PHY-2049A closed circuitPower in DC CircuitThe 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….Let’s add resistors …….Series CombinationsSlide 8Parallel Combination??What’s This???Slide 11Power Source in a CircuitA REAL Power Source is NOT an ideal batteryA Physical (Real) BatteryBack to which is brighter?Slide 16Back 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:We start at a point in the circuit and travel around until we get back to where we started.Take a trip around this circuit.Circuit ReductionMultiple BatteriesReductionAnother Reduction ExampleSTART by assuming a DIRECTION for each CurrentThe Unthinkable ….RC CircuitClose the SwitchReally Close the SwitchThis is a differential equation.Slide 35Time ConstantResult q=CE(1-e-t/RC)q=CE(1-e-t/RC) and i=(CE/RC) e-t/RCDischarging a CapacitorSlide 40If the resistance is doubled what is the power dissipated by the circuit?PHY-2049Current & CircuitsFebruary ‘08A closed circuitHot, Hot HotPower in DC Circuit REIVRIPRIIRIIVPPowerVItQVt222W:PowerQVW:isbattery by the done workofamount The battery. by theresistor the throughpushed is Q charge a t, In timeThe 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 1069.13658ohmsvoltsmxmxALRLet’s add resistors …….Series CombinationsR1 R2i iV1 V2ViiRseriesRgeneralRRRiRiRiRVVVandiRViRV)(:2121212211SERIES ResistorsThe rod in the figure is made of two materials. The figure is not drawn to scale. Each conductor has a square cross section 3.00 mm on a side. The first material has a resistivity of 4.00 × 10–3 Ω · m and is 25.0 cm long, while the second material has a resistivity of 6.00 × 10–3 Ω · m and is 40.0 cm long. What is the resistance between the ends of the rod?Parallel Combination??R1, I1R2, I2ViiRRgeneralRRRsoRVRVRViiiiRV11111..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](a) Find the equivalent resistance between points a and b in Figure P28.6. (b) A potential difference of 34.0 V is applied between points a and b. Calculate the current in each resistor.Power Source in a CircuitThe 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 (Real) BatteryInternal ResistanceRrEmfiBack to which is brighter?Back 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 rememberIn 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 resistorA 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 EQUATIONThe 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 EQUATIONThe sum of the currents entering (or leaving) a node in a circuit is ZEROTWO resistors againiR1 R2V1 V2Vjj2121RRResistors SERIESfor GeneralRRRoriRiRiRVA single “real” resistor can be modeledas follows:RabVpositionADD ENOUGH RESISTORS, MAKING THEM SMALLERAND YOU MODEL A CONTINUOUS VOLTAGE DROP.We start at a point in the circuit and travel around until we get back to where we started.If the potential rises … well it is a rise.If it falls it is a fall OR a negative rise.We can traverse the circuit adding each rise or drop in potential.The sum of all the rises around the loop is zero. A drop is a negative rise.The sum of all the drops around a circuit is zero. A rise is a negative drop.Your choice … rises or drops. But you must remain consistent.Take a trip around this circuit.Consider voltage DROPS:-E +ir +iR = 0orE=ir + iRriseCircuit Reductioni=E/ReqMultiple BatteriesReductionComputes iAnother Reduction ExamplePARALLEL12121600503012011RRSTART by assuming a DIRECTION for each CurrentLet’s write the equations.The Unthinkable ….RC CircuitInitially, no current through the circuitClose 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 ERERCqdtdqorECqdtdqRCqiREdtdqi 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