eit review - sacramento state circuits review.pdf · capacitor to the voltage difference between...
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![Page 1: EIT Review - Sacramento State circuits review.pdf · capacitor to the voltage difference between the two plates, measured in farads (F). Henry – Inductance is the property whereby](https://reader030.vdocuments.net/reader030/viewer/2022040507/5e43c9e4d23128479935205c/html5/thumbnails/1.jpg)
10/3/2006 1
EIT Review
Electrical Circuits – DC Circuits
Lecturer: Russ Tatro
Presented by Tau Beta PiThe Engineering Honor Society
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10/3/2006 2
Session OutlineBasic ConceptsBasic LawsMethods of AnalysisCircuit TheoremsOperational AmplifiersCapacitors and InductorsSummary and Questions
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10/3/2006 3
Basic Concepts
Linear, Lumped parameter systems.
Linear – response is proportional to V or I (no higher order terms needed)
Lumped Parameter Electrical effects happen instantaneously in the system.Low frequency or small size (about 1/10 of the wavelength).
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10/3/2006 4
Basic Concepts
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10/3/2006 5
Basic Concepts - Units
Volt – The Potential difference is the energy required to move a unit charge (the electron) through an element (such as a resistor).
Amp – Electric current is the time rate of change of the charge, measured in amperes (A).A direct Current (dc) is a current that remains constant with time.An alternating current (ac) is a current that varies sinusoidally with time.
Ohm – the resistance R of an element denotes its ability to resist the flow of electric current; it is measured in ohms (Ω).
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10/3/2006 6
Basic Concepts - Units
Farad – Capacitance is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates, measured in farads (F).
Henry – Inductance is the property whereby an inductor exhibits opposition to the charge of current flowing through it; measured in henrys (H).
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10/3/2006 7
Basic Concepts - Volts
Symbol: V or E (electromotive force)
Circuit usage: V or v(t) when voltage may vary.
Voltage is a measure of the DIFFERENCE in electrical potential between two points.
I say again! Voltage ACROSS two points.
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10/3/2006 8
Basic Concepts - Amps
Symbol: A (Coulomb per second)
Circuit usage: Ior i(t) when current may vary with time.
Amperage is a measure of the current flow past a point.
I say again! Current THRU a circuit element.
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10/3/2006 9
Basic Concepts - Ohms
Symbol: Ω
Circuit usage: R
Resistance is the capacity of a component to oppose the flow of electrical current.
R = V/I
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10/3/2006 10
Basic Concepts - Farad
Symbol: F
Circuit usage: C for capacitor
Capacitor resists CHANGE in voltage across it.
Passive charge storage by separation of charge.Electric field energy.
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10/3/2006 11
Basic Concepts - Henrys
Symbol: H
Circuit usage: L for inductor
Inductor resists CHANGE in current thru it.
Passive energy storage by creation of magnetic field.
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10/3/2006 12
Basic Concepts – Passive Sign Convention
Use a positive sign when:Current is the direction of voltage drop.
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10/3/2006 13
Basic Concepts – Powerp = (+/-) vi = i2R = v2/R
p = the power in wattsv = the voltage in voltsI = the current in amperes
I.A.W. with Passive Sign Convention+ (positive) – element is absorbing power.- (negative) – element is delivering power.
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10/3/2006 14
Basic Concepts - ExamplePower delivered/absorbed.
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10/3/2006 15
Basic ConceptsEnd of Basic Concepts.
Questions?
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10/3/2006 16
Basic Laws Circuit Connections:
Nodes – point of connection of two or more branches.
Branches – single element.
Loops – any CLOSED path in a circuit.
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10/3/2006 17
Basic Laws – Ohm’s LawOhms Law: v = iR
R = v/i
1 Ω = 1 V/A
Short Circuit when R = 0 Ω
Open Circuit when R = ∞ Ω
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10/3/2006 18
Basic Laws - Kirchhoff’s Laws
KVL: Kirchhoff’s Voltage LawSum of all voltages around a closed path is zero.
KCL: Kirchhoff’s Current LawSum of all currents = zerosum all currents in = sum all currents out
Based on conservation of charge:
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10/3/2006 19
Basic Laws – Series/Parallel
......111
21
++=RRReq
21
21
RRRRReq +
=
For Two Resistors in Parallel:
Parallel Resistors:
Series Resistors:Req = R1 + R2 + ……
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10/3/2006 20
Basic Laws – Voltage Divider
Voltage Divider for Series Resistors:
vRR
Rv21
11 +=
vRR
Rv21
22 +=
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10/3/2006 21
Basic Laws – Current Divider
Current Divider for Parallel Resistors:
iRR
Ri21
21 +=
iRR
Ri21
12 +=
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10/3/2006 22
Basic Laws – ExampleKCL/KVL Example
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10/3/2006 23
Basic Laws – ExampleCalculating Resistance
Req = ?
