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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 1 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 2 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 3 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 4 Philosophy…on teaching…and life • Teaching is not confined to classroom time • Conceptual understanding is key • Life really sucks sometimes…how can I help? 5 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 6 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 7 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 8 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 9 SI Units 10 Derived Units 11 Prefixes 12 Examples 13 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 14 Big Picture • Need justifies design • Design specs filter to concept, circuit model, prototype • Circuit analysis necessary for foundation 15 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 16 Voltage 17 Current 18 Ohm’s Law 19 Water Analogy • Water pressure = voltage • Water flow = current 20 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 21 Ideal Element • Passive sign convention 22 Fundamental Quantities 1.Voltage (v) 2.Current (i) 3.Charge (q) 4.Flux (Φ) 23 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 24 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 25 26 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 27 5 Ideal Basic Circuit Elements • • • • • Voltage Sources “Active Elements” Generate Electric Energy Current Sources Resistors “Passive Elements” Do NOT Generate Electric Energy Inductors Capacitors 28 Ideal Sources Voltage Source (const. voltage) Current Source (const. current) Circle means “Independent Source” 29 Dependent Sources Voltage Sources Current Sources Diamond means “Dependent Source” 30 Schematics Valid configuration Wire Assume No Resistance Node Any defined point (usually a point of intersection) 31 Schematics (w/dependents) Invalid configuration Valid configuration Valid configuration Invalid configuration 32 Schematics - GND • Ground (GND) is a common connection • Typically connect to Earth GND • Always a zero [V] reference potential GND Connect 33 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 34 Ohm’s Law Assume ideal resistance (no change w/time) Note change in sign 35 Conductance • Conductance, G – Units: siemens [S] –𝐺= 1 𝑅 36 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 37 Examples 𝑣𝑎 = 1𝐴 ∗ 8Ω = 8𝑉 𝑖𝑏 = 0.2𝑆 ∗ 50𝑉 = 10𝐴 𝑣𝑎 = −1𝐴 ∗ 20Ω = −20𝑉 𝑖𝑑 = −50𝑉 = −2𝐴 25Ω 38 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 39 Designing a Circuit Model 40 Additional Elements Short Circuit Open Circuit Switch 41 Schematic Batteries Lamp Case Spring Switch 1.5V 9V 42 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 43 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 44 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 45 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 46 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 47 KCL Example 48 KVL Example 49