L05: Capacitors and Inductors 50 Capacitors 51 Outline of the lecture: Capacitors and capacitance. Energy storage. Capacitance formula. Types of capacitors. Inductors and inductance. Inductance formula. Ideal vs. realistic inductors. Lenz s law. Types of inductors. Capacitors are one of the fundamental passive components. In its most basic form, it is composed of two plates separated by a dielectric. The ability to store charge is the definition of capacitance. A dielectric is an insulator that can be polarised by an electric field. Conductors capacitor_ Tantalum electrolytic capacitor (polarized) Dielectric The charging process Initially Source Fully Charging removed uncharged Charging a Capacitor 52 V S Dielectric Leads Plates Electrons A B A capacitor with stored charge can act as a temporary battery. Charge and Capacitance Capacitance is the ratio of charge to voltage: = Rearranging, the amount of charge on a capacitor is determined by the size of the capacitor () and the voltage (). = 53 If a 2.2 capacitor is connected to a 5 source, what is the charge?
Energy Storage 54 A capacitor stores energy in the form of an electric field that is established by the opposite charges on the two plates. The energy of a charged capacitor is given by the equation: Where: = the energy in joules C = the capacitance in farads V = the voltage in volts = 1 2 The Capacitance Formula The capacitance of a capacitor depends on three physical characteristics: =8.85 10 Where: is the relative dielectric constant. is the plate area. is the distance between the plates. 55 Note that is directly proportional to and, and inversly proportional to. Example 56 Types of Capacitors 57 Given that =4 for oil, find the capacitance of a 4 diameter capacitor immersed in oil if the plates are separated by 0.25. Answer: =8.85 10 The area is given by: = = 0.02 =1.26 10 Hence: =8.85 10 4 1.26 10 0.25 10 =178 : High working voltage. Ceramic Disk: Non-polarised. High. Solder Ceramic dielectric Lead wire soldered to silver electrode Dipped phenolic coating Silv er electrodes deposited on top and bottom of ceramic disk
Plastic Film: Non-polarised. Large plates. Types of Capacitors 58 Plastic film dielectric High-purity foil electrodes Outer wrap of polyester film Capacitor section (alternate strips of film dielectric and Lead wire foil electrodes) Solder coated end Variable Capacitors Variable capacitors typically have small capacitance values and are usually adjusted manually. A solid-state device that is used as a variable capacitor is the varactor diode; it is adjusted with an electrical signal. 59 Electrolytic: Polarised. Non-precise. High leakage current. _ Inductors Inductance is the property of a conductor to oppose a change in current. The effect of inductance is greatly magnified by winding a coil on a magnetic material. Common symbols for inductors (coils) are: 60 Air Core Iron Core Ferrite Core Variable Inductance is a measure of a coil s ability to establish an induced voltage as a result of a change in its current. Inductance Formula In the ideal case, four factors affect the amount of inductance for a coil. The equation for the inductance of a coil is: = l where = inductance in henries (). = number of turns of wire. = permeability in / (same as /) l=coil length on meters. = the cross section area of the core. 61
Example What is the inductance of a 2 long, 150 turn coil wrapped on an low carbon steel core that is 0.5 diameter? The permeability of low carbon steel is 2.5 10 /. Answer: = = 0.0025 =7.85 10 = l 62 = 150 2.5 10 7.85 10 0.02 =22 Realistic Inductors The inductance given by the previous formula is for the ideal case. In practice, inductors have winding resistance ( ) and winding capacitance ( ). An equivalent circuit for a practical inductor including these effects is: R W 63 C W L Lenz s law states that: Lenz s Law When the current through a coil changes, an induced voltage is created across the coil that always opposes the change in current. 64 Types of Inductors The most common types of inductors are shown below: 65 This will be examined in more detail at a later stage. Encapsulated Torroid coil Variable
End of Lecture! 66 Any Questions?