EE 1105: Introduction to EE Freshman Seminar

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EE 1105 Introduction to EEFreshman Seminar

• Lecture 3 Circuit Analysis
• Ohms Law, Kirkhoffs Laws

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Voltage and Current

• Voltage is the energy per unit of charge.

• Current is the rate of flow of charge.

 
Derivative slope, Integral area under curve
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Power and Energy

• Power associated with a circuit element is
  consumed by that circuit element when the value
  of power is positive.
• Conversely, power is generated, or produced by
  the element if the value consumed is negative.

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Independent Voltage Source

• Voltage may be constant or time-dependent
• Delivers nominal terminal voltage under all
  conditions

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Independent Current Source

• Current may be constant or time-dependent
• Delivers nominal terminal current under all
  conditions

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Passive Sign Convention

• Assign current flow direction according to the
  voltage polarities
• Calculate pvi, plt0 is power supplied by device,
  pgt0 is power delivered to device

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Ohms Law

• Electrical resistance is the ratio of voltage
  drop across a resistor to current flow through
  the resistor.
• Polarities are governed by the passive sign
  convention.

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Power and Energy

• Power associated with a circuit element is
  consumed by that circuit element when the value
  of power is positive.
• Conversely, power is generated, or produced by
  the element if the value consumed is negative.

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Power Consumed by Resistors

• Resistors consume power.
• v and i are both positive or both negative.

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Conductance Defined

• Conductance is the reciprocal of resistance.
• The units of conductance are called siemens (S)
• The circuit symbol is G

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Calculating Resistance
When conductor has uniform cross-section
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Temperature Coefficient of Resistance
Metallic conductors have a linear increase of
resistance with increased temperature.
To is the reference temperature (usually 20oC)
and Ro is the resistance at the reference
temperature. a is the temperature coefficient of
resistance for the material. At 20oC, some
values for a are
Material Alpha _at_ 20oC
Aluminum 0.004308
Copper 0.004041
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Power and Energy

• Power associated with a circuit element is
  consumed by that circuit element when the value
  of power is positive.
• Conversely, power is generated, or produced by
  the element if the value consumed is negative.

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Power Consumed by Resistors

• Resistors consume power.
• v and i are both positive or both negative.

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Conductance Defined

• Conductance is the reciprocal of resistance.
• The units of conductance are called siemens (S)
• The circuit symbol is G

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Circuits

• Abstraction describing how (the topology)
  electrical or electronic modules are
  interconnected.
• Closely related to a GRAPH.
• Nomenclature
• Nodes, Edges(Branches)
• Voltage drop computed between nodes
• Currents flowing along edges
• Paths (collection of edges with no node appearing
  twice),
• Loops (closed paths), meshes (loop containing no
  other loop).
• Series connection (elements sharing the same
  current)
• Parallel connection (elements sharing the same
  voltage)

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Example of a Circuit Model w/ Series Connection
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Kirchhoffs Voltage Law

• The sum of the voltage drops around a closed path
  is zero.
• Example -120 V1 V2 V3 V4 0

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Kirchhoffs Current Law

• A node is a point where two or more circuit
  elements are connected together.
• The sum of the currents leaving a node is zero.

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Apply KCL to Example
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Combine KVL Ohms Law
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Lamp Voltage Battery Voltage
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Battery Power and Lamp Power
Loss
Efficiency
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Resistors in Series
By KCL Is I1 I2
By Ohms Law V1 R1I1 and V2 R2I2
Combine Vs R1I1 R2I2 (R1 R2) Is ReqIs
In General Req R1 R2 Rn
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Resistors in Parallel (1/2)
By KVL Vs V1 V2
By KCL Is I1 I2
By Ohms Law
and
Combine
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Resistors in Parallel (2/2)
For two resistors
For many resistors
In terms of conductance
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Voltage Divider Circuit
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Loaded Voltage Divider
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Voltage Divider Equations
Unloaded
Loaded
If RL gtgt R2
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Using Loops to Write Equations
KVL _at_Loop a
KVL _at_ Loop b
KVL _at_ Loop c
Loop c equation same as a b combined.
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Using Nodes to Write Equations
KCL _at_ Node x
KCL _at_ Node y
KCL _at_ Node z
KCL _at_ Node w
lt Redundant
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Combining the Equations

• There are 5 circuit elements in the problem.
• va and vb are known.
• R1, R2 and R3 are known.
• v1, v2 and v3 are unknowns.
• ia, ib, i1, i2 and i3 are unknowns.
• There are 2 loop (KVL) equations.
• There are 3 node (KCL) equations.
• There are 3 Ohms Law equations.
• There are 8 unknowns and 8 equations.

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Example 1 (1/3)
By KCL
By Ohms Law
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Example 1 (2/3)
By KVL
Power
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Example 1 (3/3)
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Example 2 (1/4)
Find Source Current, I, and Resistance, R.
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Example 2 (2/4)
Ohms Law 36 V
KVL 48 V
Ohms Law 6 A
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Example 2 (3/4)
KCL 3 A
Ohms Law 12 V
KVL 60 V
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Example 2 (4/4)
Ohms Law 3 A
KCL 6 A
KVL 24 V
Ohms Law R3 W
KCL I9 A
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Homework 3 due next class!!Available online at
course website

• Acknowledgements Dr. Bill Dillon
• Questions?