ELEN 236 oltage, Current and Resistance oltage Current and Resistance Basics (ll bout Circuits: DC-Ch1) (Q s 1-22) Look at EpropsF Water nalogy (remember to press and hold Low, Medium, or High to get pumps to work) o Water nalogy Slide 12 has the controllable water pump o Electron Pump slide 2 has the controllable electron pump o Water Pump analogous to electron pump (voltage source) o Water Pressure is analogous to oltage o Potential energy of water analogous to potential difference in circuit o water flow is analogous to electron flow o There is resistance to both water flow and electron flow and it varies depending on properties of pipe e.g. how much energy is imparted on to each electron by a battery if the battery voltage is 9 volts (analogous to how much energy is imparted to each gram of water by a pump pumping water 9 meters up ) oltage o Units: olts () = J/C = how much energy to separate one coulomb of charge o Symbol for equations: o nalogous to potential energy of water. The higher water is pumped, the more energy it has and the more push it will have to flow through a pipe. The more voltage (potential difference) it has, the more push there will be to move electrons through a circuit. Current o Units: mperes (mps) = C/s = how many units of charge flowing past a point in one second. o Symbol for equations: I o nalogous to water flow. More water through a pipe per second, means more flow. More couloumbs of charge through a circuit per second means more current. o e.g. n electron has 1.6x10-19 Coulombs of charge on it. If a wire is carrying 1 of current, how many electrons are flowing per second to create this current. 1
Ω COM Ω COM Ω COM Ω COM ELEN236 Resistance o Units: Ohms (Ω) o Symbol for equations: R o nalogous to resistance to water flow in pipe. Use PhET CCK (C) and show how to do measurements on and I: Measurements: o oltage is Potential Difference so it is always the measurement between two points. o e.g.: oltage source is 6olts: B switch open C D o oltage is always measured between two points o e.g. Danger high voltage. Two points. wire (spark) Safe bird Dead bird wire Safe bird wire High voltage source (C) Dead bird wire Current measurement: o measured at one point. Like a coulomb counter. 2
o Requires circuit to be broken to perform measurement. Meter must become part of the path o e.g.: How would you connect this ammeter to measure current in this circuit? Light bulb Battery + - OFF COM Ohm s Law (Q s 22-33) (ll bout Circuits: DC-Ch2) (Q s 22-33) Use CCK and for several values of, measure I Plot I as a function of on a graph What is the relationship between and I? (linear) o Slope of line is inverse of resistance 1/R = I/ or R = /I or = IR E.g. in CCK, secretly change resistor value, and have students figure out what the new value is. (could put in the pencil from the grab bag) E.g. in CCK, given resistor value and a current measurement, figure out what the voltage across R must be E.g. in CCK, given resistor value and a voltage measurement, figure out what the current through R must be. Conventional Current vs. Electron Flow: o Note current direction in CCK. What we see is movement of electrons. o Conventional current is around because of Ben Franklin. He made an assumption about electric charges but got it backwards. It wasn t the positive things that moved, it s actually the negative things. o Conventional Current: Positive charges move from Higher voltage to lower voltage o Electron current: electrons move from lower voltage to higher voltage. I = 10 m. = 10. R = 1000 Ohm 3
I = 825 R = 15 mohm. = 12.4 = 240. R = 10 Ohm I = Joule s Law (ll bout Circuits: DC-Ch2) (Q s 34-46) One of the primary purposes of electrical systems is to deliver energy from a source to a destination. o Electricity is a highly effective and efficient way to deliver/distribute energy. o It does have one major drawback and that is it must be used right away, or converted into another form and stored (e.g. chemically in batteries) What do I mean by energy? o Capacity to do Work. Mechanically, Work is the exertion of force over a distance (or the vector dot product of force and distance). e.g. lift a 10kg mass 1 meter vertical W=Fd=10*1=10J. o Energy is measured in Joules nybody ever looked at their electrical bill to see what units of energy are used there? kwh (kilowatt*hours) Energy is average power times time 1 kwh is the amount of energy ten 100 W light bulbs use in one hour. How many Joules in one kwh? 1kWh = 1000 Joules/sec * 3600 sec = 3,600,000 J o Electrical systems can do work too How is energy related to power? o power is how much work can be done In a certain period of time. o P = Energy/time = J/sec = Watts Find equation to calculate electrical power given that o P = J/s o = J/C o I = C/s *I = J/C*C/s = J/s o This energy usually manifests as heat, although sometimes as light Given the P = I and = IR, come up with 4
o n equation for power that depends on I and R o n equation for power that depends on and R o e.g. If electric current is constant, which will dissipate more power a low resistance resistor, or a high resistance resistor? Explain e.g. If voltage is constant, which will dissipate more power a low resistance resistor, or a high resistance resistor? Explain e.g. How much current will it draw? In to what form of energy does light bulb convert electrical energy? What is the rate of energy use by the bulb? I = 120/300 = 0.4 P = 120*0.4 = 120 2 /300 =48W If you had a 100W bulb instead of a 48W bulb, it would obviously use more energy over time, but would that bulb s resistance be higher or lower than the 48W bulb? The resistance would have to be smaller since P = 2 /R, and is constant e.g. Calculate the power dissipated by this electric heater. The generator output voltage is 120 and the heater s resistance is 2 Ω. Generator Heater Recalculate power if voltage is doubled to 240. e.g. Calculate current drawn by this motor: 5
