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Capacitance in DC Circuits 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› The intent of this presentation is to present enough information to provide the reader with a fundamental knowledge of Capacitance in DC Circuits and to better understand basic Michelin system and equipment operations. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC It will be recalled that electrons are loosely held in the rings of each atom of a good conductor such as copper, and only a small force is required to dislodge these electrons. Good conductive materials have an abundance of free electrons in their structure. On the other hand, it is a characteristic of insulating materials to have the electrons firmly held in the rings of each atom of the material, and considerable force is required to remove these electrons. Insulating materials have practically no free electrons in their structure. If an insulating material, sometimes called a dielectric, is placed between two plates of a good conducting material, an elementary form of a capacitor has been developed. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC The diagram below represents an elementary capacitor consisting of two metal plates separated from each other by a thickness of dielectric. Under normal conditions with the capacitor de-energized, the electrons in the dielectric revolve around the positive center of each atom in circular orbits. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC In Fig. 2 the capacitor is connected to a DC voltage source. Electrons will flow from the negative side of the source to Plate 2 and electrons will flow from Plate 1 back to the source of supply. This is the normal direction of electron flow from negative to positive. Plate 1 D.C. Source Plate 1 D.C. Source Plate 2 Fig. 2 Capacitor Charging Plate 2 Fig. 3 Capacitor Fully Charging The flow will continue until the potential across the two metal plates is equal to the DC source voltage and then the flow will stop. There will be practically no flow of electrons through the dielectric (or insulating) material between the plates. Plate 2 will now have a surplus of electrons and Plate 1 will have a deficiency of electrons. The electrons in the atoms of the dielectric material will be attracted toward the positive plate. However, they cannot flow from Plate 1 to Plate 2 because the electrons in a good dielectric (insulating) material are firmly held in each atom. This causes the electron orbits of each atom in the dielectric to become distorted into a form of elliptical pattern as illustrated in Fig. 3. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC In Fig. 3 the capacitor is completely charged with the voltage across the capacitor plates equal to the DC source voltage. Therefore, there is no electron flow. To simplify these illustrations, only three atoms are shown. In an actual capacitor, the atoms in the dielectric with their orbits in this distorted pattern would be legion in number. Plate 1 Plate 1 D.C. Source D.C. Source Plate 2 Fig. 2 Capacitor Charging Plate 2 Fig. 3 Capacitor Fully Charging If the capacitor is disconnected from the DC source supply, the large number of surplus electrons on the negative plate will be held to the plate by the attraction of the positive charge on the other plate. The electrostatic field effect created by the charged plates will cause the atoms of the dielectric to remain in a state of distortion. This distortion of the atoms is a manifestation of the electrical energy stored in the capacitor. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC In Fig. 4, a resistor is connected directly across the capacitor. The capacitor will now discharge through the conducting resistor. Electrons on the negatively charged plate (Plate 2) will flow off the plate through the resistor toward Plate 1 until they are equally distributed in the circuit, and then the flow of electrons will cease. The electron flow from the capacitor plate indicates that the electrical energy stored in the electrostatic field is being released from the capacitor. As the electrons flow from the negatively charged plate, the electron orbits of each atom of the dielectric will gradually change from the distorted elliptical pattern illustrated in Fig. 4 to the normal circular ring pattern as shown in Fig. 5. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC If too great a voltage is applied to the capacitor, the electrons in the atoms of the dielectric will be pulled from orbit. This breakdown in the insulating ability of the dielectric releases the energy stored in the capacitor and, in the case of a solid dielectric material usually permanently destroys its usefulness. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitance A capacitor can store electrical energy and also return this energy back into an electric circuit. It is important at this point to understand what the term capacitance actually means. Capacitance is really the property of a circuit or circuit component which allows it to store electrical energy in electrostatic form. Capacitors store energy, but other components also create capacitance effect. For example, the two wires of a circuit separated by air will act as a capacitor, or adjacent turns of a coil winding separated only by the insulation of the wire will have some capacitance effect. The standard unit of measurement for capacitance is the FARAD and may be defined as follows: A capacitor has a capacitance of one farad when a change of one volt across its plates results in the charge of one coulomb. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitance The farad is too large of a unit of measure for the typical capacitor. Therefore a smaller unit is used called the microfarad (F). Microfarad (F) = 10-6 Nanofarad (F) = 10-9 Picofarads (F) = 10-12 The capacitance of a capacitor can be increased by: 1. Increasing the plate area and, therefore, the area of the dielectric under stress. 2. Having the metal plates as close as possible with a resultant decrease in the thickness of its dielectric. 3. Using a dielectric with as high a dielectric constant as practical. