Lightning 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: exampleDirect current circuits: example18.4 Kirchhoff’s rules and DC currentsa. Junction ruleb. Loop ruleb. Loop rule: illustrationb. Loop rule: illustrationKirchhoff’s Rules: Single-loop circuitsKirchhoff’s Rules: Single-loop circuits (cont.)18.5 RC circuitsRC circuits119/24/20039/24/2003General Physics (PHY 2140)Lecture 10Lecture 10¾ Electrodynamics9Direct current circuits9 parallel and series connections9 Kirchhoff’s rulesChapter 18http://www.physics.wayne.edu/~apetrov/PHY2140/229/24/20039/24/2003Department of Physics and Astronomyannounces the Fall 2003 opening ofThe Physics Resource CenterThe Physics Resource Centeron Monday, September 22 in Room 172Room 172of Physics Research Building.of Physics Research Building.Hours 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, 2003.339/24/20039/24/2003Lightning ReviewLightning ReviewLast lecture:1.1.Current and resistanceCurrent and resistance99Temperature dependence of resistanceTemperature dependence of resistance99Power in electric circuitsQIt∆=∆()1ooRRTTα=+−()22VPIV IRR∆=∆ = =Power in electric circuitsReview 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?449/24/20039/24/2003Introduction: elements of electrical circuits Introduction: elements of electrical circuits A branchA branch::A branch is a single electrical element or device (resistor, etA branch is a single electrical element or device (resistor, etc.).c.).A junctionA junction::A junction (or node) is a connection point between two or moreA junction (or node) is a connection point between two or morebranches.branches.If we start at any point in a circuit (node), proceed through coIf we start at any point in a circuit (node), proceed through connected nnected electric devices back to the point (node) from which we startedelectric 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, we form a closed--path (or path (or looploop).).bbbbbA circuit with 5 branches.•••bbbA circuit with 3 nodes.559/24/20039/24/200318.1 Sources of EMF18.1 Sources of EMF¾ Steady current (constant in magnitude and direction)• requires a complete circuit• path cannot be only resistancecannot be only potential drops in direction of current flow¾ Electromotive Force (EMF)• provides increase in potential E• converts some external form of energy into electrical energy¾ Single emf and a single resistor: emf can be thought of as a “charge pump”IV = IRE+-V = IR = E669/24/20039/24/2003EMFEMFEach real battery has some Each real battery has some internal resistanceinternal resistanceAB: potential increases by AB: potential increases by EEon the source of EMF, then on the source of EMF, then decreases by decreases by IrIr(because of (because of the internal resistance)the internal resistance)Thus, terminal voltage on the Thus, terminal voltage on the battery battery ∆∆V isV isNote: Note: EEis 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)ErBCRDAVIr∆=−E779/24/20039/24/2003EMF (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 isErBCR,VIrIRorIr IR∆=− ==+EEDAPower output:IRr=+E22IIr IR=+ENote: we’ll assume r negligible unless otherwise is stated889/24/20039/24/2003Measurements in electrical circuitsMeasurements in electrical circuitsVoltmeters 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.A999/24/20039/24/2003Direct Current CircuitsDirect Current CircuitsTwo Basic Principles:¾ Conservation of Charge¾ Conservation of EnergyResistance NetworksReqIabab eqabeqVIRVRI=≡10109/24/20039/24/200318.2 Resistors in series18.2 Resistors in series1. Because of the charge conservation, all charges going through the resistor R2will also go through resistor R1. Thus, currentsin R1and R2are the same,R2R1v2v1+++___vi1ABCI12III==12VIRIR∆=+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,1212eqeqVIRIR IRVRRRII∆=+∆≡==+By definition,Thus, Reqwould be12eqRRR=+11119/24/20039/24/2003Resistors 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 resistors123...eqRRRR=+++(series combination)individual resistors12129/24/20039/24/2003Resistors in series: exampleResistors in series: exampleIn the electrical circuit below, find voltage across the resistoIn the electrical circuit below, find voltage across the resistor Rr R11in terms of in terms of the resistances Rthe resistances R11, R, R22and potential difference between the battery’s and potential difference between the battery’s terminals V. terminals V. Energy conservation implies:12VVV=+11 2 2andVIR VIR==R2R1v2v1+++___vi1ABCIwith()1212,soVVIRR IRR=+ =+Then,1112RVVRR=+Thus,This circuit is known as voltage