Chapter 03. Resistance. Resistance of Conductors. Type of Material resistivity (Ω m) Type of Material. Length / Area. Resistance Formula

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1 Chapter 03 Resistance Resistance of Conductors Resistance of material depends on several factors: Type of Material, Conductor length, or l Cross-sectional area, A Temperature, T C-C Source: Tsai Circuit Analysis: Theory and Practice Delmar Cengage Learning C-C Tsai 2 Type of Material Atomic differences of materials cause variations in how electron collisions affect resistance Differences produce resistivity represented by the symbol (Greek letter rho) Units of, Ohms x meters (Ω m) or Ohms x circular mils / feet (Ω CM/ft) Type of Material resistivity (Ω m) C-C Tsai 3 C-C Tsai 4 Length / Area Resistance of a conductor Directly proportional to its length l or l = length, in meters or feet If you double the length of the wire, the resistance will double Resistance of a metallic conductor Inversely proportional to cross-sectional area A of the conductor A = cross-sectional area, in m 2 or circular mils If cross-sectional area is doubled, resistance will be one half as much C-C Tsai 5 Resistance Formula At a given temperature (usually 20 o C) R A Formula can be used with both circular and rectangular conductors C-C Tsai 6 I 1

2 Example: Aluminum Resistance Exercise 1: Problem 3.3 Calculate the required height h of the copper with a resistance of 0.02 at 20 C R A I R = (2.825 x m) x 270m / (150mm x 6mm) = 8.48 m I C-C Tsai 7 C-C Tsai 8 Electrical Wire Tables American Wire Gauge (AWG) is primary system to denote wire diameters The higher the AWG number, the smaller the diameter A given length of AWG 22 wire (16.2 /1000ft) will have more resistance than the same length of AWG 14 wire (2.52 /1000ft) Larger gauge wires (smaller AWG) can handle more current MCM = 1000 circular mils (CM) C-C Tsai 9 Circular Mils (CM) Length may also be in mils (1 mil=0.001 inch) Area may be in circular mils (CM) 1 CM = Area of a circle having 1 mil diameter 1 square mil = Area of a square with 1 mil sides 1 CM = /4 square mils C-C Tsai 10 Temperature Effects For most conductors, a temperature increase causes an increase in resistance. Increase is relatively linear Said to have a positive temperature coefficient (PTC). T R In semiconductors and insulators, a temperature increase results in decrease in resistance. Said to have a negative temperature coefficient (NTC). T R Temperature Effects Temperature coefficient is represented by Resistance (R 2 ) at a specific temperature may be calculated from resistance (R 1 ) at a different temperature by R 2 = R 1 [ 1+ ΔT ] where ΔT = T 2 T 1 is the difference between the two temperatures in Celsius degrees C-C Tsai 11 C-C Tsai 12 2

3 Temperature Coefficients Example: Aluminum Resistance Given R=20 at 20 for an Aluminum wire, determine their resistances at 100 and -40. R 100 = 20 x (100 - (-236)) / (20 - (-236)) = 26.3 R -40 = 20 x ( (-236)) / (20 - (-236)) = 15.3 Or using Eq R 2 = R 1 [ 1+ ΔT ] R 100 = 20 x ( x (100-20)) = R -40 = 20 x ( x (-40-20)) = C-C Tsai 13 C-C Tsai 14 Exercise 2 Given R=10 at 25 for an copper wire, determine their resistance at 85. Types of Resistors Resistance of a fixed resistor is constant over a wide temperature range Rated by amount of resistance Measured in ohms (Ω) Rated by power Measured in watts (W) For example: 100Ω ¼ W C-C Tsai 15 C-C Tsai 16 Type of Fixed Resistors Power Resistors Different resistors for different applications Molded carbon composition Carbon film Metal film Metal Oxide Wire-Wound Integrated circuit packages 2W 1W 0.5W 0.25W 0.125W C-C Tsai 17 C-C Tsai 18 3

