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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?
 Pause. Look at circuit.
R's in Parallel?
 Mark known voltages
Voltage Divider Circuit?
Current Divider Circuit?
 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?
ΔVoltage & Loop Currents
Use it on everything
 KCL? Current I/O at Nodes
Use it on everything
 Both?
One might be easier to use
 KVL?
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)
 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
requires [be – (ne – 1)] Loops
Usually this = Number of Enclosed Regions
 Generally

Exception
 Branch
includes a Current Source?
Number of KVL equations can be reduced
 See Section 4.7 for details

Source Transformation
+
R
Vs
=
Is
↑
R

These circuits are functionally the same
if
Vs = Is R
Source Transformation
Possible on 9 A & 8 Ω elements?
Vout
-
9A
↑
10 V
+
16 Ω
8Ω
Vout
↑
10 V
+
16 Ω
8Ω
9A
Source Transformation
Possible on 9 A & 8 Ω elements?
5Ω
Vout
↑
10 V
9A
+ 8Ω
-
5 Ω Vout
10 V
+
8Ω
72 V
16 Ω
16 Ω
Thevenin Equivalent Circuit
Named after Leon Charles Thevenin
1857 – 1926
 French Telegraph
Engineer
 1880's
Investigated Complex
Electrical Circuits

Source: Wikipedia