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# Class Note for ECE 2300 at UH

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This 10 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 22 views.

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Date Created: 02/06/15

NETWORKS ELEE 2300 LECTURE NOTES DAVE SHATTUCK SET 2 Chapter 2 Circuit Elements The review of previoust covered material continues in this chapter Here we introduce three out of five of our Basic Circuit Elements speci cally voltage sources current sources and resistors The others are inductors and capacitors Finally we will get to Kirchhoff s Laws and Ohm s Law Ideal Voltage Sources There are 2 kinds a Independent voltage sources This device says The voltage between terminals a and b will be vs I insist Show circuit schematic symbol b Dependent voltage sources There are two kinds of dependent voltage sources These devices also say the same thing but with minor changes They say The voltage between terminals will be a and b will be vs where either v8 u vX voltage dependent voltage source or vS p iX current dependent voltage source Note that while u is dimensionless p has dimensions ofvoltage per current Typically the units are Ohm which is a WA The book will always assume that the units are indeed Ohm but will not show it Show circuit schematic symbols Ideal Current Sources There are 2 kinds a Independent current sources This device says The current through me from a to b will be is I insist Show circuit schematic symbol b Dependent current sources There are two kinds of dependent current sources These devices also say the same thing but with minor changes They say The current through me from a to b will be is where either is g vX voltage dependent current source or i 3 iX current dependent current source Note that while 3 is dimensionless g has dimensions of current per voltage Typically the units are Siemens 8 also known as mhos which is a NV The book will always assume that the units are indeed S but will not show it Show circuit schematic symbols Submitted HW 2 Shattuck Section ELEE 2300 A two terminal device is used as a speaker One terminal is called A and the other is called B The voltage vS is defined as the voltage at B with respect to A The current is is de ned as the current entering terminal B It is known that for time tgt0 vS 30 sin100rads t V and iS 5 exp20s1 t A a Draw a diagram showing vS and is b Find the energy provided by the speaker fortime tgt0 c Sketch the power and energy as a function of time for 0lttlt200ms d Explain whether this makes sense in terms ofa speaker Section 22 Electrical Resistance and Ohm s Law Next up are Resistors our next Basic Circuit Element Sources voltage and current are called Active Elements They m provide power The don t always Resistors and soon inductors and capacitors are called Passive Elements They int provide power They always don t Resistors obey Ohm s Law which is that the ratio of voltage to current is a constant Speci cally R v i Show diagram Show schematic symbol and de ne v and i Note that this is de ned in terms of the passive convention R has units of voltage per current typically WA or Ohms or 0 Also this is stated the other way that is G i v where G is called the conductance It has units of current per voltage typically AV or Siemens or S In the past this was called Mhos with a symbol ofan upside down 0 Now for a resistor 2 2 p v I I R v R but this holds only for resistors Note that this power is always positive This is an expression for power absorbed By our rules we should write this 2 R 2 R pabs v I I v Question Can a resistor have a negative value Ans The answer really depends on how we de ne our terms Let me answer it this way Resistors which are models of the pieces of carbon that we wrap with with ceramic and connect metal leads to are always positive valued However a resistance can be negative in the sense that we can have something that behaves according to the condition R v i where this is true even if we have used the passive convention We cannot achieve this without something that can provide power Typically we do this with a dependent source Show an example of this Section 23 Construction ofa Circuit Model This is a good section but I have already talked about most of it Please read it Do example 25 in class Section 24 Kirchhoff s Laws Note there are 2 h s in this name Next note is that we may not have of cially said the following so let s do it now 0 Lines in circuit schematics represent wires or connections of zero resistance 0 Nodes are de ned as points where two or more elements join 0 A Closed Loop can be de ned in this way Start at a node and go in any direction and end up where you start This is a closed loop Note that this loop does not have to follow elements It can jump across open space It is like Superman So with this background here are Kirchhoff s Laws Kirchhoffs Current Law KCL the algebraic signed sum of currents in any node is zero Kirchhoffs Voltage Law KVL the algebraic signed sum ofvoltages around any closed loop is zero You all have seen this before So let s move immediately to some examples Do simple circuit and do dependent source example Using KVL KCL and Ohm s Law we can solve any circuit with sources and resistors So what are we going to do the rest ofthe semester Well we are going to nd ways to do this more quickly And we are going to nd ways to do this systematically Submitted HW3 ELEE 2300 Shattuck Section a Using the diagram below and using different values of RX make a plot ofthe relationship between vX and iX b From your plot what is iX when vX 0 c From your plot what is vX when iX 0 d Find the equation for the relationship between vX and iX Chapter 3 Simple sic Resistive Circuits These circuits are simple only in a relative sense We will use only constant valued sources These are called dc sources Jargon The Phoenician says ac alternating varying changing with time dc constant Despite their original meanings alternating current direct current the terms ac current and dc current are not considered redundant We will cover in this chapter three kinds of things 1 Equivalent circuits series parallel deltatowye 2 Circuit analysis shortcuts voltage divider current divider 3 Meters voltmeter ammeter ohmmeter Wheatstone bridge Section 31 Resistors in Series This is our rst equivalent circuit It is important to recognize what equivalent means We will use equivalent circuits widely in Electrical Engineering We need to get this straight right now Equivalent means equivalent with respect to the outside world Think ofa box around the circuit elements in question The equivalency applies only to the behavior at the terminals that come out of the box In particular the energy or power associated with what is going on inside the box may be different from the original circuit The Phoenician says 2 components are in series ifthey have the same current same exact charge carriers going through them If n resistors are in series they can be replaced with an equivalent