Electric Field Model: Current 1

Modeling Electric Fields in Circuits

TWENTY-EIGHTH STATEWIDE MEETINGOF HIGH SCHOOL PHYSICS

AND PHYSICAL SCIENCE TEACHERS

Department of Physics and AstronomyThe University of Maine - Orono, ME

Friday, March 14, 2008

James Vesenka, University of New EnglandDepartment of Chemistry and Physics

jvesenka@une.edufaculty.une.edu/cas/jvesenka

Electric Field: Current Page 2

Classical Mechanics

Particle Model

Waves Oscillating Particle Model

Electricity &

Magnetism

Field Model

Particle of Mass mGravitational Field g

Gravitational Force Fg

Potential Energy Eg

Potential Vg &Tools

Particle of Charge qElectric Field E

Electrostatic Force FE

Potential Energy EE

Potential V & Tools

Magnetic dipole µMagnetic Field B

Magnetic Force FB

Cross Product/RHRInduction

Particle of Mass mConstant Velocity

F = 0

E -> current IOhms Law, Circuits

I -> Magnetic Field B

Particle of Mass mChanging VelocityF ≠ 0, projectile

motion

Conservation of EnergyEtotal = W+Q+R

Impulse/MomentumFt = p

ptotal = mv = constantConservation of Linear

Momentum

Central ForceF = (mv2/r) inwardRotational Mechanics

Source of Waves:Simple Harmonic

OscillatorLinear Restoring Force

SHO KinematicsEnergy Conservation

Mechanical Waves:Sound Waves

Energy PropagationSuperposition Principle

Doppler Shift

Light Waves & Interference

Diffraction/RefractionPolarization/Colors

Fluid StaticsDensity "stuff/space"

Pressure P

2nd Semester Physics

1st Semester Physics

Fluid DynamicsMacroscopic motion

Fluids Multiple Particle Model

The Big Picture

Electric Field: Current Page 3

Modeling CycleStart/stop

Definitions Operations

Decisions

Paradigm Lab

Pre-lab

Operational

Definitions

Multiple Representatio

ns

Graph, Math

Diagram, Verbal

Test-Works?

NoRefine

Yes

Consensus

Application

Exam

Electric Field: Current Page 4

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 5

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 6

Electric Field vs. Time Lab Results Part A f(t)=“Bings”, q (t),

I(t)

t (s)10 30

0.37

1.0

f(t) = f(0)exp[(-0.1/s)t(s)]

f(t) = f(0)exp(-t/)

= “decay constant” time

f(t)/f(0) = 0.37 when t/ = 1

+++

---

+ -

ti tm tf

E, I big E, I small

E, I zero

Electric Field: Current Page 7

Electric Field Drives Current

Uniform E throughout a wire because of uniform charge distribution.

ELEL ER ER

EL

Etotal Etotal

-

-

-

-

-

-

-

-

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+ +

+ + -

-

-

-

-

-

- -

- -

Etotal

ER

EtotalEtotal

ERELEL

ER

EL ER

Etotal

-

-

+

+

Electric Field: Current Page 8

Charge Density Picture Uniform E throughout a wire because of

uniform charge density.

ELEL ER ER

EL

Etotal Etotal -Etotal

ER

EtotalEtotal

ERELEL

ER

“Conventional” Current

“I”+

Electron Current “I-”

-

=-

-

-

-

-

-

- -

- -Low

Potential+

+

+

+

+

+

+ +

+ +

=

High Potential

Electric Field: Current Page 9

Charge Density I Strength of E depends on the

distribution of charge.

V+

V-

-I

+++++

-----

+ + + + +

- - - - ----

-

-

-

+++

+

+

+

+ + + + +

- - - - -

++

--

++

+

+

--

-

-

E

+I

Electric Field: Current Page 10

Charge Density II The longer the parallel lines, the

more positive the charge.

V+

V-

E

+I

-I

Electric Field: Current Page 11

PRS ?

