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Lecture 1:Intro & Circuit VariablesNilsson 1.1-1.6, 2.1-2.4
ENG17 : Circuits I
Spring 2015
March 31, 2015
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Overview
• 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
• 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
• 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– 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
• 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
• 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
• 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
• 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
• 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
• Positive Power = Power Delivered to Circuit
• Negative Power = Power Extracted from Circuit
𝑝=𝑑𝑤𝑑𝑡
𝑝=𝑖𝑣
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Overview
• 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
• Voltage Sources• Current Sources• Resistors• Inductors• Capacitors
“Active Elements”Generate Electric Energy
“Passive Elements”Do NOT Generate Electric Energy
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Ideal SourcesVoltage 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
WireAssume No Resistance
NodeAny defined point (usually a point of intersection)
Valid configuration
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Schematics (w/dependents)
Valid configurationInvalid configuration
Invalid configurationValid 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
• 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
Note change in sign
Assume ideal resistance(no change w/time)
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Conductance
• Conductance, G– Units: siemens [S]
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Power & Ohm’s Law
𝑉=𝐼𝑅
𝑃= 𝐼𝑉
Therefore…
Ohm’s Law
Power Relationship
𝑃= 𝐼2𝑅
𝑃=𝑉 2
𝑅 𝑃= 𝐼 2
𝐺
𝑃=𝑉 2𝐺or
or
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Examples
𝑣𝑎=1𝐴∗8Ω=8𝑉
𝑣𝑎=−1 𝐴∗20Ω=−20𝑉 𝑖𝑑=−50𝑉25Ω
=−2𝐴
𝑖𝑏=0.2𝑆∗50𝑉=10 𝐴
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Overview
• 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
1.5V 9V
Batteries Lamp
Case
SwitchSpring
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Overview
• 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
Use common subscripts
Establish Reference Polarities
Establish Nodes that Connect Elements
7 unknowns…need 7 equations
From Ohm’s Law: 𝑣1=𝑖1𝑅1
𝑣𝑐=𝑖𝑐𝑅𝑐
𝑣 𝑙=𝑖𝑙𝑅 𝑙
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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
𝑁𝑜𝑑𝑒𝑎 : 𝑖𝑠−𝑖1=0𝑁𝑜𝑑𝑒𝑏 : 𝑖1+𝑖𝑐=0𝑁𝑜𝑑𝑒𝑐 :−𝑖𝑐−𝑖𝑙=0𝑁𝑜𝑑𝑒𝑑 : 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
𝑣 𝑙−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
𝑣1=𝑖1𝑅1
𝑣𝑐=𝑖𝑐𝑅𝑐
𝑣 𝑙=𝑖𝑙𝑅 𝑙
𝑖𝑠− 𝑖1=0𝑖1+𝑖𝑐=0−𝑖𝑐−𝑖𝑙=0𝑖𝑙−𝑖𝑠=0
𝑣 𝑙−𝑣𝑐+𝑣1−𝑣𝑠=0𝑖𝑠=𝑖1=−𝑖𝑐=𝑖𝑙
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KCL Example
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KVL Example
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