resistor Req where ReqR1R2R3Rn Section 32 Resistors in Parallel The Phoenician says 2 components are in parallel if they have the same voltage across them have the same two terminals If n resistors are in parallel they can be replaced with an equivalent resistor Req where 1Req 1R11R2 1R3 1Rn If n 2 and only if n 2 then the product overthe sum rule applies Req R1 R2R1 R2 Section 33 The VoltageDivider Circuit This is an example of a handy tool for circuit analysis It is actually nothing more than a short cut we take because the situation occurs so often If a voltage v is known across two series resistors the voltage across one of T them is VR1 VT R1 R1 R2 Show proof of this Note that the polarities in the diagram This rule assumes voltage polarities for vR1 and vT in the same reference direction Section 34 The CurrentDivider Circuit This is another example of a handy tool for circuit analysis If a current iT is known through two parallel resistors the current through one of them is 39R1 39TR2R1 R2 Show proof of this Note that the polarities in the diagram This rule assumes current polarities for iR1 and LI in the same reference direction Do example problem Testing the voltage divider rule in class Educators are regularly encouraged to generate enthusiasm and attention by showing the real world applicability of the the subjects covered in class Therefore we will now test the voltage divider rule to see whether it really works in practice A voltage source a battery is connected across two series resistors The resistor values are R1 10MQ R2 82MQ We will measure the source Its value is V 8 Based on this the predicted value for vR1 will be VR1VSR1R1 R2 The predicted vR1 The measured vR1 error measured referencereference 100 Percentage error How would you interpret this answer This is why our next study will be of meters It is easy to make serious mistakes if we do not understand what meters do to a circuit when we use it to measure a circuit We will study digital meters this semester The old homework and several other old problems referto d Arsonvalbased meters We will not cover d Arsonvalbased meters this semester Submitted HW2A Use the measurements that we have just taken in class to nd the resistance of the voltmeter that was used State your assumptions Make an estimate of the possible error in your measurements Section 35 The Voltmeter and Ammeter A voltmeter or ammeter can be characterized in part by its full scale readings However the key to the use of these devices is to recognize that each can be modeled by a resistor Thus when you make a measurment and you put a meter in the circuit you are changing the circuit You are adding a resistor What effect will this have VWI it be signi cant We can answer these questions using the circuit analysis concepts that we have already learned Ammeters Ammeters are meters that measure current If we are measuring current we are measuring a path dependent variable Therefore to make such a measurement we typically have to break the circuit and insert the meter There are some kinds of ammeters that operate in a different way We will ignore these special cases for the rest of this course Current measurements have to be made in series Three things to remember about ammeters 1 Ammeters are always for this course placed in series with the branch where they are used to measure current You must break the circuit to insert the ammeter 2 Ammeters read the current that goes through them If an ammeter changes the circuit by being present it measures the current that goes through it after that change has taken place 3 Ammeters are effectively resistors for the purposes of solving the circuits that include them Voltmeters Voltmeters are meters that measure voltage If we are measuring voltage we are measuring a path independent variable Therefore to make such a measurement we typically have to apply the terminals ofthe voltmeter to the 2 terminals across which the voltage is to be measured Voltage measurements have to be made in parallel Three things to remember about voltmeters 1 Voltmeters are always placed in parallel with the thing being measured You do not break the circuit to insert the voltmeter 2 Voltmeters read the voltage that is across them If a voltmeter changes the circuit by being present it measures the voltage that is across it with that change 3 Voltmeters are effectively resistors for the purposes of solving circuits that include them Solve problem 336 Section 38 Ohmmeter Circuit Ohmmeters are meters that measure resistance In an ohmmeter we will be measuring a resistance which does not provide power In orderto have a needle move or to have anything else happen we need power Thus an ohmmeter must have a source The key to an ohmmeter is that it measures the ratio ofthe voltage across its terminals to the current through its terminals It always assumes that it is connected to a resistor and nothinq but a resistor This is the basic underlying concept about ohmmeters SurgeonElectrician Warning Do not make measurements on resistors while they are in their circuits This can lead to bad measurements Section 36 Wheatstone Bridge The Wheatstone Bridge is an ohmmeter that uses an ammeter as a null detector Draw the diagram for the Wheatstone Bridge Note that R1 R2 and R3 are known The resistor RX is the unknown resistor to be measured R3 is adjustable but is still known To make the measurement R is adjusted until the ammeter reads zero 3 At thIs pomt v3 vX Thus vsR3R1 R3 vs RXRX R2 The voltage vS cancels which leaves R3 R1 R3 RXRX R2 If we solve this for RX we get RX R3R2 R1 Note that the resistance ofthe ammeter does not matter as no current goes through it during the actual measurement instant Also note that the voltage vs cancels when we apply the 2 VDR s which means that if its value changes the measurement will still work very well It doesn t matter if the battery runs down some Section 310 The Delta to Wye Equivalent circuit This is an equivalent circuit however it is new to us in that it is a three terminal equivalent circuit The basic principle remains the same Show the two versions If we are going from a delta to a wye we use RRRR R R 1 b c a b c R2 Ra RC Ra Rb RC R3Rb RaRaRbRC If we are going from a wye to a delta we use RaR1R R R R3R1R1 2 2 3 RbR1R2R2R3R3R1R2 RCR1R2R2R3R3R1R3 The proof ofall this is simple in concept No matter what we do the same thing must happen outside the equivalents no matter what For example if we drop one terminal and nd the resistance between the other two resistors it will work For example if we drop terminal b connect it to nothing at all and then nd the resistance between terminals a and c Rae Rac Rb H Rc Ra R1 R3 How many times can we do this Ans We can do this two more times How many times do we need Ans We need a total ofthree relations This gives us three equations in six unknowns lfthe original circuit is known the values of those 3 resistors are known That gives us three equations and three unknownsand we can survive

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