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ENGS2613 Intro Electrical Science
Week 2
23 & 25 January 2017
Dr. George Scheets
Read 2.1 – 2.5
 Problems 1.15, 16, & 29; 2.1, 12, & 16
 Quiz #1, 27 January

 Solve
I's, V's, P's given a circuit
 See Fall 2016 Quiz #1
 Yours
will be ≈ 20% easier
Quiz #1
Closed Book & Neighbor
 Up to 3 unattached sheets of notes OK
Keep on your desk
 Calculator OK- No Sharing
 Smart Phones NOT OK
 Reaching down for something in backpack?

 Get
permission first
Wires Generally Have Resistance


12 gauge copper wire
(diameter = 0.091 inches)
R ≈ 0.002 Ω/foot
Exception: Superconducting wires have R ≈ 0
Can carry very large currents
77 K = -321◦ F
Sources: www.cirris.com/learning-center/calculators/133-wire-resistance-calculator-table
& www.suptech.com/Cables_Oct_10.pdf
Circuit Elements as of 23 January

Active Devices (Ideal. Can generate power)
Current flow is Hi → Lo V outside device
 Independent
Voltage Source
 Independent Current Source
 Dependent Voltage Source
 Dependent Current Source

Passive Device (can't generate power)
Current flow is Hi → Lo V inside device
 Resistor
 Wire
(Resists current flow)
Standard Assumptions

Sustained current requires a loop
 Path

Connecting wires have R = 0 Ω
 No

from High to Low voltage side of source
voltage drop regardless of current
Treat ground as = 0 volts
Ohm's Law: V = IR
Voltage drop across device =
(Current thru it)(Resistance)
 Power: P = VI

Simple Circuits
V+ = 0 Volts
+
-
+
50 Ω
9V
V+ = 9 Volts
50 Ω
V2 = 0 Volts 9 V
40 Ω
V- = 0 Volts
No current loop exists.
Hence no current flows.
Using V = IR…
V2 = 9 Volts
40 Ω
V- = 9 Volts
Resistors in Series

Exact same current flows thru R1 & R2?
Yes? R = R1 + R2
I
+
- +
-
R1
+
R2
-
R = R1 + R2
I
Electrocution & You


Current is the killer
120 VAC
 Dangerous
wet
Image Source: www.redit.com
if you're
Current Amounts
Source: hypertextbook.com/facts/2000/JackHsu.shtml
Source:www.physics.ohio-state.edu/~p616/safety/fatal_current.html
Hand-to-Hand Resistance, Dry



1.228 MΩ
I = V/R
= 120 VAC
1,228,000
= 97.72 μ amps AC
= 0.097 m amps AC
= 0.000097 amps AC
≈ 0.0001 amps AC
You'll Feel This
Hand-to-Hand Resistance, Wet



522 KΩ
I = V/R
= 120 VAC
522,000
= 229.9 μ amps AC
= 0.2299 m amps AC
≈ 0.0002 amps AC
You'll Feel This
Hand-to-Hand Resistance, Wet
& Salty



213 KΩ
I = V/R
= 120 VAC
213,000
= 563.4 μ amps AC
= 0.5634 m amps AC
You'll Feel This
120 V AC

Respect It!

Full Body Immersion in Water
Can Be Deadly

For Example: Today.Com
Current Amounts
Those in the water were here.
Source: hypertextbook.com/facts/2000/JackHsu.shtml
Source:www.physics.ohio-state.edu/~p616/safety/fatal_current.html
Residential Areas

240 V AC to House
Insulated Lines
 120
V AC
Neutral
120 V AC

Top Wire
Not Insulated
 Sine
Wave
 ≈ 13,200 V AC
Hand-to-Hand Resistance, Wet



522 KΩ
I = V/R
= 13,200 VAC
522,000
= 25.3 m amps AC
TROUBLE!!
Current Amounts
Source: hypertextbook.com/facts/2000/JackHsu.shtml
Source:www.physics.ohio-state.edu/~p616/safety/fatal_current.html
High Voltage Situations
Someone Can't Let Go?
Do NOT grab them to pull away
 Ranked Options
Kill Power
Pry Them Off
Non-metallic Tool
Knock Them Off
More Dangerous

High Voltage Situations

In a Car under fallen Power Lines?
 Stay
There!
Car sits on 4 rubber insulators

Have to get out?
 Do
NOT step out
Do Not simultaneously touch Car & Ground
or (Power Line & Ground)
 Leap Out
Still May Kill You if Ground is Wet
Lightning

30,000 amps & 15 Coulombs
→ 500 μsec
120,000 amps & 350 Coulombs
→ 2.9 msec

Human Struck?
10% - 25% Death Rate
Source: Wikipedia
Kirchhoff's Laws
Named after Gustav Kirchhoff
1824 - 1887
 Prussian Physicist
University Professor
 1845: Developed His Laws
While a Student

 Became
his PhD dissertation
Source: Wikipedia
Kirchoff's Current Law

Plumbing System
3 Gps
α Gps
β Gps
α + β Must = 3

Electrical System
αA
3A
βA
α + β Must = 3
Node generally = Wire
Current going in = Current going out
Kirchoff's Voltage Law
6 PSI
+
+
50 Ω
9V
Pump
3 PSI

40 Ω
+
-
1 PSI

-
9V
Plumbing System
+5 – 3 – 2 = 0 psi


0 Volts
Electrical System
CW KVL Loop
+

4V
9-5-4=0
CCW KVL Loop
+
4+5–9=0
DC Circuit with Resistors

To Solve, Need…
Ohm's Law
Kirchhoff's Current Law
Kirchhoff's Voltage Law

… Properly Applied Algebra
Using Kirchhoff's Voltage Law

Draw current loops



Label voltage drops for each element





MUST follow current directions
Passive device (Resistor):
 Current into + side, Current out on – side
Active device (Voltage or Current Source):
 Current exits + side, Current enters – side
+ side is at a higher voltage than – side (if current direction is correct)
Write equation for voltage drops or gains around loop




Arbitrary direction (clockwise or counter-clockwise)
Hit each circuit element at least once (preferably only once)
Arbitrary direction (with or against current flow)
Going from – side to + side? Positive value in equation
Going from + side to – side? Negative value in equation
Solve Equations