Modeling Electric Fields in Circuits
TWENTY-EIGHTH STATEWIDE MEETING
OF HIGH SCHOOL PHYSICS
AND PHYSICAL SCIENCE TEACHERS
Department of Physics and Astronomy
The University of Maine - Orono, ME
Friday, March 14, 2008
James Vesenka, University of New England
Department of Chemistry and Physics
jvesenka@une.edu
faculty.une.edu/cas/jvesenka
Electric Field Model: Current
1
1st Semester Physics
Classical
Mechanics
Particle
Model
The Big Picture
Fluids
2nd Semester Physics
Multiple
Particle Model
Waves
Particle of Mass m
Constant Velocity
F = 0
Conservation of Energy
Etotal = W+Q+R
Particle of Mass m
Changing Velocity
F ≠ 0, projectile motion
Impulse/Momentum
Ft = p
ptotal = mv = constant
Conservation of Linear
Momentum
Central Force
F = (mv2/r) inward
Rotational Mechanics
Fluid Statics
Density "stuff/space"
Pressure P
Fluid Dynamics
Macroscopic motion
Electricity &
Magnetism
Field
Model
Particle of Mass m
Gravitational Field g
Gravitational Force Fg
Potential Energy Eg
Potential Vg &Tools
Magnetic dipole µ
Magnetic Field B
Magnetic Force FB
Cross Product/RHR
Induction
E -> current I
Ohms Law, Circuits
I -> Magnetic Field B
Particle of Charge q
Electric Field E
Electrostatic Force FE
Potential Energy EE
Potential V & Tools
Electric Field: Current
Oscillating
Particle
Model
Source of Waves:
Simple Harmonic
Oscillator
Linear Restoring Force
SHO Kinematics
Energy Conservation
Mechanical Waves:
Sound Waves
Energy Propagation
Superposition Principle
Doppler Shift
Light Waves &
Interference
Diffraction/Refraction
Polarization/Colors
Page 2
Modeling Cycle
Start/stop
Definitions
Decisions
Operations
Consensus
Pre-lab
Paradigm Lab
Operational
Multiple
Representations
Application
Graph, Math
Exam
Definitions
Diagram, Verbal
Refine
No
Test-Works?
Electric Field: Current
Yes
Page 3
Discussion: Flashlight Physics
Two identical flashlights: one is
connected to a “fresh” battery the
other to a “charged” capacitor.
Predict what will happen after each
flashlight is switched on.
How do you know?
Electric Field: Current
Page 4
Operational Definitions
Electric Current = charge difference in a
given time through a section of wire.
I  q/t
Electric field “drives” the current.
Units: coulomb/second  ampere (A)
André Marie Ampère



Explained forces between current carrying wires
1775 - 1836
French Physicist
Electric Field: Current
Page 5
Electric Field vs. Time
Lab Results Part A
f(t)=“Bings”, q (t), I(t)
1.0
0.37
t (s)
ti
+ + + E, I big
tm
+
tf
10
30
f(t) = f(0)exp[(-0.1/s)t(s)]
f(t) = f(0)exp(-t/t)
-
t = “decay constant” time
E, I small E, I zero
f(t)/f(0) = 0.37 when t/t = 1
Electric Field: Current
Page 6
Electric Field Drives Current
Uniform E throughout a wire because of
uniform charge distribution.
+
Etotal
+ E
+R
+ +
+ +
+ +
+ +
+
Etotal
EL + + EL ER +
Etotal
EL ER -
+
+ +
+ +
-
Etotal
EL ER
-
Etotal
- -
- -EL
EL ER - -
Electric Field: Current
Etotal
- - - -
ER - - -
Page 7
Charge Density Picture
Uniform E throughout a wire because of
uniform charge density.
High
Potential
+
+ +
+ +
+ + =
Etotal
EL
EL ER
-
Low
Potential
- - =
+ +
+ +
Etotal
ER
- - -
- - -
Etotal
EL ER
Electric Field: Current
“Conventional”
Current “I”
Etotal
EL ER
-
Etotal
EL
ER
Electron
Current “I-”Page 8
Charge Density I
Strength of E depends on the
distribution of charge.
+
+
+
+
+
+
+
+
+ + + + +
+
+
V+
+
+
+
+ +I
+
+
+
+
+
+
+
+
E
-
- - - - -
V-
-
-
-
-
-
-
-
Electric Field: Current
-
-I
-
Page 9
Charge Density II
The longer the parallel lines, the more
positive the charge.
V+
E
V-
+I
Electric Field: Current
-I
Page 10
PRS ?
Where is the current the largest?
Where is it the smallest?
A. Smallest in battery,
largest in resistor
B. Smallest in resistor,
largest in battery
C. Same in battery and
resistor
+
+
+
+
+
+
+
+ + + +
+
+
+
- - - - - -
+
+
+
+
+
+
-
-
-
-
Demo: Student Current
Conservation of charge: Electrical current
can be neither created nor destroyed.
Electric Field: Current
Page 11
Review: Ohm’s Law
Lab Results
∆V(V)
5.0
V
+
+
+
-
Capacitor
A
10
I(A)
1.0
10
∆V(V)
t (s)
t (s)
E = -V/x
I (A)
Resistor
Electric Field: Current
∆V(V) = (5
V/A)I(A)
Page 12
Ohm’s Law
∆V=(5 V/A) I=(0.2 A/V)∆V
∆V vs I:
∆V = IR
 R = Resistance
 Units: V/A = W