Req = ?
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10/3/2006 24
Basic Laws – ExampleVoltage Divider
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10/3/2006 25
Basic Laws – ExampleCurrent Divider
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10/3/2006 26
Basic LawsQuestions?
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10/3/2006 27
Break for 5 minutes.Chinese Proverb: This too shall pass.
Or as the Kidney stone patient hopes:This too shall pass,
but not soon enough!
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10/3/2006 28
Methods of AnalysisNodal Analysis –
assign voltages in branches and find currents.
Mesh Analysis –assign currents in a loop and find voltages.
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10/3/2006 29
Methods of AnalysisNode Analysis:
1. Select a reference node.2. Apply KCL to each of the nonreference
nodes.3. Solve the resulting simultaneous equations.
Number of equations = # of nodes - 1
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10/3/2006 30
Methods of AnalysisNode Analysis:
Select a reference node.This becomes the “zero” reference.
All voltages become a rise in voltage from this reference node.
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10/3/2006 31
Methods of AnalysisNode Analysis:
Apply KCL:There are a number of slightly different approaches in applying KCL.The approach you use MUST be consistent!
IMHO – assume voltage drop away from node.This means the current is leaving the node.
IMHO – in my humble opinion
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10/3/2006 32
Methods of Analysis – ExampleLet us work a node problem.
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10/3/2006 33
Methods of AnalysisSupernode: when a voltage source connects to
nonreference nodes. Recall that a ideal voltage source provides
WHATEVER current the circuit requires.Procedure:1. Short the voltage source. That is: form a single
node of the ends of the voltage source.2. Write the constraint equation for the voltages.3. Write the standard node equations for the
supernode.
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10/3/2006 34
Methods of Analysis
Remember the constraint equation!v1 – 2V = v2
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10/3/2006 35
Methods of AnalysisMesh Analysis:A mesh is a loop which does not contain any other
loops within it. 1. Assign mesh currents to the n meshes.2. Apply KVL to each mesh. Express the
voltages in terms of Ohm’s law.3. Solve the resulting n simultaneous equations.
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10/3/2006 36
Methods of Analysis – ExampleLet us work a mesh problem.
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10/3/2006 37
Methods of AnalysisSupermesh: when two meshes share a current
source.Recall that a ideal current source provides
WHATEVER voltage the circuit requires.Procedure:1. Open the current source. That is form a single
mesh for the two mesh sharing the current source.
2. Write the constraint equation for the currents.3. Write the standard mesh equation for the
supermesh.
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10/3/2006 38
Methods of Analysis
Remember to write the constraint equation!i1 – 6A – i2 = 0
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10/3/2006 39
Methods of AnalysisSupermesh or Supernode?
1. Do what the test tells you!
2. Pick the approach with the least equations.
3. Node equations are usually easier.
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10/3/2006 40
Methods of AnalysisEnd of Methods of Analysis.
Questions?
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10/3/2006 41
Circuit Theorems1. Superposition2. Source Transformation3. Thevenin’s Theorem4. Norton’s Theorem5. Maximum Power Transfer
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10/3/2006 42
Circuit Theorems - Superposition
Determine the contribution of each independent source to the variable in question. Then sum these “responses” to find the total response.
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10/3/2006 43
Circuit Theorems - Superposition1. Turn off all independent sources except one.
Voltage source V = 0 when shorted.Current source A = 0 when opened.
2. Solve the circuit.3. Repeat until all sources handled. 4. Sum the individual responses to get the total
response.
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10/3/2006 44
Circuit Theorems –Source Transforms
A source transformation exchanges a voltage source with a series resistor with a current source and a parallel resistor.
Riv ss =
Rvi s
s =
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10/3/2006 45
Circuit Theorems – ExampleLet us work a source transformation problem.
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10/3/2006 46
Circuit Theorems – ExampleLet us work a source transformation problem.
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10/3/2006 47
Circuit Theorems –Thevenin’s Theorem
Thevenin’s Theorem: a linear two-terminal network can be replaced with an equivalent circuit of a single voltage source and a series resistor.