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitance The charge on the plates of a capacitor with a given applied voltage is directly proportional to the capacitance of the capacitor. This charge is measured in coulombs and is directly proportional to the charging voltage. Therefore, if the charge on the plates is directly proportional to both the capacitance and the impressed voltage: The formula for calculating Capacitance is: Q = V * C This expression may be written in three forms: Q V C , or V Q Q , or C C V To illustrate the use of this formula, Assume a capacitor takes a charge of 0.005 coulombs when connected across a 100-volt DC source. Determine the capacitance of the capacitor in microfarads: 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Dielectric Characteristics Three factors were listed earlier in this unit, which affect the capacitance of a capacitor. One of these factors is the type of insulating material used for the dielectric. In practice, most capacitors are constructed using a dielectric having a higher dielectric constant than air. Just what does the term "dielectric constant" mean? First, the dielectric constant of an insulating material measures its effectiveness when used as the dielectric of a capacitor. Air is assumed to have a dielectric constant of 1. If a two-plate capacitor with air as a dielectric has the air replaced by paper impregnated with paraffin, its capacitance will increase. If the capacitance is doubled when using paper in place of air, then the dielectric constant of paper will be 2. This dielectric constant indicates the degree of distortion of the orbits of the electrons in the insulating material used for the dielectric for a given applied voltage. In the following table are the dielectric constants of some typical insulating material. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Dielectric Characteristics MATERIAL DIELECTRIC CONSTANT (K) 1.0 4.0 to 10.0 4.3 to 4.7 7.0 4.1 to 4.9 2.4 to 3.0 6.4 to 7.0 2.2 to 4.6 2.0 to 2.6 1.9 to 2.2 3.0 to 7.0 2.0 to 4.2 Air Bakelite Castor Oil Cellulose Acetate Pyrex Glass Lucite Mica Insulating Oils Paper Paraffin Rubber Compounds Hard Rubber 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Dielectric Characteristics If the voltage across the plate of a capacitor becomes too high, the dielectric may rupture. In other words, an excessively high potential tears electrons from the orbits of the atoms of the dielectric structure and the dielectric becomes a conducting material. This results in permanent damage to the dielectric as it is burned or punctured by the high potential. To assure adequate insulation protection, the insulating qualities of various dielectrics are given a "Dielectric Strength Rating", either in "volts-per-centimeter" or the "volts-per-mil" of thickness required to break down the dielectric. The dielectric strength rating is not to be confused with the dielectric constant as these two terms are entirely different. For example, the dielectric of paper is about 2 and that of Pyrex glass is approximate 4. However, the dielectric strength in terms of volts\millimeter for the paper is about 1200 volts as compared with only 325 volts of the Pyrex glass. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Parallel An increase in the capacitance can also be obtained by increasing the number of plates, which make up the capacitor. This is the same as increasing the plate area. Lead Lead Fig. 6 Fig. 6 shows a multi-plate capacitor with the plates in such a way as to have a maximum in plate area. It will be noted that alternate plates are common or paralleled. 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Parallel When capacitors are connected in parallel, the effect is the same as increasing the number of plates. This means that the total capacitance is equal to the sum of the capacitance of the individual capacitors. For example, in Fig. 7, three capacitors of 30, 10, and 15 microfarads are connected in parallel across the line voltage, designated as V. The charge on each capacitor in coulombs is: The total Capacitance Is equal to: C1 + C2 + C3 C1=30F C2=10F The voltage across the parallel circuit is: VT = VC1 = VC2 = VC3 C3=15F VT Fig. 7 Capacitors in Parallel QC1 = VC1 x C1 QC2 = VC2 x C2 QC3 = VC3 x C3 The total charge of the three capacitors in parallel is: Q Total = VT x CT Q Total = QC1 + QC2 + QC3 The total capacitance for the three capacitors in parallel is: CT = C1 + C2 + C3 CT = 30F + 10F + 15F = 55F 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Series When capacitors are in series, there is a single circuit path with all the dielectrics of the individual capacitors connected in succession. This is equivalent to increasing the thickness of the dielectric of one capacitor. As a result the total capacitance of the circuit is less than the capacitance of any individual capacitor. When capacitors are charged in a series circuit, the same numbers of electrons flow to each capacitor. Hence, each capacitor has the same charge in coulombs or each has the same value of charge (Q). C1=30F C2=10F C3=15F VT Fig. 8 Capacitors in Series 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Series The charge on each capacitor is the same: C1=30F QT = QC1 = QC2 = QC3 C2=10F C3=15F VT The voltage across the total series circuit is: Fig. 8 Capacitors in Series VT = VC1 + VC2 + VC3 The voltage can also be expressed with charge and capacitance: 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Series To find the equation to calculate the total capacitance in a series capacitive circuit, let’s substitute the previous equation for charge into the voltage relationship. C1=30F C2=10F C3=15F VT Fig. 8 Capacitors in Series Since (QT = QC1 = QC2 = QC3) then the following equation is true: Using the microfarad ratings of the three capacitors given in Fig. 8, the total capacitance of the series capacitor bank is: 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Series Exercises: 1. Calculate CT. C1=1F C2=1F VT 2. Calculate CT C1=1F C2=1F VT 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Series Exercises: 3. Calculate CT. C1= ? F VT C2=7F C3=8F 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Series Exercises: 4. Calculate CT. 5. Calculate Q on each capacitor 6. Calculate V on each capacitor C1=200F C2=50F C3=10F VT = 60 volts 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Series Exercises: 7. Calculate CT, QT, QC1, QC2, VC1, VC2 VC1 C1=20F VC2 C2=30F VT=100V 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#› Capacitance in DC Capacitors in Series Exercises: 8. Calculate CT, QT 10F 5F 50F VT=50V 01 – Capacitance in DC Presentation : IMS – Tech Managers Conference Author : IMS Stafff Author : IMS Staff 20F Creation date : 31 Oct 2012 Creation date : 08 March 2012 Classification : D3 Classification : D3 Conservation : Page : ‹#›
