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Transcript
EE301 Lesson 2: Resistance (Chapter 3) and Ohms Law (Chapter 4) 1 Learning Objectives • Describe the concept of resistance. • Use Ohm’s law to calculate current, voltage, and resistance values in a circuit. • Discuss the difference between an open circuit and a short circuit. • Given a color code table, determine the value and tolerance of fixed resistors using their color codes. • Demonstrate how to measure current, voltage, and resistance in a circuit. 2 Resistance of Conductors • Resistance is the opposition to charge movement. • As electrons move through a material, they constantly collide with atoms in the material and with other electrons. • These collisions cause some of the energy carried by the charge to be released as heat. • So resistance is dependent on several factors: − − − − type of material length of the conductor cross-sectional area temperature 3 Resistance of Conductors • Type of material: • Atomic differences of materials cause variations in how electron collisions affect resistance. • Differences produce resistivity. • Resistance is directly proportional to the resistivity. The higher the resistivity, the greater is the resistance of the conductor. • Resistivity is represented by the symbol (Greek letter rho). • Units of : Ohms * meters (Ω∙m). 4 Resistance of Conductors • Length of conductor: • Resistance is directly proportional to the conductors length. The longer the conductor, the greater the resistance. • If you double the length of the wire, the resistance will double. • = length • Measured in meters or feet. • Cross-sectional area: • Resistance is inversely proportional to cross-sectional area of the conductor. The greater the area of the conductor, the less resistance. • If cross-sectional area is doubled, resistance will be one half as much. • A =Cross-sectional area, in m2. 5 Resistance of Conductors • Temperature: • For most conductors, a temperature increase causes an increase in resistance. • Increase is relatively linear. • However, not that for semiconductors and insulators, an increase in temperature results in decrease in resistance. 6 Resistance of Conductors • Resistance of a conductor at a given temperature can be expressed mathematically: R [ohms, ] A where resistivity, in ohm-meters ( m) length, in meters (m) A(CM) A cross-sectional area (m 2 ) 1x10-3 inches = 1 mil ACM = (diametermils)2 & 7 Example Problem 1 • You need to measure length of this copper coil but don’t want to unroll it. Resistance measured is 103.7 Ohms. Diameter is 0.01 inches. Find the length. Knowns : R 103.7 copper 10.37CM / ft R= ρl , where A CM = (d mils ) 2 A d mils = 1in 1000mil * =10mil 100 1in A CM = (10 mil) 2 = 100 CM 103.7 Ω= (10.37 CM-Ω/ft)l 100 CM 1x10-3 inches = 1 mil = 1/1000 inch 8 103.7 Ω * 100 CM (10.37 CM-Ω/ft) & ACM = (diametermils)2 1000 ft Fixed Resistors • Used to provide control of electrical circuits. • Produced in various shapes and sizes. 9 Variable Resistors • Variable resistors (VAR) have an adjustable value of resistance and have two principle functions: 1. Potentiometers are used to adjust voltage. 2. Rheostats are used to adjust current. − VARs are used to adjust volume, set level of lighting, adjust temperature,… a a Rab Rab b b Rbc Rbc c c 10 Resistor color coding Resistors usually have 4, 5 or 6 color bands. 4 color bands: 5 color bands: Band 1: First Digit Band 1: First Digit Band 2: Second Digit Band 2: Second Digit Band 3: Multiplier (10X) Band 3: Third Digit Band 4: Tolerance Band 4: Multiplier (10X) Band 5: Tolerance gray Sometimes a 5th or 6th band is added (Reliability) to meet MILSPEC requirements. NOTE: That for a 4-band resistor, if the 4th band is not present, it is assumed that the resistor has a tolerance of ± 20% 11 Resistor color coding Yellow = 4 Purple = 7 Orange = 3=>103 Red = 2% Read left To right 47*103 = 47k Ω ±2% MULTIPLIER (i.e) 4 = 104 5 = 105 IF THIRD BAND gray 2nd Digit 1st Digit 3rd Digit Multiplier Tolerance Green = 5 Blue = 6 Black = 0 Red = 2 =>102 Brown = 1% 560*102 = 56kΩ ±1% 12 Example Problem 2 Determine the resistance of a carbon resistors having the color codes shown in the figure below. Make sure you identify that this is a 4-band resistor Make sure you identify that this is a 5-band resistor Brown = 1 10 * 101 = 100 Ω Black = 0 Brown = 101 Gold = ± 5% tolerance => ± 5 Ω R = 100 Ω ± 5% Green = 5 564 x 105 = 56.4 MΩ Blue = 6 Yellow = 4 Green = 105 Silver = ± 10% tolerance => ± 5.64MΩ R = 56.4 MΩ ± 10% gray 13 Ohm’s Law • Every conversion of energy from one form to another can be related to this equation. • In electric circuits, the effect we are trying to establish is the flow of charge, or current. • The potential difference, or voltage, between two points is the cause (“pressure”), and the opposition is the resistance encountered. 14 Ohm’s Law • Georg Ohm discovered experimentally that voltage and current in a wire were linearly related to each other by a constant (Resistance) E IR [volts, V] where, E is voltage in volts R is resistance in ohms I is current in amperes Plotting Ohm’s Law • Current in a resistive circuit: − Directly proportional to its applied voltage. − Inversely proportional to its resistance. 15 Ohm’s Law • Two different symbols are commonly used to represent voltage. − E for sources. − V for loads (such as the voltage drop across a resistor). • When using Ohm’s Law be careful that you use the voltage across the load (in the above that would be the voltage across the resistor (R). 16 Ohm’s Law • In summary, therefore, the absence of an applied “pressure” such as voltage in an electric circuit will result in no reaction in the system and no current in the electric circuit. • Current is a reaction to the applied voltage and not the factor that gets the system in motion. • EXAMPLE: The greater the pressure in a hose, the greater is the rate of water flow through the hose, just as applying a higher voltage to the same circuit results in a higher current. 17 Example Problem 3 Determine the current provided by the source in the system below. I E IR [volts, V] Rearrange the equation => 18 E I [amperes, A] R 100V I = 2 [amperes, A] 50 Open Circuits • Current can only exist where there is a conductive path. • When the current is zero, the circuit will have an infinite resistance (remember Ohm’s Law). • This is called an open circuit. E E R I 0 E E I 0A R 19 Short Circuits • Short circuits occur when a very low (or near zero) resistance is placed across a circuit. • Since resistance is near zero, all current will bypass the rest of circuit and go through the short (again, recall Ohm’s Law). • With zero resistance, current draw will approach the limits of the power source (infinite current), frequently causing damage to wiring or the power source. E E I A R 0 E E R 0 I 20 Measuring Voltage • Voltage and current is measured using voltmeters and ammeters, or a Digital Multi-Meter (DMM). • Measure voltage by placing the voltmeter leads across the component whose voltage you wish to measure. • Polarity can be determined by probe placement. “Auto-polarity” 21 Meter Symbol: Voltmeter 22 Current Representation • The current depicted in the following circuits is identical. 23 Measuring Current • The current that you wish to measure must pass through the meter. • Be careful that the meter’s maximum current rating is not exceeded! 24 Meter Symbol: Ammeter 25 Voltage Polarity and Current Direction • For the voltage across a resistor, always place the plus sign at the tail of the current reference arrow. • To ensure the correct voltage sign on the DMM, place the red lead where you think the “+” sign should be. • For correct current polarity, the current should enter the red lead of the DMM. 26 Measuring Resistance • An ohmmeter is a device used to measure the resistance of a component. • Resistance cannot be measured when voltage is supplied to the circuit. 28 Measuring Component Resistance • You must isolate the component that you are measuring from the circuit! 29 Measuring Total Resistance • You must remove the power source prior to measuring total resistance! 30 QUESTIONS? 37