Now calculate efficiency if the wires have 1 ohm of resistance and the motor still draws 10 of current. efficiency = (the power from the source resistive losses)/power from source = (Psource I 2 R)/Psource Now calculate efficiency of the motor if there is 1 Ω of resistance in the wires (advanced: requires knowledge of KL and KCL): 6
Resistance and Resistors (Q s 47-70) (ll bout Circuits: DC-Ch2) (Q s 47-70) Resistance o Units: Ohms (Ω) o Symbol for equations: R o nalogous to resistance to water flow in pipe. o e.g. For a given water pressure applied to a hose, what factors will determine the flow rate of the water? cross-sectional area, hose length and properties of hose o e.g. For a given voltage applied across a wire, what factors will determine the current? cross-sectional area wire length properties of wire o R = (ρl)/ ρ is resistivity and the lower the value, the more conductive a material is Silver 1.59x10-8 Ωm Copper 1.72x10-8 Ωm luminum 2.82 10 8 Ωm Carbon 3.5x10-5 Ωm Silicon 6.4x10 2 Ωm Sulfur 10 15 Ωm Teflon 10 24 Ωm e.g. 12 gauge Copper wire has a cross sectional area of 3.31 mm 2. What is the resistance between the two ends of 10 meters of 12 gauge copper wire? 3.31 mm 2 = 3.31x10-6 m 2. R = (1.72x10-8 Ωm * 10m) / 3.31x10-6 m 2 = 0.052Ω How much power would be dissipated by this wire if it carried 10 mps of current: P = I 2 R = 10 2 * 0.052 = 5.2W From Wikipedia (Inga Shaba): The Inga-Shaba EHDC Transmission Line is a 1200 mile (1920 km) long high-voltage direct current overhead electric power transmission line in the Democratic Republic of Congo, linking the Inga hydroelectric complex at the mouth of the Congo River to mineral fields in Shaba, currently Katanga. 7
o Power Delivered 1 : 560 MW o oltage: 1000k o Lines use luminum: ρ = 2.82 10 8 Ωm o Wire Size Guestimation: 0.001m 2. o Find the efficiency of this system: Pgen = Pload + Plosses. To provide 560MW at 1,000,000 requires how much current? I = P/ = 560,000,000/1,000,000 = 560 Resistance of wire = (ρl)/ = (2.82 10 8 Ωm * (1,920,000m*2)) / 0.001m 2 = 108.3Ω Power Losses in the wire: Ploss = I 2 R wire = 560 2 *108.3 = 33,962,880W = 34.0 MW Efficiency = 560 MW / (560MW + 34MW) * 100% = 94.3% If oltage was doubled: To provide 560MW at 2,000,000 requires how much current? I = P/ = 560,000,000/2,000,000 = 280 Power Losses in the wire: Ploss = I 2 R wire = 280 2 *108.3 = 8,489,779W = 8.5 MW Efficiency = 560 MW / (560MW + 8.5MW) = 98.5% Gauge merican Wire Gauge (WG): http://en.wikipedia.org/wiki/merican_wire_gauge Take a look at this table, and see if you can figure out what all of the columns are. For any column, you don t understand, ask me. The one column that may not be clear is the ampacity column 1 ssume the 560MW is power delivered, not power generated but I don t know for sure 8
mpacity is basically current carrying capacity of a wire before it or the surroundings are negatively effected. It is based on: temperature rating of the insulation around the wire o insulation will melt/burn long before Cu or l melts resistivity/resistance of the conductor the ability to dissipate heat o dependent on surroundings and ambient temperature o if temp is not standard room temperature, ampacity will need to be derated. Resistors Get some real resistors for demo. (resistance real/ideal, power rating, type) o Connect ¼ watt 10 ohm resistor to 9 volt battery. What happens? Why? schematic symbols for resistors: Why would you want a component whose sole purpose is to impede the flow of electrons? o limit max current to a safe value o split voltage into proportions o scale voltage or current o provide a non-shorting path to discharge electricity When a resistor conducts electric current, its temperature increases. Explain how this phenomenon is significant to the application of resistors in electric circuits. In other words, why would we care about a resistor s temperature increasing? lso, what does this indicate about the technical ratings of resistors? side from having a specific resistance rating (i.e. a certain number of ohms), what other rating is important for proper selection of resistors in electric circuits? Potentiometers e.g. three points of electrical contact. 9
1 3 2 What happens to resistance between points when wiper moves toward point 1: Resistance between 1 and 2 Resistance between 2 and 3 Resistance between 1 and 3 This is effectively a variable resistor or potentiometer., and here are some other representations of potentiometers: Schematic symbol Internal view Internal view Motion Motion Motion Why does it not make sense to say that turning the potentiometer so the wiper moves up will increase the resistance of the potentiometer. One application of a potentiometer: + - Mtr Potentiometer 24 DC - + s the wiper moves from right to left, what will happen to the current? ssume the motor can be modeled as a constant resistor. What will happen to the power delivered to the motor? Explain what the potentiometer does in this application. Temperature Dependence of Resistors Don t do the questions about temperature dependence. R = R + R α T R αt = R 1+ α( T T )] [ T R R R R R R R T = resistance of conductor at temperature T. R R = Resistance of conductor at reference temperature T R. α= Temperature coefficient of resistance at reference temperature T R. The resistance of substances change depending on the temperature. Conductors (metals) have a positive temperature coefficient. Semiconductors typically have a negative temperature coefficient. 10