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Transcript
Physics 3204: Current Electricity Notes Factors Affecting Current • the natural state of electrons in a wire, or other conductor, is to simply spread out • a battery, or other power supply, will given electrons energy to move through a complete circuit • the physics convention is that electrons will flow through a circuit from the direction of the negative terminal of a battery back through to the positive • engineers use the opposite convention (positive flow) • current is measured by an ammeter, galvanometer, or multimeter placed in series battery resistor A A ammeter correct incorrect • current is affected by several key factors > > > > > resistance of the material temperature crosssectional area energy / voltage number of pathways 1 Physics 3204: Current Electricity Notes Circuit Diagrams Key symbols Resistor: Ammeter: A Power Supply: Voltmeter: V Switch: Fuse: Ex) What does the ammeter read? 6V A 3Ω Ex 2) What does the voltmeter read? 4.5 A A 3.8Ω V 2 Physics 3204: Current Electricity Notes Kirchoff's Laws Current Law: current into a junction is equal to the current that comes out of the junction • current in series is constant (no junction) • current in parallel separates (total current constant) Ex 1) An ammeter in series with a resistor reads 5 A. What is the current through the resistor? Ex 2) There is 10 A of current into a parallel junction. If 3 A of current enters the first path, what is the current in the second path? Ex 3) In the previous example, why might the current be different in each path? . 3 Physics 3204: Current Electricity Notes Voltage Law: the total potential decrease (voltage drop) is equal to the total potential gain (voltage gain) in a given loop • in series, the voltage used will total the voltage available • in parallel, the total voltage in each branch will be equal (not spilt) Ex 1) What is the potential difference across the second resistor? 6V 2 V Ex 2) What is the potential difference across each resistor? 6V 4 Physics 3204: Current Electricity Notes Resistance • total resistance, or equivalent resistance depending on the situation is different in series and parallel • in series, resistance is additive (much like drive thru, each item of resistance makes the total resistance greater) • in parallel, resistance has an inverse relationship (must like grocery store lineups, the more open lanes the faster everyone moves regardless of the speed of any given line) Series: RT = R1 + R2 + R3 + ..... Parallel: 1/RT = 1/R1 + 1/R2 + 1/R3 + ..... Ex) A 5 Ω, 3 Ω, and 6 Ω resistor are put together. What is the total resistance if: a) the are all in series b) the are all in parallel c) they are arranged as shown 3 Ω 5 Ω 6 Ω 5 Physics 3204: Current Electricity Notes Putting It Together learn to organize yourself, possibly with a table 1) Given the following circuit. a) What is the total current b) What is the voltage across the 2 Ω resistor? 6V 5 Ω 2 Ω . 6 Physics 3204: Current Electricity Notes 2) Given the following circuit. a) What is the total current? b) What is the total resistance? c) What is the voltage drop across the 4 Ω resistor? 2 A 2 Ω 4 A . 7 Physics 3204: Current Electricity Notes Extra Practice 16 V 4.0 A 3 Ω 1) Calculate the missing values 2.5 Ω 12 V 2) 2.5 Ω 5.0 Ω Calculate the missing values 3) 6 V 5 Ω 4 Ω 2.0 A fuse Will the fuse blow? 8 Physics 3204: Current Electricity Notes 2 Ω Ex 2) 9 V 4 Ω 4 Ω Find the following 1) Total resistance 2) Current through the 2 ohm resistor. 3) Voltage drop across the resistor in series with the battery. 9 Physics 3204: Current Electricity Notes (i) What is the total resistance? (ii) What is the current through each resistor? Cheat Sheet (i) What is the total resistance? • Find equilivalent resistance of 2 and 3 • Use series rule for resistance to find total resistance (ii) What is the current through each resistor? • Find total current using ohm's law (V = I R) • Use series rule to determine current through 1 and 4 • Find voltage drop across 1 and 4 • Use voltage rule for parallel to determine voltage in 2 and 3 • Find current through 2 and 3 using ohm's law 10 Physics 3204: Current Electricity Notes Combination Circuits • many circuits have some parts that are in series and others that are in parallel • in order to deal with these, we often create equivalent resistances for the different sections Ex) 4 Ω 6 V 3 Ω 2 Ω 1) What is the total resistance? 2) What is the potential difference across the 4 Ω resistor? 3) What is the current through the 3 Ω resistor? 