A. Smallest in battery, largest in resistor

B. Smallest in resistor, largest in battery

C. Same in battery and resistor

++++

----

+ + + +

- - - - ----

-

-

+++

+

+ ++

--

++

+

--

-

+ +

- - -

Where is the current the largest? Where is it the smallest?

Conservation of charge: Electrical current can be neither created nor destroyed.

Demo: Student Current

Electric Field: Current Page 12

Review: Ohm’s Law Lab Results

∆V(V) = (5 V/A)I(A)

I (A)

∆V(V)

V

A

Capacitor

Resistor

E = -V/x

+++

---

I(A)

t (s)10

1.0

∆V(V)

t (s)10

5.0

Electric Field: Current Page 13

Ohm’s Law ∆V vs I:

∆V = IR R = Resistance Units: V/A =

Georg Simon Ohm 1787-1854

Representations Verbal, Graphical,

Diagrams Motion Map, Forces,

Energy and charge conservation

∆V (V)I (A)

I=(0.2 A/V)∆V∆V=(5 V/A)

Electric Field: Current Page 14

PRS ?

A. A=B=C=D=E

B. A=D=E>B=C

C. A>B=C>D=E

D. B=C>A=D=E

E. B=C>A>D=E

A

V VV

How do the bulb brightness (called the “Luminance”, symbol “”, compare in three circuits containing identical batteries and identical bulbs drawn below?

B

C

D E

Electric Field: Current Page 15

Ohm’s Law Ratio: Diagram I = ∆V/R

R =

consta

nt

V RI I

∆V

= co

nsta

nt

x

x

A

A

Electric Field: Current Page 16

Electric Field Model R = x/A [units: m*m/m2] I = ∆V/R = E∆x/R =E∆x/x/A =EA/

E I

E/ co

nst.

A/ co

nst.

E

A

EA

con

st.

I increases with E-Field and AreaI decreases with resistivity

Electric Field: Current Page 17

PRS ?

A. EA=EB=EC=ED=EE

B. EA=ED=EE>EB=EC

C. EA>EB=EC>ED=EE

D. EB=EC>EA=ED=EE

E. EB=EC>EA>ED=EE

EA EEED

EC

EBVV

V

xxx

x

Brightness depends on current which depends on the electric field E. Use the field concept to predict how the bulb brightnesses will behave.

Electric Field: Current Page 18

Light Bulb Answer As E decreases, so does I and brightness.

EA EEED

EC

EB

V+

V-

E = -V/x2x

xV=V+-V-

Energy Conservation: Vin

= VB+VC

Charge Conservation: Iin =

ID+IE IN

Electric Field: Current Page 19

Conservation of Energy Energy is constant:

VAB = VDC + VDE

IReff = IR1 + IR2 => Rseries = R1 + R2 = Ri

E

IN

V(V

)I (A

)

t(s)

t(s)

Vbat

VR1

R1

R2

I

VR2

VR1

Vbat VR2

Ax (m)

V (V)

B EC D A

A

B

E

C

D

D

Electric Field: Current Page 20

Conservation of Charge Potential difference is same in parallel (||):

VR1 = VR2 = Vbat = V

Current “splits”: I = I1 + I2 V/R|| = V/R1 + V/R2 1/Reff = 1/R1 + 1/R2 => 1/R||=1/Ri

R1 R2 V(V

)I (A

)

I

VR

1

t(s)

t(s)IN

Vbat

VR1,VR2

I1 I2V

R2Vbat

Electric Field: Current Page 21

Circuit Lab Quiz Diagram What happens to the current at A? The current splits: I = I1+I2 At B? I1+I2 = I

+ + + + + +- - - - - -

A

BWhat is q and E through each resistor?

II1 I2

II1 I2

E

E1 E2

+++ +++

--- ---

+++ +++

+ +

+ + + +

Electric Field: Current Page 22

Snap Circuit Set -upSnap Circuits by Elenco, www.elenco.com

Electric Field: Current Page 23

Typical Ohmic Data