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Lecture 1:
Intro & Circuit Variables
Nilsson 1.1-1.6, 2.1-2.4
ENG17 : Circuits I
Spring 2015
March 31, 2015
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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Dr. Kyle Montgomery
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B.S. 2004 University of Houston
3 years @ Schlumberger
M.S. 2008 Purdue University
Ph.D. 2012 Purdue University
– Thesis: Novel Approaches for Wide Bandgap
Solar Cells
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What I do now…besides teach…
• Advise students
• Research
– Novel solar cells w/compound
semiconductors
– New materials for lighting, solar cells, and
beyond
– High speed, high power transistors
– Alternative energy storage solutions
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Philosophy…on teaching…and life
• Teaching is not confined to classroom time
• Conceptual understanding is key
• Life really sucks sometimes…how can I
help?
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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ENG17: Circuits 1
• Electrical quantities and elements
• Resistive Circuits
• Transient and steady-state responses of
RLC circuits
• Sinusoidal excitation and phasors
• Complex frequency and network functions
• Power Calculations
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Course Structure
• TAs
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Matt Clements
Songjie Bi
Chi Van Pham
Burcu Ercan
Yuhao Liu
Xin Zhao (Tuesday discussions)
Nathan Ellis (Thursday discussions)
• Course Website is:
– http://www.kmontgomery.net/teaching/eng17/
– Smartsite used primarily for grades
• Also using Piazza
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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SI Units
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Derived Units
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Prefixes
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Examples
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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Big Picture
• Need justifies
design
• Design specs filter
to concept, circuit
model, prototype
• Circuit analysis
necessary for
foundation
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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Voltage
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Current
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Ohm’s Law
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Water Analogy
• Water pressure = voltage
• Water flow = current
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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Ideal Element
• Passive sign convention
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Fundamental Quantities
1.Voltage (v)
2.Current (i)
3.Charge (q)
4.Flux (Φ)
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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Power ≠ Energy
• Power = Time Derivative of Energy
• UNITS!
– Power in Watts
– Energy in Watt-hrs or Joules
𝑝=
𝑑𝑤
𝑑𝑡
𝑝 = 𝑖𝑣
• Positive Power = Power Delivered to
Circuit
• Negative Power = Power Extracted from
Circuit
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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5 Ideal Basic Circuit Elements
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Voltage Sources
“Active Elements”
Generate Electric Energy
Current Sources
Resistors
“Passive Elements”
Do NOT Generate Electric Energy
Inductors
Capacitors
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Ideal Sources
Voltage Source
(const. voltage)
Current Source
(const. current)
Circle means
“Independent Source”
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Dependent Sources
Voltage Sources
Current Sources
Diamond means
“Dependent Source”
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Schematics
Valid configuration
Wire
Assume No Resistance
Node
Any defined point
(usually a point of intersection)
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Schematics (w/dependents)
Invalid configuration
Valid configuration
Valid configuration
Invalid configuration
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Schematics - GND
• Ground (GND) is a common connection
• Typically connect to Earth GND
• Always a zero [V] reference potential
GND Connect
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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Ohm’s Law
Assume ideal
resistance
(no change w/time)
Note change in sign
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Conductance
• Conductance, G
– Units: siemens [S]
–𝐺=
1
𝑅
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Power & Ohm’s Law
Ohm’s Law
𝑉 = 𝐼𝑅
Power Relationship
𝑃 = 𝐼𝑉
Therefore…
𝑃 = 𝐼2𝑅
𝑉2
𝑃=
𝑅
or
𝑃 = 𝑉 2𝐺
or
𝐼2
𝑃=
𝐺
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Examples
𝑣𝑎 = 1𝐴 ∗ 8Ω = 8𝑉
𝑖𝑏 = 0.2𝑆 ∗ 50𝑉 = 10𝐴
𝑣𝑎 = −1𝐴 ∗ 20Ω = −20𝑉
𝑖𝑑 =
−50𝑉
= −2𝐴
25Ω
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Overview
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•
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•
•
Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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Designing a Circuit Model
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Additional Elements
Short Circuit
Open Circuit
Switch
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Schematic
Batteries
Lamp
Case
Spring
Switch
1.5V
9V
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Overview
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Personal Introduction
Course Introduction
Units
Circuit Analysis
Voltage / Current
Basic Circuit Element
Power / Energy
Voltage & Current Sources
Electrical Resistance
Circuit Model
Kirchhoff’s Laws
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The Setup
Establish Nodes that
Connect Elements
Use common
subscripts
7 unknowns…need 7 equations
Establish Reference
Polarities
From Ohm’s Law: 𝑣1 = 𝑖1 𝑅1
𝑣𝑐 = 𝑖𝑐 𝑅𝑐
𝑣𝑙 = 𝑖𝑙 𝑅𝑙
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Kirchhoff’s Current Law (KCL)
The algebraic sum of all the currents at any node in a
circuit equals zero.
Therefore:
• Assign signs to currents at each node
• Positive (+) for current leaving a node
• Negative (-) for current entering a node
• Or vice versa
𝑁𝑜𝑑𝑒 𝑎: 𝑖𝑠 − 𝑖1 = 0
𝑁𝑜𝑑𝑒 𝑏: 𝑖1 + 𝑖𝑐 = 0
𝑁𝑜𝑑𝑒 𝑐: −𝑖𝑐 − 𝑖𝑙 = 0
𝑁𝑜𝑑𝑒 𝑑: 𝑖𝑙 − 𝑖𝑠 = 0
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Kirchhoff’s Voltage Law (KVL)
The algebraic sum of all the voltages around any closed
path in a circuit equals zero.
Therefore:
• Assign signs to voltages in a loop
• Positive (+) for voltage rise
• Negative (-) for voltage drop
• Or vice versa
𝑣𝑙 − 𝑣𝑐 + 𝑣1 − 𝑣𝑠 = 0
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Observations
• 7 equations  4 equations
– Because I and V are related
through R, we only need one
• With only 2 branches at a node
(in series), we only need to
know 1 current
𝑖𝑠 = 𝑖1 = −𝑖𝑐 = 𝑖𝑙
𝑣1 = 𝑖1 𝑅1
𝑣𝑐 = 𝑖𝑐 𝑅𝑐
𝑣𝑙 = 𝑖𝑙 𝑅𝑙
𝑖𝑠 − 𝑖1 = 0
𝑖1 + 𝑖𝑐 = 0
−𝑖𝑐 − 𝑖𝑙 = 0
𝑖𝑙 − 𝑖𝑠 = 0
𝑣𝑙 − 𝑣𝑐 + 𝑣1 − 𝑣𝑠 = 0
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KCL Example
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KVL Example
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