1. Fall 2001ENGR201 Capacitance & Inductance1 Capacitor, also called electrical condenser, device for storing an electrical charge. In its simplest form a capacitor is two metal plates separated by a non-conducting layer called the dielectric. Air, mica, ceramics, paper, oil, and vacuums are used as dielectrics. When one plate is charged with electricity, the other plate acquires an opposite charge. The amount of electric charge a capacitor can hold is its capacitance. Because capacitors conduct direct current for only an instant, they are used to prevent direct current from entering parts of electric circuits. Large capacitors make it possible for power lines to transmit more power. Chapter 5 – Capacitance & Inductance (http://encarta.msn.com)

2. Fall 2001ENGR201 Capacitance & Inductance2 Schematic Symbol Capacitance – Diagram and Symbol

3. Fall 2001ENGR201 Capacitance & Inductance3 There are many different styles of capacitors, generally characterized by the type of dielectric material used and the application for which the capacitor is intended: General-purpose capacitors have dielectrics made of paper impregnated with oil or wax, mylar, polyestyrene, glass, or ceramic materials. Mica, glass, ceramic dielectrics are often used in high-frequency applications. Aluminum electrolytic capacitors use aluminum plates separated by a moistened borax paste and can provide relatively high values of capacitance in small volumes. These capacitors are often used in power supplies and motor-starting applications. Tantalum electrolytic capacitors have lower losses and more stable values (i.e. with respect to temperature) than aluminum electrolytics. Capacitor Types

4. Fall 2001ENGR201 Capacitance & Inductance4 http://www.seacorinc.com Capacitor Pictures (Also see Figure 5.2)

5. Fall 2001ENGR201 Capacitance & Inductance5 C is measured in Farads (F) A is the area (in m 2 )of the parallel plates d is the distance (in m) between the plates  is permitivity of the dielectric (  0 is the permitivity of free space, and  0 =8.85  10 -12 F/m Capacitor Characteristics

6. Fall 2001ENGR201 Capacitance & Inductance6 Two charged bodies separated by distance r will exert a force on each other, attractive or repulsive depending on whether the bodies have the opposite or same charge. This force is can be written: Since the force is inversely proportional to  the permitivity of the medium, the smaller the permitivity, the greater the force. Therefore, materials with a high permitivity do not support a strong (electrostatic) force field. Capacitor Characteristics

7. Fall 2001ENGR201 Capacitance & Inductance7 Capacitor Characteristics One farad is a large value. To illustrate, calculate the plate area needed to construct a 1F capacitor if: the plates are separated by 0.1mm (1.0  10 -4 m) and using air as a dielectric (  =  0 = 8.85  10 -12 F/m)

8. Fall 2001ENGR201 Capacitance & Inductance8 Capacitor Characteristics Typically, capacitors are measured in microfarads (  F or uF), nanofarads (nF) or picofarads (pf). Capacitance in a circuit may be deliberate (we insert a capacitor) or unintentional and simply due to the way in which a circuit is constructed (two long parallel conductors separated by air or plastic). This unintentional capacitance is called stray capacitance, and it may affect the operation of a circuit significantly.

9. Fall 2001ENGR201 Capacitance & Inductance9 An electrostatic force field is created between the plates. The current which flows in the conductors to the capacitor does not flow through the dielectric. Rather, the electrostatic field (force field) set up by the differential charge causes charge (electrons) to be removed from one plate as charge (electrons) is deposited on the other. There appears to be a continuous flow of current through the capacitor. Our primary interest is the terminal characteristics of a capacitor, which can be described with the following equations. Capacitor Operation - - - + The charge differential between the plates of a capacitor stores energy.

10. Fall 2001ENGR201 Capacitance & Inductance10 + v c (t) - i c (t) The charge stored in a capacitor is proportional to the voltage across the capacitor. The current through a capacitor is proportional to the rate of change of the voltage Manipulating and integrating the previous equation allows us to express the voltage in terms of the current: Capacitor Equations

11. Fall 2001ENGR201 Capacitance & Inductance11 The change in the voltage across a capacitor is proportional to the area under the current (which is the amount of charge added to or subtracted from the capacitor). Capacitor Equations + v c (t) - i c (t)

12. Fall 2001ENGR201 Capacitance & Inductance12 Since p(t) = v(t)  i(t)  Energy, w(t), is the integral of p(t), which yields: Unlike a resistor, which always absorbs power, a capacitor may absorb or deliver power (store energy as we store charge and increase the strength of the electrostatic field and release energy as we remove charge and the electrostatic field collapses). That is, p(t) may be positive or negative for a capacitor. + v c (t) - i c (t) Capacitor Power & Energy Equations

13. Fall 2001ENGR201 Capacitance & Inductance13 Like the capacitor, an inductor is a circuit element capable of storing energy. Generally, an inductor is made by forming coils of wire around a core. The core may be air, nonmagnetic material, or magnetic material such as iron. Schematic Symbol Inductance

14. Fall 2001ENGR201 Capacitance & Inductance14 Current flowing through the wire creates an electromagnetic (force) field around the wire. The strength of the field is affected by the number of coils, the amount of current, and the magnetic properties of the core. Inductance may occur in a circuit unintentionally due to the way the circuit is constructed. Such inductance is called stray inductance. Inductance

15. Fall 2001ENGR201 Capacitance & Inductance15 The voltage across an inductor is proportional to the rate of change of inductor current. Manipulating and integrating the previous equation allows us to express the current in terms of the voltage: The change in current through an inductor is proportional to the area under the inductor voltage. Inductance Equations + v L (t) - i L (t)

16. Fall 2001ENGR201 Capacitance & Inductance16 Since p(t) = v(t)  i(t)  Energy, w(t), is the integral of p(t), which yields: Unlike a resistor, which always absorbs power, an inductor may absorb or deliver power (store energy as we increase the strength of the electromagnetic field or release energy as the field collapses). That is, p(t) may be positive or negative for an inductor. Inductance Power Equations + v L (t) - i L (t)

17. Fall 2001ENGR201 Capacitance & Inductance17 Capacitors in Parallel Since all the capacitors are in parallel they have a common voltage, v x (t). Applying KCL yields: In order for these two circuits to be equivalent we conclude: (Capacitors in parallel act like resistors in series.)

18. Fall 2001ENGR201 Capacitance & Inductance18 Since all the capacitors are in series they have a common current, i x (t). Applying KVL yields: Capacitors in Series

19. Fall 2001ENGR201 Capacitance & Inductance19 Capacitors in Series Capacitors in series act like resistors in parallel – we add the reciprocals of the individual values.

20. Fall 2001ENGR201 Capacitance & Inductance20 Inductors in Series and Parallel Using similar reasoning that was used for capacitors, we can find equivalents for inductors in series or in parallel. If n inductors are connected in series, they can be replaced by an equivalent inductance L eq, where (Inductors in series act like resistors in series.) If n inductors are connected in parallel, they can be replaced by an equivalent inductance L eq, where (Inductors in parallel act like resistors in parallel.)