VTH is the open circuit voltage
RTH is the equivalent resistance of the circuit.
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10/3/2006 48
Circuit Theorems –Thevenin’s Theorem
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10/3/2006 49
Circuit Theorems – ExampleLet us work a Thevenin problem.
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10/3/2006 50
Circuit Theorems – ExampleLet us work a Thevenin problem.
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10/3/2006 51
Circuit Theorems –Norton’s Theorem
TH
THN R
VI =
Norton’s Theorem: a linear two-terminal network can be replaced with an equivalent circuit of a single current source and a parallel resistor.
IN is the short circuit current.
RTH is the equivalent resistance of the circuit.
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10/3/2006 52
Circuit Theorems – ExampleLet us work a Norton problem.
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10/3/2006 53
Circuit Theorems – Example
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10/3/2006 54
Circuit Theorems –Maximum Power Transfer
The maximum power delivered to a load is when the load resistance equals the Thevenin resistance as seen from the load.
THL RR =
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10/3/2006 55
Circuit Theorems –Maximum Power Transfer
When
Then
THL RR =
TH
TH
RVp4
2
max =
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10/3/2006 56
Circuit TheoremsEnd of Circuit Theorems.
Questions?
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10/3/2006 57
Break for 5 minutes.Nerves and butterflies are fine - they're a
physical sign that you're mentally ready and eager. You have to get the butterflies to fly in formation, that's the trick.
~Steve Bull
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10/3/2006 58
Operational AmplifiersOP Amp – name derived from this circuits ability
to perform various mathematical operations.
Why us? Another chance to use Node Analysis!
When not? Op Amp with capacitor or inductor? No Laplace skills? Then guess an answer and move along.
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Operational AmplifiersIdeal Op Amp assumptions:1. in = ip = zero
2. vn = vp
3. Vout is equal to or less than the input power voltage.
CCout VV ±≤
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Operational AmplifiersUse node analysis to solve the problem. If you
recognize the type and like to memorize:
Inverting Op Amp:
Noninverting Op Amp:
inputinput
feedbackout V
RR
V −=
inputinput
feedbackout V
RR
V ⎟⎟⎠
⎞⎜⎜⎝
⎛+= 1
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Operational Amplifiers – ExampleLet us work an Op Amp problem.
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Operational AmplifiersEnd of Operational Amplifiers.
Questions?
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Capacitors and InductorsA Capacitor consists of two conducting plates
separated by an insulator.
Capacitance is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates. Capacitance is measured in Farads.
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Capacitors and InductorsThe voltage across a capacitor cannot change
abruptly.
A capacitor is an open circuit to dc.
dtdvCi =
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Capacitors and InductorsCapacitors add in parallel - CAP
Series Capacitance
...21 ++= CCCeq
...111
21
++=CCCeq
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Capacitors and InductorsAn Inductor consists of a coil of conducting wire.
Inductance is the property where an inductor opposes change to current flow. Inductance is measured in Henrys.
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Capacitors and InductorsThe current thru an inductor cannot change
abruptly.
An inductor is a short circuit to dc.
dtdiLv =
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Capacitors and InductorsInductors add in series.
Parallel Inductance
...21 ++= LLLeq
...111
21
++=LLLeq
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Capacitors and Inductors – ExampleOverall behavior of an inductor
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Capacitors and Inductors – ExampleOverall behavior of an inductor
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Capacitors and Inductors – ExampleOverall behavior of a capacitor
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Capacitors and InductorsEnd of Capacitors and Inductors.
Questions?
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Summary Passive SignPower: p = viOhm’s Law v = ir = i2R = V2/RKCL – Sum of currents = zeroKVL – Sum of voltage in loop = zeroSeries/Parallel ElementsVoltage/Current Divider
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Summary Source TransformationThevenin EquivalentNorton Equivalent Ideal Op AmpCapacitorInductor
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SummaryWhat we did not cover:
Response of 1st order RC/RL circuitsUnbounded responseResponse of 2nd order RLC circuitsSinusoidal Steady-State analysis3 Phase AC power
Be sure to study these areas as time permits.
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Good Luck on the EIT Exam! It is a timed exam. Answer what you know. Mark what you might know and come back later. Do not get bogged down on a few questions. Move along! Remember that it is a multiple choice exam. Look for hints in the answers.If totally in doubt – Guess by using your intuition and science.
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EIT Review
Electrical Circuits – DC Circuits
Lecturer: Russ Tatro
Presented by Tau Beta PiThe Engineering Honor Society