Lecture 07Dis week …J and EConsider a wireMicro-View “Resistivity”PowerThe figure below gives the electrical potential V(x) along a copper wire carrying a uniform current, from a point at higher potential (x=0m) to a point at a lower potential (x=3m). The wire has a radius of 2.45 mm. What is the current in the wire?We have all we need….Series CombinationsParallel Combination??What’s This???Moving on …..Power Source in a CircuitA REAL Power Source is NOT an ideal batteryA Physical BatteryBack to PotentialConsider a “circuit”.To rememberNEW LAWS PASSED BY THIS SESSION OF THE FLORIDUH LEGISLATURE.TWO resistors againA single “real” resistor can be modeled as follows:Take a trip around this circuit.Circuit ReductionMultiple BatteriesReductionAnother Reduction ExampleNOTICE ASSUMED DIRECTION OF TRAVELSlide 28The Unthinkable ….RC CircuitClose the SwitchReally Close the SwitchThis is a differential equation.Slide 34Time ConstantResult q=CE(1-e-t/RC)q=CE(1-e-t/RC) and i=(CE/RC) e-t/RCDischarging a CapacitorSlide 39If the resistance is doubled what is the power dissipated by the circuit?Lecture 07Current & CircuitsOctober 11, 2005Dis week …Monday – finish resistance and current and begin electric circuit.There is a new WA on board.Friday – Quiz on Monday-Wednesday’s materialNEXT FRIDAY – Examination #2Studying is a good idea!J and EEJand 0A 1letELVJLVALAVRAVAiJJAiConsider a wiredddneJAnetNecurrenttAnNMicro-View “Resistivity”meEameEad a depends on the material and is the mean time between collisionsease of motion – mobilityresistance to motion - scatteringmneEEEmnenevJd221PowerVi+-ELECTRONsBattery supplies energy to the resistor which, in turn, dissipates it in the form of heat.Work done on charge Q = Q x V RiiRiiVVtQtQVPPPOWERtimeWork2/REMEMBER: P=iV and P=i2RThe figure below gives the electrical potential V(x) along a copper wire carrying a uniform current, from a point at higher potential (x=0m) to a point at a lower potential (x=3m). The wire has a radius of 2.45 mm. What is the current in the wire?copper12 volts 0 voltsWhat does the graph tell us??*The length of the wire is 3 meters.*The potential difference across the wire is 12 volts.*The wire is uniform.Let’s get rid of the mm radius and convert it to area in square meters:A=r2 = 3.14159 x 2.452 x 10-6 m2orA=1.9 x 10-5 m 2Material is Copper so resistivity is (from table) = 1.69 x 10-8 ohm metersWe have all we need….ma 49.41067.21012RVi:Law sOhm' From67.2 109.1 0.3m-ohm 1069.13658ohmsvoltsmxmxALRSeries CombinationsR1 R2i iV1 V2ViiRseriesRgeneralRRRiRiRiRVVVandiRViRV)(:2121212211Parallel Combination??R1, I1R2, I2ViiRRgeneralRRRsoRVRVRViiiiRV11111..212121What’s This???In Fig. 28-39, find the equivalent resistance between points (a) F and H and [2.5] (b) F and G . [3.13]Moving on …..Fun and Frolic With Electric CircuitsPower Source in a CircuitVThe ideal battery does work on charges moving them (inside) from a lower potential to one that is V higher.A REAL Power Sourceis NOT an ideal batteryVE or Emf is an idealized device that does an amount of work E to move a unit charge from one side to another.By the way …. this is called a circuit!Internal ResistanceA Physical BatteryInternal ResistanceRrEmfiBack to PotentialRepresents a charge in spaceChange in potential as one circuitsthis complete circuit is ZERO!Consider a “circuit”.This trip around the circuit is the same as a path through space.THE CHANGE IN POTENTIAL FROM “a” AROUND THE CIRCUIT AND BACK TO “a” is ZERO!!To rememberIn a real circuit, we can neglect the resistance of the wires compared to the resistors.We can therefore consider a wire in a circuit to be an equipotential – the change in potential over its length is slight compared to that in a resistorA resistor allows current to flow from a high potential to a lower potential.The energy needed to do this is supplied by the battery. VqW NEW LAWS PASSED BY THIS SESSION OF THE FLORIDUH LEGISLATURE.LOOP EQUATIONThe sum of the voltage drops (or rises) as one completely travels through a circuit loop is zero.Sometimes known as Kirchoff’s loop equation.NODE EQUATIONThe sum of the currents entering (or leaving) a node in a circuit is ZEROTWO resistors againiR1 R2V1 V2Vjj2121RRResistors SERIESfor GeneralRRRoriRiRiRVA single “real” resistor can be modeledas follows:RabVpositionADD ENOUGH RESISTORS, MAKING THEM SMALLERAND YOU MODEL A CONTINUOUS VOLTAGE DROP.Take a trip around this circuit.Consider voltage DROPS:-E +ir +iR = 0orE=ir + iRriseCircuit Reductioni=E/ReqMultiple BatteriesReductionComputes iAnother Reduction ExamplePARALLEL12121600503012011RRNOTICE ASSUMED DIRECTION OF TRAVELVoltage Drops:-E1 –i1R1 + i2R2 + E2 +i1R1 = 0From “a”-i3R1 + E2 – E2 –i2R2 =0NODEI3 +i2 = i1In the figure, all the resistors have a resistance of 4.0 and all the (ideal) batteries have an emf of 4.0 V. What is the current through resistor R?The Unthinkable ….RC CircuitInitially, no current through the circuitClose switch at (a) and current begins to flow until the capacitor is fully charged.If capacitor is charged and switch is switched to (b) discharge will follow.Close the SwitchI need to use E for ENote RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)Really Close the SwitchI need to use E for ERERCqdtdqorECqdtdqRCqiREdtdqi since0Equation LoopNote RC = (Volts/Amp)(Coul/Volt) = Coul/(Coul/sec) = (1/sec)This is a differential equation.To solve we need what is called a particular solution as well as a general solution.We often do this by creative “guessing” and then matching the guess to reality.You may or may not have studied this topic … but you WILL!RCREaeCERERCqdtdqCEqRERCqdtdqKeqqatpatp1RCEEaE/R0CEa0for t/)e-CE(1)()e-CE(1q and -CEKKCE0solution from and 0q 0,When tand 0dq/dt charged,fully is device When the:solution particularat Look Solution Generalat-at-Time
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