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Applied Circuit Analysis Chapter 2 - Resistance Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Resistivity • Materials tend to resist the flow of electricity through them. • This property is called “resistance.” • The resistance of an object is a function of its length, l, and cross sectional area, A, and the material’s resistivity: R l A 2 Resistivity of Common Materials 3 Ohm’s Law • In a resistor, the voltage across a resistor is directly proportional to the current flowing through it. V IR • The resistance of an element is measured in units of Ohms, Ω, (V/A). • The higher the resistance, the less current will flow through for a given voltage. • Ohm’s law requires conforming to the passive sign convention. 4 Circular Wires • Most wires we use for connecting circuit elements together are circular in cross section. • The diameter of the wire determines the maximum current that it can handle, with a larger diameter being able to handle more current. • The American Wire Gauge (AWG) is frequently used. 5 American Wire Gauge • Diameters are measured in thousands of an inch, or mils. • The unit of cross-sectional area used is circular mils: 1 CM 4 sq mil • If the diameter of the wire is in mils, then the area in circular mils is: 2 ACM d mil 6 AWG • The following table applies to bare copper wire only: 7 AWG II 8 Types of Resistors • There exist different types of resistors, created for different applications. • The primary function of resistors is to limit current, divide voltage, and dissipate power. • Resistors are either fixed or variable. 9 Fixed Value Resistors • The two most common types of fixed resistors are wirewound and composition. • Wirewound resistors are used when it is necessary to dissipate a lot of heat. • Wirewound resistors use the diameter and length of the wire to determine resistance. • Composition resistors use a mixture of conducting and non-conducting materials to vary the resistance. 10 Variable Resistors • There are two main types of variable resistors: potentiometers and rheostats. • The potentiometer, or pot for short is a three terminal device with a sliding contact. • By sliding the contact along the resistive element, the resistance between the fixed terminals and the wiper varies. 11 Rheostats • A rheostat is a two or three terminal device used to control the amount of current within a circuit. • As the rheostat is adjusted for more resistance, less current flows. • The same variable resistor can be used either as a pot or a rheostat. 12 Linearity • Not all materials obey Ohm’s Law. • Resistors that do are called linear resistors because their current voltage relationship is always linearly proportional. • Diodes and light bulbs are examples of non-linear elements. 13 Resistor Color Codes • Only very large resistors are big enough to have their resistance printed on them. • The commonly used resistors however are too small to print on. • Instead they use a series of colored bands to indicate the values. • The first three bands (A,B,C) indicate the resistance value. 14 Color Codes • Within these first three, A is the first significant figure and B is the second significant figure. • C is the power of 10 multiplied against AB. 15 Color Codes II • The fourth band (D) indicates the tolerance of the resistance; how far from the stated value it may be. • If it is not present, then a tolerance of 20% is assumed. • If a fifth band is present (E), it indicates reliability; how many components may change their value after working for 1,000 hours. 16 Color Codes III 17 Standard Resistor Values • Contrary to what one might expect, resistors do not come in all possible values. • Rather, a series of agreed upon standard values are available at reasonable cost. • Often these values can be used in a circuit design with minor changes to parameters, or combinations may be made. 18 Standard Values 19 Measurement • The three basic parameters that one may wish to measure in a circuit are voltage ,V, current, I, and resistance, R. • The corresponding meters that can measures these parameters are the voltmeter, ammeter, and ohmmeter respectively. • It is common these days to have a single meter that serves all three functions, called a multimeter. 20 Digital vs. Analog • Multimeters come in two types: digital and analog. • The digital meter converts the measured value to a digitized number and shows the value on a display. • The analog meter uses display the consists of a needle that moves across a calibrated meter. • The needle points to the measured value. 21 Digital vs. Analog II • Below are examples of both types of meter 22 Voltmeter • To measure voltage, the voltmeter/multimeter is connected across the element to be measured. • This configuration is referred to as a parallel connection. 23 Ammeter • To measure current, the ammeter/multimeter is connected in series with the element. • This means that the circuit must be “broken” in order to insert the meter. • For a positive reading, current must enter the terminal marked as positive (+). 24 Ohmmeter • To measure resistance, the ohmmeter/multimeter must be connected across the element of interest. • If this element is still connected within a circuit, the measured resistance may include other elements in the circuit. 25 Ohmmeter II • The ohmmeter may also be used to check for open and short circuits. • If there is a break in the circuit then the resistance will appear as being very large, off the scale of the meter. • If there is a short, then the meter will read nearly zero ohms. 26 Best Practices • When working the any meter, it is best to follow these rules: 1.If possible, turn the circuit off before connecting the meter. 2.To avoid damaging the meter, set the range to the highest value first and turn it down as needed. 3.When measuring DC current or voltage observe proper polarity. 27 Best Practices II • When using a multimeter, make sure you set the meter in the correct mode (ac, dc, V, A, Ω), including moving the test leads to the appropriate jacks. • When the measurement is completed, turn off the meter to avoid draining the meter’s internal battery. 28 Safety • When working on circuits, the possibility of electric shock is always present. • The shock comes from current passing through your body. • Depending on the amount of current, the effects can range from a tingling feeling to death. 29