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EIT Review
Electrical Circuits DC Circuits
Lecturer: Russ Tatro
Presented by TauBeta Pi
The Engineering Honor Society
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Session Outline
Basic Concepts Basic Laws
Methods of Analysis
Circuit Theorems
Operational Amplifiers
Capacitors and Inductors Summary and Questions
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Basic Concepts
Linear, Lumped parameter systems.
Linear response is proportional to V or I(no higher order terms needed)
Lumped ParameterElectrical effects happen instantaneously in the system.
Low frequency or small size (about 1/10 of the wavelength).
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Basic Concepts
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Basic Concepts - Units
Volt The Potential difference is the energy required to move a unitcharge (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 sinusoidallywithtime.
Ohm the resistance R of an element denotes its ability to resist the
flow of electric current; it is measured in ohms ().
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Basic Concepts - Units
Farad Capacitance is the ratio of the charge on one plate of acapacitor to the voltage difference between the two plates, measured infarads (F).
Henry Inductance is the property whereby an inductor exhibits
opposition to the charge of current flowing through it; measuredinhenrys (H).
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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 inelectrical potential between two points.
I say again!
Voltage ACROSS two points.
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Basic Concepts - Amps
Symbol: A (Coulomb per second)
Circuit usage: I
or i(t) when current may vary with time.
Amperage is a measure of the current flow past apoint.
I say again!Current THRU a circuit element.
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Basic Concepts - Ohms
Symbol:
Circuit usage: R
Resistance is the capacity of a component tooppose the flow of electrical current.
R = V/I
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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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Basic Concepts - Henrys
Symbol: H
Circuit usage: L for inductor
Inductor resists CHANGE in current thru it.
Passive energy storage by creation of magneticfield.
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Basic Concepts Passive Sign Convention
Use a positive sign when:
Current is the direction of voltage drop.
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Basic Concepts Power
p = (+/-) vi = i2R = v2/R
p = the power in wattsv = the voltage in volts
I = 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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Basic Concepts - Example
Power delivered/absorbed.
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Basic Concepts
End of Basic Concepts.
Questions?
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Basic LawsCircuit Connections:
Nodes point of connection of two or more
branches.
Branches single element.
Loops any CLOSED path in a circuit.
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Basic Laws Ohms LawOhms Law: v = iR
R = v/i
1
= 1 V/A
Short Circuit when R = 0
Open Circuit when R =
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Basic Laws - Kirchhoffs Laws
KVL: Kirchhoffs Voltage Law
Sum of all voltages around a closed path iszero.
KCL: Kirchhoffs Current Law
Sum of all currents = zero
sum all currents in = sum all currents out
Based on conservation of charge:
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Basic Laws Series/Parallel
......
111
21
++=RRReq
21
21
RR
RRReq
+
=
For Two Resistors in Parallel:
Parallel Resistors:
Series Resistors:Req= R1 + R2 +
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Basic Laws Voltage Divider
Voltage Divider for Series Resistors:
vRR
Rv
21
11
+=
vRR
R
v 21
2
2 +=
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Basic Laws Current Divider
Current Divider for Parallel Resistors:
iRR
Ri
21
21
+=
iRR
R
i21
12 +=
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Basic Laws ExampleKCL/KVL Example
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Basic Laws ExampleCalculating Resistance
Req = ?
Req = ?
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Basic Laws ExampleVoltage Divider
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Basic Laws ExampleCurrent Divider
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Basic Laws
Questions?
f
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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!
M th d f A l i
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Methods of Analysis
Nodal Analysis
assign voltages in branches and find currents.
Mesh Analysis
assign currents in a loop and find voltages.
M th d f A l i
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Methods of Analysis
Node 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
M th d f A l i
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Methods of Analysis
Node Analysis:
Select a reference node.This becomes the zero reference.
All voltages become a rise in voltage fromthis reference node.
M th d f A l i
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Methods of Analysis
Node Analysis:
Apply KCL:There are a number of slightly differentapproaches 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
M th d f A l i E l
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Methods of Analysis Example
Let us work a node problem.
M th d f A l i
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Methods of Analysis
Supernode: when a voltage source connects tononreferencenodes.
Recall that a ideal voltage source providesWHATEVER current the circuit requires.
Procedure:
1. Short the voltage source. That is: form a singlenode of the ends of the voltage source.
2. Write the constraint equation for the voltages.3. Write the standard node equations for the
supernode.
Methods of Anal sis
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Methods of Analysis
Remember the constraint equation!
v1 2V = v
2
Methods of Analysis
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Methods of Analysis
Mesh Analysis:
A mesh is a loop which does not contain any otherloops within it.
1. Assign mesh currents to the n meshes.
2. Apply KVL to each mesh. Express thevoltages in terms of Ohms law.
3. Solve the resulting n simultaneous equations.
Methods of Analysis Example
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Methods of Analysis Example
Let us work a mesh problem.
Methods of Analysis
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Methods of AnalysisSupermesh: when two meshes share a current
source.
Recall that a ideal current source providesWHATEVER voltage the circuit requires.
Procedure:
1. Open the current source. That is form a singlemesh for the two mesh sharing the currentsource.
2. Write the constraint equation for the currents.3. Write the standard mesh equation for the
supermesh.
Methods of Analysis
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Methods of Analysis
Remember to write the constraint equation!i1 6A i2 = 0
Methods of Analysis
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Methods of Analysis
Supermeshor Supernode?