11 Physics 3204: Current Electricity Notes (i) What is the total resistance? (ii) What is the voltage across resistor 2? (iii) Will the fuse blow? Cheat Sheet (i) What is the total resistance? • Find equilivalent resistance of 2 and 3 • Use series rule for resistance to find total resistance (fuse provides no resistance) (ii) What is the voltage across resistor 2? • Find total current using ohm's law • Use series rule to determine current through 1 • Use ohm's law to determine voltage across 1 • Use parallel rule to determine voltage across 2 (iii) Will the fuse blow? • Fuses blow when max current is reached • Since the fuse is in series with 3, find current through 3 using ohm's law 12 Physics 3204: Current Electricity Notes Resistance • a measure of how current is restricted through an object • measured in ohms • resistance depends on: 1) resistivity of the material (ρ "rho") • constant for a given material • for example, all copper wires have the same resistivity (1.7 x 108 Ω m) but many have a different resistance 2) crosssectional area (A) • A = πr2 for a circular wire • larger area allows more room for current to flow 3) length (L) • greater length causes more obstacles over the whole path impeding current 4) Temperature (not in equation) • increased temperature causes electrons to move quicker causing more collisions • this leads to an overall increase in resistance R = ρ L / A 13 Physics 3204: Current Electricity Notes Ex) Tungsten has a resistivity of 5.6 x 108 Ω m. What is the resistance of a 1.2 m long tungsten wire with a radius of 1.0 x 103 m? Ex 2) A pencil has a length of 0.17 m and the "lead" has an area of 1.5 x 102 m. Graphite has ρ = 3.6 x 105 Ω m. What is the resistance of the pencil? 14 Physics 3204: Current Electricity Notes • typically, the resistance is calculated based on changing factors Ex 3) A 200 m piece of wire has a resistance of 1.7 Ω. What is the resistance of a 50 m piece cut from it? Ex 4) A piece of copper has a resistance of 5.0 Ω. If it is compressed so that the length is halved and the area is tripled, what is the new resistance? 15 Physics 3204: Current Electricity Notes Sources of Electrical Energy Voltaic Cells Piezoelectric Energy Thermoelectric Energy Photoelectric Energy Generators 16 Physics 3204: Current Electricity Notes Power • recall that > P = W x t > V = W / q > I = q / t • from this we can see the equation for electrical power • using Ohm's law, we can also determine two additional power equations Using V = I R Using I = V / R • while power can be a standalone question, it is typically added on to circuit diagram questions 17 Physics 3204: Current Electricity Notes 1) A 120 V source is used to power a 1.0 A charger. How much power is dissipated in the charger? 2) A 11 W bulb is connected to a 120 V source. What current flows through the bulb? 3) A 8.0 Ω resistor is connected to a 1.5 V battery. What is the power dissipated by the resistor? 4) A 3.0 Ω and a 5.0 Ω resistor are connected in parallel with a 12 V battery. What is the power generated by the battery? . 18 Physics 3204: Current Electricity Notes Cost of Electricity 19 Physics 3204: Current Electricity Notes • the power company charges for electricity based on the kilowatt hour (a convenient unit for energy) • to determine the number of kWh used, we simply multiply the power (in kW) by the time used (in hours) • this can then be multiplied by the current electricity rate (currently 11.178¢ per kWh) • in simplest form cost = P t r where P is power in kW t is time in hours r is rate in either ¢ per kWh or $ per kWh Ex) One 60 W incandescent lightbulb is replaced with an 8 W LED light. If the bulbs were both operated for 5 hours a day, how much was saved? Ex 2) In a particular home there are 25 13 W CFL bulbs. If the average time used per day is 6 hours, how much would it cost to operate them over a month? . 20 Physics 3204: Current Electricity Notes Energy Use in Canada • keep in mind that the energy use in most examples will be quite low compared to what you might expect • this is because most of the energy in a typical home goes toward the heating of air and / or water • these costs tend to be harder to estimate as it is harder to determine the exact run time of heaters and the wattages can be difficult to obtain 21 Physics 3204: Current Electricity Notes 22 Physics 3204: Current Electricity Notes 23 Physics 3204: Current Electricity Notes 24 Physics 3204: Current Electricity Notes 25 Physics 3204: Current Electricity Notes 26 Physics 3204: Current Electricity Notes 27 Physics 3204: Current Electricity Notes 28