Georg Simon Ohm

I (A)
∆V (V)
1787-1854
Representations
Verbal, Graphical, Diagrams
 Motion Map, Forces, Energy
and charge conservation

Electric Field: Current
Page 13
PRS ?
How do the bulb brightness (called the
“Luminance”, symbol “L”, compare in three
circuits containing identical batteries and
identical bulbs drawn below?
A.
B.
C.
D.
E.
LA=LB=LC=LD=LE
LA=LD=LE>LB=LC
LA>LB=LC>LD=LE V
LB=LC>LA=LD=LE
LB=LC>LA>LD=LE
LA
V
Electric Field: Current
LB
V
LD
LC
Page 14
LE
Ohm’s Law Ratio: Diagram
I = ∆V/R
R r x A I
A
∆V = constant
R = constant
V I
x
Electric Field: Current
Page 15
Electric Field Model
R = rx/A
[units: Wm*m/m2]
I = ∆V/R = E∆x/R =E∆x/rx/A =EA/r
I increases with E-Field and Area
I decreases with resistivity
EA const.
r
E
Electric Field: Current
A
A/r const. E/r const.
E I
Page 16
PRS ?
Brightness depends on current which depends
on the electric field E. Use the field concept
to predict how the bulb brightnesses will
behave.
A.
B.
C.
D.
E.
EA=EB=EC=ED=EE
EA=ED=EE>EB=EC
EA>EB=EC>ED=EE V
EB=EC>EA=ED=EE
EB=EC>EA>ED=EE
EA
V
x
Electric Field: Current
EB
EC
x
x
V ED
x
Page 17
EE
Light Bulb Answer
As E decreases, so does I and brightness.
EB
EA
ED
EE
EC
V+
x
V=V+-VE = -V/x
VEnergy Conservation:
Vin = VB+VC
IN
2x
Charge Conservation:
Iin = ID+IE
Electric Field: Current
Page 18
Conservation of Energy
V (V)
Energy is constant:
VAB = VDC + VDE
 IReff = IR1 + IR2 =>

Rseries = R1 + R2 = Ri
I
A
IN
V(V)
D
VR1
B Vbat
VR2
E
ABCDEA
Vbat
R2
D
E
Electric Field: Current
I (A)
C
R1
x (m)
t(s)
VR2
VR1
t(s)
Page 19
Conservation of Charge
Potential difference is same in parallel (||):

VR1 = VR2 = Vbat = V
I1
IN
R2
I2
Electric Field: Current
V(V)
R1
I (A)
Vbat
VR2
I
VR1
Current “splits”: I = I1 + I2
V/R|| = V/R1 + V/R2
1/Reff = 1/R1 + 1/R2 => 1/R||=1/Ri
Vbat
t(s)
VR1,VR2
t(s)
Page 20
Circuit Lab Quiz Diagram
What happens to the current at A?
The current splits: I = I1+I2
At B?
I
I1+I2 = I
I I
What is
q and E
through
each
resistor?
+ + + + + +
- - - - - -
+++
+++
+
+
I1
1
E1
+
--Electric Field: Current
2
A
B
I
+++
+++
+
+
E2
I2
+
E
--Page 21
Snap Circuit Set -up
Snap Circuits by Elenco, www.elenco.com
Electric Field: Current
Page 22
Typical Ohmic Data
Electric Field: Current
Page 23