ENGS2613 Intro Electrical Science Week 5 Read 4.4 – 4.8 Problems 3.30; 4.3, 6, 7, 17, & 22 Exam #1, Friday, Chapters 1.1 – 4.8 < Source Transformations HKN Review, Thursday, 7:00 pm, PS141 Quiz 3 Results Hi = 10, Low = 2, Ave = 6.81, Deviation = 1.82

Exam #1 Friday Closed Book & Neighbor Up to 3 unattached sheets of notes OK Keep on your desk Have them on hand before you start Calculator OK Smart Phones NOT OK Reaching down for something in backpack? Get permission first Budget your time!

A Possible Exam Technique 4 pages, 50 minutes 1st Pass Allocate 10 minutes a page Not done after 10? Move on. 2nd Pass Have at least 9-10 minutes left Seen all problems Should know where it's cost-effective to go Don't get sucked into a single page!!!

DC Circuit with Resistors R's in Series? R's in Parallel? Voltage Divider Circuit? Current Divider Circuit? Pause. Look at circuit. Mark known voltages Mark known currents Is it possible to simplify? Worth doing so? Can you use Ohm's Law? Have 2 of 3 (ΔV, I, or R)? Can you use KCL? Know I's thru a node, except one? Formally use KCL or KVL KCL: Write current equations based on Node Current I/O KVL: Write voltage add/drop equations (ΔV's) based on Current Loops

What are you Comfortable With? KVL? ΔVoltage & Loop Currents Use it on everything KCL? Current I/O at Nodes Use it on everything Both? One might be easier to use

Some Terminology ne: Number of Essential Nodes Essential Node = Node with > 2 elements attached be: Number of Essential Branches Path from 1 Essential Node to another… …that doesn't pass thru another Essential Node… …and has Unknown Current Mesh Loop that does not Enclose any other Loop Nodal Analysis (KCL) a.k.a. Node Voltage Method Requires ne – 1 equations Mesh Current Analaysis (KVL) Requires be – (ne – 1) # equations Frequently this = # Enclosed Regions

Node Voltage Method (KCL) Identify Essential Nodes If necessary, make one ground Define Essential Node voltages If voltage known, write # value. If unknown, assign label. Draw & label currents in/out of each node. Mark voltage drops accordingly (+ & -) Apply KCL at each Essential Node (except ground) Generally ne -1 equations Solve

Mesh Current Method (KVL) Draw [be – (ne – 1)] Current Loops Frequently this = Number of Enclosed Regions Label Voltage Drop or Increase (+ or -) Caused by each loop Have a current source? Note Δvoltage across, if known. Otherwise assign a label (such as V1 = voltage across source). Write KVL around each loop Solve

Planar Circuit Figure 4.2 in the text shows an example of a non-planar circuit. Source: Our textbook

Some Exceptions Node Voltage Method (KCL) Exception Generally requires (ne – 1) KCL equations Exception Voltage Source only element between 2 Essential Nodes? Number of KCL equations can be reduced See Section 4.4 for details Mesh Current Method Generally requires [be – (ne – 1)] Loops Usually this = Number of Enclosed Regions Branch includes a Current Source? Number of KVL equations can be reduced See Section 4.7 for details

Source Transformation Vs R + - Is R ↑ = These circuits are functionally the same if Vs = Is R

Source Transformation Possible on 9 A & 8 Ω elements? Vout 10 V + - 9 A ↑ 8 Ω 16 Ω Vout 10 V + - 9 A ↑ 16 Ω 8 Ω

Source Transformation Possible on 9 A & 8 Ω elements? 5 Ω Vout - ↑ 10 V 9 A 16 Ω 8 Ω + Vout 10 V + - 72 V 16 Ω 8 Ω 5 Ω

Thevenin Equivalent Circuit Named after Leon Charles Thevenin 1857 – 1926 French Telegraph Engineer 1880's Investigated Complex Electrical Circuits Source: Wikipedia