Effect of the Construction of Simple Capacitors to its Capacitance Conductive Plates Capacitors A capacitor is a device that is used to store electrical potential energy. It has many uses, including tuning the frequency of radio receivers, eliminating sparking in automobile ignition systems, and storing energy in electronic flash units. A typical design for a capacitor consists of two parallel metal plates separated by a small distance or sometimes Dielectric an insulating material called a dielectric. Each capacitor plate carries a charge of the same magnitude, one positive and the other negative. The ability of a capacitor to store Figure 1. Typical Parallel Metal Plate Capacitor. a charge on its conductive plates is its capacitance value measured in Farads (F). Formula for Capacitance (C): The magnitude of the charge (Q) on each plate of a capacitor is directly proportional to the magnitude (V) of the potential difference between C = /Ap ; SI unit is Coulomb per Volt(C/V) or the plates. Farad (F) Electric Field (E) Between the Plates: The magnitude of the Electric field (E) between plates is given by the E = EDErA - ; = surface charge density formula surface charge density (o) divided by area (A) of one of the metal plates or charge (Q) divided by the product of the absolute permittivity (zo), = absolute permittivity relative permittivity (&) and area (A) of one of the metal plates. Where, of &. = s,= absolute permittivity 8.85 x10-12Nm /C2. (refer to attachment A.1 for the values of Er) A = area of one of the metal plates Electric Potential Difference The magnitude of the electric potential difference (4V) between the two plates (4V) Between the Plates: is the product of Electric field (E) and the distance (d) between the two metal plates. Furthermore, it can also be equated, by using the previous equation, to the product of AV = Ed = Qd TEJETA Charge (Q) and distance (d) divided by the product of absolute permittivity (co), relative permittivity (&) and area (A).Different Constructions of the Capacitors with their Capacitance Values: Conductive Plates 2TEOErL R d C = 4neger 72- 121 C= In(#2/ R ) C = EDEr /d Q E = E= E =- Q Dielectric 4TIEDEr(12-11)2 2TEEr( 12-11) FoErA A Cylindrical Q(12-1) AV = AV = - InR AV = 0d/ 2 / AEDET Parallel-Plate Spherical A = charge per unit area (C/m?) Sample Problem: A parallel plate capacitor has a square plate of side 6.0 cm and separated by a distance of 2 mm. (a) Calculate the capacitance of this capacitor. (b) If a 15 V battery is connected to the capacitor, what is the charge stored in any of the plates? (The value of &, = 8.85 x10-12Nm2/C2 & of & = 1) Given: Solution: A = 6.0 cm x 6.0 cm EDA Q = CV A = 3.6 x 10-3 m C= d d = 2 mm = 2.0 x 10-3 m C = (8.85 x 10-12 Nm /C2)(3.6 x 10-3 m?) Q = 1.593 X 10-11F (15V) V = 15 V 2.0 x 10-3m Q = 2.39 x 10-10 C C =7 3.186 x 10-1+N/C2 C = Q = ? 2.0 x 10-3m C = 1.593 x 10-11 F Q = 23.9 x 10-9 C = 23.9 nC ACTIVITY: Solve the following problems. Use the rubrics as your guide in presenting your solution (refer to attachment A.2 at the next page). 1. Calculate the voltage of a battery connected to a parallel plate capacitor with a plate area of 3.0 cm and a plate separation of 5mm if the charge stored on the plates is 6.0 x 1015C. (The dielectric used is Teflon) 2. A cylindrical capacitor has a length of 6 cm is made of two concentric rings with an inner radius of 2.5 cm and an outer radius of 3.5 cm. How much charge is present in this capacitor if it is connected to a 15 V battery? (&, = 1)A.1 Different Values of Relative Permittivity (&) Based on the Material Material Er Material ET Vacuum Quartz 5 Freon Diamond 5-6 Air 1.0005 Wet soil 5-15 Styrofoam 1.03 Mica (ruby) 5.4 Polyurethane foam 1.1 Steatite 5.8 Paper 1.3-3 Sodium chloride (NaCl) 5.9 Wood 2-5 Porcelain 6 Dry soil 2-6 Neoprene 6.6 Paraffin 2.1 Silicon nitride (Sig N4) 7.2 Teflon 2.1 Marble 8 Vaseline 2.16 Alumina (Al203) 8.8 Polyethylene 2.25 Animal and human muscle 10 Oil 2.3 Silicon (Si) 11.9 Rubber 2.4-3 Gallium arsenide 13 Polystyrene 2.56 Germanium 16 PVC 2.7 Ammonia (liquid) 22 Amber 2.7 Alcohol (ethyl) 25 Plexiglass 3.4 Tantalum pentoxide 25 Nylon 3.6-4.5 Glycerin 50 Fused silica (SiO2) 3.8 Ice 75 Sulfur 4 Water 81 Glass 4-10 Rutile (TiO2) 89-173 Bakelite 4.74 Barium titanate (BaTiOs) 1.200 * For static or low-frequency applied electric fields, at room temperature