4 Variable Resistors Resistance may be changed (varied) Adjust volume, set level of lighting, adjust temperature Have three terminals Center terminal connected to wiper arm Used for potentiometers and rheostats C-C Tsai 19 Color Coding of Resistors Large resistors: Resistor values and tolerances printed on cases Smaller resistors: Surface Mount Devices Use color coding Colored bands provide a recognizable code Read from left to right Left is defined as side of resistor closest to band C-C Tsai 20 Color Code Colored bands on a resistor provide a code for determining Value Tolerance Reliability C-C Tsai 21 4-Color Code Resistor Color 1 Color 2 Color 3 Color 4 Color 5 Number 1 Number 2 Powers of 10 Tolerance Reliability 黑 Black 棕 Brown ±1% 1% 紅 Red ±2% 0.1% 橙 Orange % 黃 Yellow % 綠 Green ±0.5% 藍 Blue 紫 Violet 灰 Grey 白 White 金 Gold 10-1 ±5% 銀 Silver 10-2 ±10% ±20% C-C Tsai 22 Example: Color-Code Resistor R = 18 x 10 3 Ω 5% = 18kΩ 5% = 18k Ω 0.9k Ω with a reliability of 0.1% Example: 4-Color Code Resistor Example 1: 綠藍紅金 R = 56 x 10 2 Ω 5% = 5.6kΩ 5% Example 2: 橙紅金金 C-C Tsai 23 R = 32 x 10-1 Ω 5% = 3.2 5% C-C Tsai 24 4

5 5-Color Code Resistor Color 1 Color 2 Color 3 Color 4 Color 5 Number 1 Number 2 Number 2 Powers of 10 Tolerance 黑 Black 棕 Brown ±1% 紅 Red ±2% 橙 Orange 黃 Yellow 綠 Green ±0.5% 藍 Blue 紫 Violet 灰 Grey 白 White 金 Gold 10-1 ±5% 銀 Silver 10-2 ±10% C-C Tsai 25 Example: 5-Color Code Resistor Example 1: R = 272 x 10 3 Ω 1% = 272kΩ 1% Example 2: 紅紫紅橙棕 棕黑紅黃棕 R = 102 x 10 4 Ω 1% = 1.02M 1% C-C Tsai 26 Exercise 3: What Resistances are for Color-code Resistors? Exercise3 (continued) C-C Tsai 27 C-C Tsai 28 Measuring Resistance Ohmmeter can be used to measure resistance for determining short or open circuit Remove all power sources to circuit Isolate component Connect probes across component Ensure Ohmmeter is set to correct range Do not worry about polarity C-C Tsai 29 Measuring Resistance Remove all power sources to circuit Isolate component C-C Tsai 30 5

6 Measure Resistance for Determining Shorts Short circuit Low resistance conductor is connected between two points in a circuit Current will bypass using path of least resistance Ohmmeter indicates very low or zero resistance when used to measure a short circuit Measure Resistance for Determining Opens Open circuit Conductor is broken between points under tests Ohmmeter indicates infinite resistance when used to measure an open circuit C-C Tsai 31 C-C Tsai 32 Thermistors Two-terminal transducer Resistance changes with temperature Applications include electronic thermometers and thermostatic control circuits for furnaces Most have negative temperature coefficients Photoconductive Cells Two-terminal transducers Resistance determined by amount of light May be used to measure light intensity or to control lighting Used in security systems Linear response (negative slope) L R T R C-C Tsai 33 C-C Tsai 34 Nonlinear Resistance Ohmic device Linear current-voltage relationship Nonohmic device Nonlinear current-voltage relationship Some components may have both ohmic and nonohmic regions Diodes Diode is a semiconductor device Permit charge to flow in one direction only Very little resistance in forward direction Very high resistance in reverse direction (Open circuit) C-C Tsai 35 C-C Tsai 36 6

7 Measuring Diodes In reverse direction, resistance is very high In forward direction, has very little resistance LED Light Emitting Diode In reverse direction, LED off. In forward direction, LED on, I D =10~20mA, about V LED = 1.7V E A R V C-C Tsai 37 C-C Tsai 38 Varistors Resistors sensitive to voltage High resistance when voltage is below breakdown value Low resistance when voltage is above breakdown value Used in sensitive circuits to protect circuit from excessive voltage Conductance Measure of a material s ability to allow flow of charge Conductance is reciprocal of resistance G = 1/R Unit is Siemens (S) C-C Tsai 39 C-C Tsai 40 Superconductors Low temperatures Resistance of some materials goes to almost zero Temperature is called critical temperature Meissner Effect Cooled below its critical temperature Magnetic fields may surround but not enter the superconductor C-C Tsai 41 Kernel abilities 1. How to calculate the resistance of a wire? Please give an example. 2. How to recognize the resistance and tolerance of a color-code resistor? Please give an example. 3. What is the characteristics for a thermistor or a photoconductive cell? Please give their example. 4. What is LED and its characteristics? Please give an example. C-C Tsai 42 7

8 Exercise 4 using Multisim 1. Please show the schematic with Multisim to use DMM to measure DC voltage (or current) associated with variable resistor. 2. Please show the schematic with Multisim to use DMM to light LEDs by varying DC voltage associated with variable resistor. C-C Tsai 43 8