Transcript Chapter 26: DC Circuits

Chapters 25.4 and 26 to 26.3
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How current flows
x
1
2
3
2
EMF—Electromotive Force

Any chemical, solar, mechanical, heat
method of creating a potential difference
Batteries
 Alternator, dynamo
 Solarcell, photovoltaic
 Thermocouple

Symbol E
 Units: volts

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A simple circuit
i
4
EMF Devices
Ideal EMF device– no internal resistance
 Real EMF device– some internal
resistance

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Batteries

Several Different Types of
Batteries (called cells)

Wet Cell (left)



Car Batteries
High Current Apps
Dry Cells (Zn-Cu paste)

e-e-
Dry Cell Ratings


PbO2
PbSO
Pb 4
PbSO4


PbO2

Pb

Pb


H2
SO4


20 mA
80 mA
150 mA
Akaline Cells

PbO2
AAA
AA 25 mA
C
D
AAA
AA 300 mA
C
D
200 mA
500 mA
600 mA
EMF=1.5 V
Cells are constant voltage
sources: 1.5 3 6 9 12 15 24 48 V
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Internal Resistance

The battery itself can
have some
resistance to current
flow
PbO2
Pb

PbO2
Pb

PbO2
Pb

H2
SO4
Could be terminals
Could be plates or
paste
Could be
combination
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Internal Resistance

We treat the internal
resistance as if an
external resistor had
been added to the
circuit just ahead of
the positive terminal
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Terminal Voltage (Effective Voltage)
EMF
R
Vab=Va-Vb=EMF-iR
va
vb
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Loop Rule

The algebraic sum of changes in potential
encountered in a complete traversal of the
circuit must be zero.


AKA Kirchoff’s Loop Rule
Consider
Dr. Womble
Nashville
Panama City
Total Elevation Change = 0
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From an electrical perspective
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Resistance rule

For a move through a resistor in the
direction of current, the change in
potential is –iR

If the move opposes the current then the
change in potential is +iR.
move
+iR
Va-Vb= -iR
Va
i
Vb
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EMF Rule

For a move from the negative terminal to
the positive terminal then the change in
potential is +EMF

For a move from “+” to “-” then the change
in potential is -EMF
move
-EMF
+EMF
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Putting these ideas into practice i.e
changing a circuit into an equation
X
1. Pick a direction for the
current.
2. Pick a direction of
circuit traversal
3. Sum the potentials as
you traverse the circuit
My move
R=65 W
EMF=5 V
i
From X,
+iR+EMF=0
EMF=-iR
5=-65i
i=-0.076 A or -76 mA
The negative sign means that
we guessed the wrong direction
for the current.
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Resistors in Series

Connected resistances are said to be in series when
a potential difference that is applied across their
combination is the sum of the resulting potential
differences across all the resistances.
R3
R2
E-iR1-iR2-iR3=0
E
E
Req
i
EMF 
R1  R2  R3
EMF 
i
Req
R1
So Req=R1+R2+R3
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Reducing Networks, If You Can,
then DO SO!
Always try to reduce the total number of
variables by using the equivalent
resistance.
 For N resistors in series, the equivalent
resistance is


Req=R1+R2+….+RN
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How to find a potential difference

To find the potential difference between any two
points
1.
2.
3.
Start at one point
Traverse the circuit following any path
Add algebraically the changes in potential
Point A
R3
i
R2
Point B
R1
Blue—
Va –iR3-iR2=Vb
Va-Vb=i(R3+R2)
E
Red—
Va-E+iR1=Vb
Va-Vb=E-iR1
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One last word on internal resistance

Recall Power, P=Vi
a
X
r
E-ir=0
Va+ir-E=Vb
Va-Vb=E-ir
P=iV <-(Va-Vb)
P=i(E-ir)
P=Ei-i2r
i
E
b X
Power
of EMF
Device
Thermal
dissipation
(losses)
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Junction Rule

Sum of all currents entering a junction must
equal the sum of all currents leaving the
junction.
i3
i1
i3
i1
i2
i2
i1+i3=i2
i1
i3
i1+i2=i3
i2
i1+i2+i3=0
IN = OUT
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Resistors in Parallel

Connected resistances are said to be in parallel
when a potential difference that is applied across
their combination results in that same potential
difference across each resistance.
i1
i
E
i3
E
R1
R2
R3
i=i1+i2+i3
i
E
i2
Req
V
V V V
 

Req R1 R2 R3
1
1
1
1
1
 

 Req 
Req R1 R2 R3
1
1
1 
 
 
 R1 R2 R3 
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Resistor Color Codes

Color Codes
Color
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
Gold
Silver
No Color
Value
0
1
2
3
4
5
6
7
8
9
Tolerance
1%
2%
3%
4%
1 2 3
T
Band1*10+Band2 x 10^ Band 3
+/- Band T
5%
10%
20%
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Guidelines for Problem Solving
Replace network of resistors with their equivalents (if possible)
If you can’t simplify to a single loop, then use the junction rule and the
loop rule to set up a series of equations. Be sure to:
1.
2.
1.
Pick a direction of current (sign is a mathematical convention)
1.
2.
If you traverse a resistor against the current then +iR else –iR
If you traverse an EMF source from low potential to high potential then the
EMF is positive, else negative.
You have the following arbitrary choices
3.
1.
2.
3.
4.
Directions of currents
Which loops to use
Direction of traversal of each loop
Starting point and ending point
ABOVE ALL, REMEMBER:
4.
1.
2.
TRAVERSE THE LOOP COMPLETELY
ONCE YOU HAVE CHOSEN A DIRECTION OF THE CURRENT YOU
MUST STICK WITH THIS DIRECTION UNTIL YOU HAVE FINISHED THE
PROBLEM.
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