AnnouncementsReview of Circuit AnalysisVoltage and CurrentBasic Circuit ElementsResistorIdeal Voltage SourceWireIdeal Current SourceI-V Relationships GraphicallyKirchhoff’s LawsKirchhoff’s Voltage Law (KVL)KVL TricksWriting KVL EquationsElements in ParallelKirchhoff’s Current Law (KCL)KCL EquationsElements in SeriesResistors in SeriesSlide 19Voltage DivisionSlide 21EE 42 Lecture 39/3/2004AnnouncementsWebsite for EE42:http://inst.eecs.berkeley.edu/~ee42Website for EE43:http://inst.eecs.berkeley.edu/~ee43EE 42 Lecture 39/3/2004Review of Circuit AnalysisFundamental elementsWireResistorVoltage SourceCurrent SourceKirchhoff’s Voltage and Current LawsResistors in SeriesVoltage DivisionEE 42 Lecture 39/3/2004Voltage and CurrentVoltage is the difference in electric potential between two points. To express this difference, we label a voltage with a “+” and “-” :Here, V1 is the potential at “a” minusthe potential at “b”, which is -1.5 V.Current is the flow of positive charge. Current has a value and a direction, expressed by an arrow:Here, i1 is the current that flows right;i1 is negative if current actually flows left.These are ways to place a frame of reference in your analysis. 1.5VabV1-+i1EE 42 Lecture 39/3/2004Basic Circuit ElementsWire (Short Circuit)Voltage is zero, current is unknownResistor Current is proportional to voltage (linear)Ideal Voltage Source Voltage is a given quantity, current is unknownIdeal Current SourceCurrent is a given quantity, voltage is unknownEE 42 Lecture 39/3/2004ResistorThe resistor has a current-voltage relationship called Ohm’s law:v = i Rwhere R is the resistance in Ω, i is the current in A, and v is the voltage in V, with reference directions as pictured.If R is given, once you know i, it is easy to find v and vice-versa.Since R is never negative, a resistor always absorbs power…+vRiEE 42 Lecture 39/3/2004Ideal Voltage SourceThe ideal voltage source explicitly definesthe voltage between its terminals.Constant (DC) voltage source: Vs = 5 VTime-Varying voltage source: Vs = 10 sin(t) VExamples: batteries, wall outlet, function generator, … The ideal voltage source does not provide any information about the current flowing through it. The current through the voltage source is defined by the rest of the circuit to which the source is attached. Current cannot be determined by the value of the voltage.Do not assume that the current is zero!VsEE 42 Lecture 39/3/2004WireWire has a very small resistance. For simplicity, we will idealize wire in the following way: the potential at all points on a piece of wire is the same, regardless of the current going through it.Wire is a 0 V voltage sourceWire is a 0 Ω resistorThis idealization (and others) can lead to contradictions on paper—and smoke in lab.EE 42 Lecture 39/3/2004Ideal Current SourceThe ideal current source sets the value of the current running through it.Constant (DC) current source: Is = 2 ATime-Varying current source: Is = -3 sin(t) AExamples: few in real life!The ideal current source has known current, but unknown voltage.The voltage across the voltage source is defined by the rest of the circuit to which the source is attached. Voltage cannot be determined by the value of the current.Do not assume that the voltage is zero!IsEE 42 Lecture 39/3/2004I-V Relationships GraphicallyivResistor: Line through origin with slope 1/RivIdeal Voltage Source: Vertical lineivIdeal Current Source: Horizontal lineWire:Vertical line through originEE 42 Lecture 39/3/2004Kirchhoff’s LawsThe I-V relationship for a device tells us how current and voltage are related within that device.Kirchhoff’s laws tell us how voltages relate to other voltages in a circuit, and how currents relate to other currents in a circuit.KVL: The sum of voltage drops around a closed path must equal zero.KCL: The sum of currents leaving a node must equal zero.EE 42 Lecture 39/3/2004Kirchhoff’s Voltage Law (KVL)Suppose I add up the potential drops around the closed path, from “a” to “b” to “c” and back to “a”. Since I end where I began, the total drop in potential I encounter along the path must be zero: Vab + Vbc + Vca = 0It would not make sense to say, for example, “b” is 1 V lower than “a”, “c” is 2 V lower than “b”, and “a” is 3 V lower than “c”. I would then be saying that “a” is 6 V lower than “a”, which is nonsense!We can use potential rises throughout instead of potential drops; this is an alternative statement of KVL.abc+ Vab - +Vbc - -Vca +EE 42 Lecture 39/3/2004KVL TricksA voltage rise is a negative voltage drop.Look at the first sign you encounter on each element when tracing the closed path.If it is a “-”, it is a voltage rise and you willinsert a “-” to rewrite as a drop. + -V2Path+ -V1PathAlong a path, I might encounter a voltage which is labeled as a voltage drop (in the direction I’m going). The sum of these voltage drops must equal zero.I might encounter a voltage which is labeled as a voltage rise (in the direction I’m going). This rise can be viewed as a “negative drop”. Rewrite: +-V 2Path -EE 42 Lecture 39/3/2004Writing KVL EquationsWhat does KVLsay about thevoltages alongthese 3 paths?Path 1:0vvvb2aPath 2:0vvvc3bPath 3:0vvvvc32avcva++321+ vbv3v2+ +-abcEE 42 Lecture 39/3/2004Elements in ParallelKVL tells us that any set of elements which are connected at both ends carry the same voltage.We say these elements are in parallel.KVL clockwise, start at top:Vb – Va = 0Va = VbEE 42 Lecture 39/3/2004Kirchhoff’s Current Law (KCL)Electrons don’t just disappear or get trapped (in our analysis). Therefore, the sum of all current entering a closed surface or point must equal zero—whatever goes in must come out.Remember that current leaving a closed surface can be interpreted as a negative current entering:i1is the same statement as-i1EE 42 Lecture 39/3/2004KCL EquationsIn order to satisfy KCL, what is the value of i?KCL says:24 μA + -10 μA + (-)-4 μA + -i =018 μA – i = 0i = 18 μA i 10 A 24 A -4 AEE 42 Lecture 39/3/2004Elements in SeriesSuppose two elements are connected with nothing coming off in between.KCL says that the
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