1. Do what the test tells you!
2. Pick the approach with the least equations.
3. Node equations are usually easier.
Methods of Analysis
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Methods of Analysis
End of Methods of Analysis.
Questions?
Circuit Theorems
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Circuit Theorems
1. Superposition
2. Source Transformation
3. Thevenins Theorem4. Nortons Theorem
5. Maximum Power Transfer
Circuit Theorems - Superposition
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Circuit Theorems - Superposition
Determine the contribution of each independent
source to the variable in question. Then sumthese responses to find the total response.
Circuit Theorems - Superposition
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Circuit Theorems - Superposition
1. 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 totalresponse.
Circuit Theorems S T f
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Source TransformsA source transformation exchanges a voltage
source with a series resistor with a currentsource and a parallel resistor.
Riv ss =
Rvi ss =
Circuit Theorems Example
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Circuit Theorems Example
Let us work a source transformation problem.
Circuit Theorems Example
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Circuit Theorems Example
Let us work a source transformation problem.
Circuit Theorems Th i Th
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Thevenins Theorem
Thevenins Theorem: a linear two-terminal
network can be replaced with an equivalentcircuit of a single voltage source and a seriesresistor.
VTH is the open circuit voltage
RTH is the equivalent resistance of the circuit.
Circuit Theorems Th i Th
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Thevenins Theorem
Circuit Theorems Example
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Circuit Theorems Example
Let us work a Thevenin problem.
Circuit Theorems Example
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Circuit Theorems Example
Let us work a Thevenin problem.
Circuit Theorems Nortons Theorem
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Norton s Theorem
TH
THN R
V
I =
Nortons Theorem: a linear two-terminal network can bereplaced with an equivalent circuit of a single current sourceand a parallel resistor.
IN is the short circuit current.
RTH is the equivalent resistance of the circuit.
Circuit Theorems Example
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Circuit Theorems Example
Let us work a Norton problem.
Circuit Theorems Example
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p
Circuit Theorems Maximum Power Transfer
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Maximum Power TransferThe maximum power delivered to a load is when
the load resistance equals the Theveninresistance as seen from the load.
THL RR=
Circuit Theorems Maximum Power Transfer
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Maximum Power TransferWhen
Then
THL RR =
TH
THR
Vp 4
2
max =
Circuit Theorems
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End of Circuit Theorems.
Questions?
Break for 5 minutes.
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Nerves and butterflies are fine - they're aphysical sign that you're mentally ready
and eager. You have to get the butterfliesto fly in formation, that's the trick.
~Steve Bull
Operational Amplifiers
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p p
OP Amp name derived from this circuits abilityto 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.
Operational Amplifiers
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p p
Ideal Op Amp assumptions:
1. in = ip = zero
2. vn = vp
3. Vout is equal to or less than the input powervoltage.
CCout VV
Operational Amplifiers
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Use node analysis to solve the problem. If yourecognize the type and like to memorize:
Inverting Op Amp:
NoninvertingOp Amp:
input
input
feedback
out VR
RV =
inputinput
feedback
out VR
R
V
+=
1
Operational Amplifiers Example
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Let us work an Op Amp problem.
Operational Amplifiers
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End of Operational Amplifiers.
Questions?
Capacitors and Inductors
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A Capacitor consists of two conducting platesseparated by an insulator.
Capacitance is the ratio of the charge on one plate
of a capacitor to the voltage difference betweenthe two plates. Capacitance is measured inFarads.
Capacitors and Inductors
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The voltage across a capacitor cannot changeabruptly.
A capacitor is an open circuit to dc.
dt
dvCi =
Capacitors and Inductors
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Capacitors add in parallel - CAP
Series Capacitance
...21++=
CCCeq
...111
21
++=
CCCeq
Capacitors and Inductors
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An Inductor consists of a coil of conducting wire.
Inductance is the property where an inductoropposes change to current flow. Inductance is
measured in Henrys.
Capacitors and Inductors
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The current thru an inductor cannot changeabruptly.
An inductor is a short circuit to dc.
dt
diLv=
Capacitors and Inductors
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Inductors add in series.
Parallel Inductance
...21++=
LLLeq
...111
21
++=
LLLeq
Capacitors and Inductors Example
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Overall behavior of an inductor
Capacitors and Inductors Example
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Overall behavior of an inductor
Capacitors and Inductors Example
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Overall behavior of a capacitor
Capacitors and Inductors
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End of Capacitors and Inductors.
Questions?
Summary
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Passive Sign
Power: p = vi
Ohms Law v = ir = i2R = V2/R
KCL Sum of currents = zero
KVL Sum of voltage in loop = zero Series/Parallel Elements
Voltage/Current Divider
Summary
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Source Transformation
Thevenin Equivalent
Norton Equivalent
Ideal Op Amp
Capacitor Inductor
Summary
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What we did not cover:
Response of 1st order RC/RL circuits
Unbounded response
Response of 2nd order RLC circuits
Sinusoidal Steady-State analysis 3 Phase AC power
Be sure to study these areas as timepermits.
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Good Luck on the EIT Exam! It is a timed exam. Answer what you
know. Mark what you might know andcome back later. Do not get bogged downon a few questions. Move along!
Remember that it is a multiple choiceexam. Look for hints in the answers.
If totally in doubt Guess by using yourintuition and science.
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EIT Review
Electrical Circuits DC Circuits
Lecturer: Russ Tatro
Presented by TauBeta Pi
The Engineering Honor Society
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