Slide 1Slide 2Lightning ReviewIntroduction: elements of electrical circuits18.1 Sources of EMFEMFEMF (continued)Measurements in electrical circuitsDirect Current Circuits18.2 Resistors in seriesResistors in series: notesResistors in series: example18.3 Resistors in parallelResistors in parallel: notesResistors in parallel: exampleDirect current circuits: exampleSlide 1718.4 Kirchhoff’s rules and DC currentsa. Junction ruleb. Loop ruleb. Loop rule: illustrationSlide 22Kirchhoff’s Rules: Single-loop circuitsKirchhoff’s Rules: Single-loop circuits (cont.)18.5 RC circuitsRC circuits1101/15/1901/15/19General Physics (PHY 2140)Lecture 10Lecture 10 ElectrodynamicsDirect current circuits parallel and series connections Kirchhoff’s rulesChapter 18http://www.physics.wayne.edu/~apetrov/PHY2140/2201/15/1901/15/19Hours of operationHours of operation::Mondays, Tuesdays, Wednesdays 11 AM to 6 PMThursdays and Fridays 11 AM to 3 PMUndergraduate students taking PHY2130-2140 will be able to get assistance in this Center with their homework, labwork and other issues related to their physics course. The Center will be open: Monday, September 22 to Wednesday, December 10, 2003.Department of Physics and Astronomyannounces the Fall 2003 opening ofThe Physics Resource CenterThe Physics Resource Centeron Monday, September 22 in Room 172Room 172 of Physics Research Building. of Physics Research Building.3301/15/1901/15/19Lightning ReviewLightning ReviewLast lecture: 1.1.Current and resistanceCurrent and resistanceTemperature dependence of resistanceTemperature dependence of resistancePower in electric circuitsPower in electric circuitsQItD=D( )1o oR R T Ta� �= + -� �( )22VP I V I RRD= D = =Review Problem: Consider a moose standing under the tree during the lightning storm. Is he ever in danger? What could happen if lightning hits the tree under which he is standing?4401/15/1901/15/19Introduction: elements of electrical circuits Introduction: elements of electrical circuits A branchA branch:: A branch is a single electrical element or device (resistor, etc.). A branch is a single electrical element or device (resistor, etc.).A junctionA junction:: A junction (or node) is a connection point between two or more A junction (or node) is a connection point between two or more branches.branches.If we start at any point in a circuit (node), proceed through connected If we start at any point in a circuit (node), proceed through connected electric devices back to the point (node) from which we started, electric devices back to the point (node) from which we started, without without crossing a node more than one timecrossing a node more than one time, we form a closed-path (or , we form a closed-path (or looploop).).    A circuit with 5 branches.---A circuit with 3 nodes.5501/15/1901/15/19 Steady current (constant in magnitude and direction)• requires a complete circuit• path cannot be only resistancecannot be only potential drops in direction of current flow Electromotive Force (EMF)• provides increase in potential • converts some external form of energy into electrical energy Single emf and a single resistor: emf can be thought of as a “charge pump”IV = IR+ -V = IR = 18.1 Sources of EMF18.1 Sources of EMF6601/15/1901/15/19EMFEMFEach real battery has some Each real battery has some internal resistanceinternal resistanceAB: potential increases by AB: potential increases by  on on the source of EMF, then the source of EMF, then decreases by Ir (because of decreases by Ir (because of the internal resistance)the internal resistance)Thus, terminal voltage on the Thus, terminal voltage on the battery battery V isV isNote: Note:  is the same as the is the same as the terminal voltage when the terminal voltage when the current is zero (open circuit)current is zero (open circuit)rRABCDV IrD = -E7701/15/1901/15/19EMF (continued)EMF (continued)Now add a load resistance RNow add a load resistance RSince it is connected by a Since it is connected by a conducting wire to the battery conducting wire to the battery → → terminal voltage is the same as terminal voltage is the same as the potential difference across the the potential difference across the load resistanceload resistanceThus, the current in the circuit isThus, the current in the circuit isrRABCDIR r=+E,V Ir IR orIr IRD = - == +EEPower output:2 2I I r I R= +ENote: we’ll assume r negligible unless otherwise is stated8801/15/1901/15/19Voltmeters measure Potential Difference (or voltage) across a device by being placed in parallel with the device.VAmmeters measure current through a device by being placed in series with the device.AMeasurements in electrical circuitsMeasurements in electrical circuits9901/15/1901/15/19ab eqabeqV IRVRI=�ReqIabDirect Current CircuitsDirect Current CircuitsTwo Basic Principles:Conservation of ChargeConservation of EnergyResistance Networks101001/15/1901/15/191 21 2eqeqV IRIR IRVR R RI ID =+D� = = +18.2 Resistors in series18.2 Resistors in series1 2I I I= =1. Because of the charge conservation, all charges going through the resistor R2 will also go through resistor R1. Thus, currents in R1 and R2 are the same,1 2V IR IRD = +2. Because of the energy conservation, total potential drop (between A and C) equals to the sum of potential drops between A and B and B and C,By definition,Thus, Req would be1 2eqR R R= +R2R1v2v1+++___vi1ABCI111101/15/1901/15/19Resistors in series: notesResistors in series: notesAnalogous formula is true for any number of resistors,Analogous formula is true for any number of resistors,It follows that the equivalent resistance of a series It follows that the equivalent resistance of a series combination of resistors is greater than any of the combination of resistors is greater than any of the individual resistorsindividual resistors1 2 3...eqR R R R= + + +(series combination)121201/15/1901/15/19Resistors in series: exampleResistors in series: exampleR2R1v2v1+++___vi1ABCIIn the electrical circuit below, find voltage across the resistor RIn the electrical circuit below, find voltage across the resistor R11 in terms of in terms of the resistances Rthe resistances R11, R, R22 and potential difference between the battery’s and potential difference between the battery’s terminals V. terminals V. 1 2V V V= +Energy conservation implies:with1 1 2 2andV IR V IR= =Then,( )1 21 2, soVV I R R