, t p10 = mm Thickness for 1 sheet of paper, t p = mm Table 1: Dielectric Constant of Paper No. of Papers, n d = n t p (mm) 1/d (mm 1 ) Capacitance (nf) Thickness for 10 sheets of plastic film, t f10 = mm Thickness for 1 sheet of plastic film, t f = mm Table 2: Dielectric Constant of Plastic No. of Plastic films, n d = n t f (mm) 1/d (mm 1 ) Capacitance (nf) Page 4 of 7
5 For paper, the gradient of the graph, C/ (1/d) = nfmm The relative dielectric constant of paper, (ε r ) paper = For plastic, the gradient of the graph, C/ (1/d) = nfmm The relative dielectric constant of plastic, (ε r ) plastic = Discussions: 1. Describe how we make sure the overlapping area of the parallel plates is consistent throughout the experiment? 2. Propose a method to reduce the error in measuring the thickness of the paper / plastic films. 3. Justify whether it is reasonable to assume the thickness for every sheet of paper / plastic film is the same as far as the dielectric constant measurement method concerned. 4. Is the graph of C versus (1/d) a perfect straight line? If not, analyze the causes of this deviation. 5. Justify whether the measurement results are satisfactory. Page 5 of 7
6 (ii) Energy Storage Capacity For 1000µF electrolytic capacitor: Voltage with dc power supply connected, V 1 = V Voltage with dc power supply disconnected, V 2 = V Timeconstant of discharging circuit, τ = R C = s Discharging Time, T = s For 2200µF electrolytic capacitor: Voltage with dc power supply connected, V 1 = V Voltage with dc power supply disconnected, V 2 = V Timeconstant of discharging circuit, τ = R C = s Discharging Time, T = s Discussions: 6. Describe how we make sure that the voltage is measured as accurately as possible. 7. Propose a method to reduce the error in measuring the discharging time. 8. Examine the relationship between the discharging time and the timeconstant of the discharging circuit. 9. Justify whether the measurement results are satisfactory. 10. If we assume the thickness of dielectric media in the electrolytic capacitors is 1 µm, and the relative dielectric constant is 20, compute the required sizes for the parallel plates. Compare these values with the actual size of the capacitors. Deduce how the manufacturers manage to pack the parallel plates into the actual volumetric dimensions of the capacitors? Page 6 of 7
7 7. LABORATORY REPORT The report should contain the following: (1) This lab sheet (covering the Objectives, List of instruments/components, Basic Theory, and Tabulation of observed and computed data). (2) Graphs of the measurement results (3) Discussion, and (4) Conclusion. Please obtain signature from the lecturer before you leave the lab: Date : IMPORTANT NOTES TO THE STUDENTS: 1. Read the lab sheet before attending the experiment session. 2. Bring along the necessary GRAPH PAPERS and calculator to the lab. 3. The completed laboratory report must be submitted to the laboratory technician AT THE END OF THE EXPERIMENT SESSION. 4. Each student is required to submit an INDIVIDUAL REPORT. Page 7 of 7
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