Review of Circuit Analysis Fundamental elements Wire Resistor Voltage Source Current Source Kirchhoff s Voltage and Current Laws Resistors in Series Voltage Division Spring 2005 EE 42 Lecture 2 1 Voltage and Current Voltage is the difference in electric potential between two points To express this difference we label a voltage with a and b a 1 5V Here V1 is the potential at a minus V1 the 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 i1 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 Spring 2005 EE 42 Lecture 2 2 Basic Circuit Elements Wire Short Circuit Voltage is zero current is unknown Resistor Current is proportional to voltage linear v iR Ideal Voltage Source Voltage is a given quantity current is unknown Ideal Current Source Current is a given quantity voltage is unknown Spring 2005 EE 42 Lecture 2 3 Resistor The resistor has a currentvoltage relationship called Ohm s law i R v iR where R is the resistance in i is the current in A and v is the voltage in V with reference directions as pictured v 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 Spring 2005 EE 42 Lecture 2 4 Ideal Voltage Source The ideal voltage source explicitly defines Vs the voltage between its terminals Constant DC voltage source Vs 5 V Time varying voltage source Vs 10 sin t V Examples 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 Spring 2005 EE 42 Lecture 2 5 Wire Wire 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 source Wire is a 0 resistor This idealization and others can lead to contradictions on paper and smoke in lab Spring 2005 EE 42 Lecture 2 6 Ideal Current Source The ideal current source sets the Is value of the current running through it Constant DC current source Is 2 A Time varying current source Is 3 sin t A Examples 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 Spring 2005 EE 42 Lecture 2 7 I V Relationships Graphically i i v v iR i VS v v i IS Resistor Line through origin with slope 1 R Ideal Voltage Source Vertical line Ideal Current Source Horizontal line Wire Vertical line through origin any current no voltage across wire Spring 2005 EE 42 Lecture 2 8 Kirchhoff s Laws The 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 Kirchhoff s Voltage Law KVL The sum of voltage drops around a closed path must equal zero Kirchhoff s Current Law KCL The sum of currents entering a node must equal zero Spring 2005 EE 42 Lecture 2 9 Kirchhoff s Voltage Law KVL a b Suppose I add up the potential drops Vab around the closed path from a to b to c and back to a Since I end where I began the total Vbc drop in potential I encounter along the c path must be zero Vab Vbc Vca 0 It 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 Alternatively we can use potential rises throughout instead of potential drops this is an alternative statement of KVL V ca Spring 2005 EE 42 Lecture 2 10 KVL Tricks A voltage rise is a negative voltage drop Along 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 that is labeled as a voltage rise in the direction I m going This rise can be viewed as a negative drop Rewrite Path Path Look at the first sign you encounter on Path each element when tracing the closed path If it is a it is a voltage rise and you will insert a to rewrite it as a drop Spring 2005 EE 42 Lecture 2 V1 V2 V2 11 Writing KVL Equations 1 va b v2 vb v3 2 What does KVL say about the voltages along these 3 paths a c vc 3 Path 1 va v 2 vb 0 Path 2 vb v3 vc 0 Path 3 va v2 v3 vc 0 Spring 2005 EE 42 Lecture 2 12 Elements in Parallel KVL tells us that any set of elements that are connected at both ends carry the same voltage We say these elements are in parallel KVL clockwise start at top Vb Va 0 Va Vb Spring 2005 EE 42 Lecture 2 13 Kirchhoff 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 i1 Spring 2005 is the same statement as EE 42 Lecture 2 i1 14 KCL Equations In order to satisfy KCL what is the value of i KCL says 24 A 10 A 4 A i 0 24 A 4 A 18 A i 0 i 18 A Spring 2005 10 A EE 42 Lecture 2 i 15 Elements in Series Suppose two elements are connected with nothing no wire coming off in between KCL says that the elements carry the same current We say these elements are in series i1 i2 0 Spring 2005 i1 i2 EE 42 Lecture 2 16 Resistors in Series Consider resistors in series This means they are attached end to end with nothing coming off in between current has no choice of where to go i R1 i R1 R2 i R2 R3 i R3 VTOTAL Each resistor has the same current labeled i Each resistor has voltage iR given by Ohm …
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