Physics 2102 Physics 2102 Lecture 13: WED 11 FEBLecture 13: WED 11 FEBCapacitors III / Current & Capacitors III / Current &

ResistanceResistance

Physics 2102

Jonathan Dowling

Ch25.6–7QuickTime™ and a

decompressorare needed to see this picture.

Ch26.1–3

QuickTime™ and a decompressor

are needed to see this picture.Georg Simon Ohm (1789-1854)

We Are Borg.Resistance Is Futile!

Exam 01:Sec. 2 (Dowling) Average: 67/100A: 90–100 B: 80–89 C: 60–79 D: 50–59

Graders:Q1/P1: Dowling (NICH 453, MWF 10:30AM-11:30AM)Q2/P2: Schafer (NICH 222B, MW 1:30-2:30 PMQ3/P3: Buth (NICH 222A, MF 2:30-3:30 PM )Q4/P4: Lee (NICH 451, WF 2:30-3:30 PM

Solutions:http://www.phys.lsu.edu/classes/spring2009/phys2102/Go over the solutions NOW. Material will reappear on FINAL!

(ii) (4 pts) What is the direction of the net electrostatic force on the central particle due to the other particles?

F≠E! Units!

F≠E!

Most common mistake to Compute Magnitude and Direction of Electric Field instead of Electric Force at Central Point.

F

This problem from our slides first week of class.

xq3

x–L

F13

F32

Charges Alone Could Cancel to Left and To Right. Must discuss Big & Small Charge versus Small and Big Distance: Q vs. 1/r2

Common mistake: To putq3 at –L to Left “By Symmetry” This would only make sense if q3 and q2 were held and q1 was free. But we are told q1 and q2 are fixed and q3 is free to move. So no symmetry!

Common mistake: Wrong x.

This is Sample Problem from Book We worked on Board

€

rF 31 =

r F 32 ⇒

k q3 q1

r312

=k q3 q2

r312

4kQ2

x 2=

kQ2

x − L( )2 ⇒

4

x 2=

1

x − L( )2

4 x − L( )2

= x 2 ⇒ ± 2 x − L( ) = x

+2 x − L( ) = x or − 2 x − L( ) = x

x = 2L or x = 2L /3Not to right.

Dielectric ConstantDielectric Constant

• If the space between capacitor

plates is filled by a

dielectric, the capacitance

INCREASES by a factor

• This is a useful, working

definition for dielectric

constant.

• Typical values of are 10–200+Q –Q

DIELECTRIC

C = A/dC = A/d

The and the constant o are both called dielectric constants. The has no units (dimensionless).

The and the constant o are both called dielectric constants. The has no units (dimensionless).

Atomic View

Emol

Ecap

Molecules set up counter E field Emol that somewhat cancels out capacitor field Ecap.

This avoids sparking (dielectric breakdown) by keeping field inside dielectric small.

Hence the bigger the dielectric constant the more charge you can store on the capacitor.

Example Example

• Capacitor has charge Q, voltage V

• Battery remains connected while dielectric slab is inserted.

• Do the following increase, decrease or stay the same:– Potential difference?– Capacitance?– Charge?– Electric field?

dielectric slab

ExampleExample

• Initial values: capacitance = C; charge = Q; potential difference = V; electric field = E;

• Battery remains connected

• V is FIXED; Vnew = V (same)

• Cnew = C (increases)

• Qnew = (C)V = Q (increases).

• Since Vnew = V, Enew = V/d=E (same)

dielectric slab

Energy stored? u=0E2/2 => u=0E2/2 = E2/2

SummarySummary• Any two charged conductors form a capacitor.• Capacitance : C= Q/V

• Simple Capacitors:Parallel plates: C = 0 A/d

Spherical : C = 4 0 ab/(b-a)

Cylindrical: C = 2 0 L/ln(b/a)

• Capacitors in series: same charge, not necessarily equal potential; equivalent capacitance 1/Ceq=1/C1+1/C2+…

• Capacitors in parallel: same potential; not necessarily same charge; equivalent capacitance Ceq=C1+C2+…

• Energy in a capacitor: U=Q2/2C=CV2/2; energy density u=0E2/2

• Capacitor with a dielectric: capacitance increases C’=kC

What are we going to What are we going to learn?learn?

A road mapA road map• Electric charge Electric force on other electric charges Electric field, and electric potential

• Moving electric charges : current • Electronic circuit components: batteries, resistors, capacitors

• Electric currents Magnetic field Magnetic force on moving charges

• Time-varying magnetic field Electric Field• More circuit components: inductors. • Electromagnetic waves light waves• Geometrical Optics (light rays). • Physical optics (light waves)

The resistance is related to the potential we need to apply to a device to drive a given current through it. The larger the resistance, the larger the potential we need to drive the same current.

) (abbr. OhmAmpere

Volt [R] :Units Ω≡=

Georg Simon Ohm (1789-1854)

"a professor who preaches such heresies is unworthy to teach science.” Prussian minister of education 1830

iV

R ≡ iRVRV

i == and : thereforeand

Ohm’s laws

Devices specifically designed to have a constant value of R are calledresistors, and symbolized by

Electrons are not “completely free to move” in a conductor. They move erratically, colliding with the nuclei all the time: this is what we call “resistance”.

Resistance is NOT Resistance is NOT Futile!Futile!

€

i ≡dq

dt =

C

s

⎡ ⎣ ⎢

⎤ ⎦ ⎥≡ Ampere[ ] = A[ ]

€

i ≡dq

dt =

C

s

⎡ ⎣ ⎢

⎤ ⎦ ⎥≡ Ampere[ ] = A[ ]

Jr

:Vector Er

as direction Same ∫ ⋅= AdJirr

that such

E i

JdA

If surface is perpendicular to a constant electric field, then i=JA, or J=i/A

Drift speed: vd :Velocity at which electrons move in order to establish a current.

E i

L

A

Charge q in the length L of conductor: eLAnq )(=

n =density of electrons, e =electric charge

dvL

t = d

d

veAn

vL

eLAntq

i ===en

J

eAn

ivd ==

dvenJrr

=

Current density and Current density and drift speeddrift speed

The current is the flux of the current density!

2mAmpere

][ =JUnits:

These two devices could have the same resistanceR, when measured on the outgoing metal leads.However, it is obvious that inside of them different things go on.

Metal“field lines”

resistivity: JEJE rr

ρρ == ,vectorsas ,or

Resistivity is associatedwith a material, resistancewith respect to a deviceconstructed with the material. ρ

σ 1 :tyConductivi =

Example:A

L

V+-

Ai

JLV

E == ,LA

R

Ai

LV

==ρAL

R ρ=

Makes sense!For a given material: resistance LessThicker

resistance MoreLonger

→→

Resistivity and Resistivity and resistanceresistance

( resistance: R=V/I )

€

ρ ≡ Ωm[ ] = Ohm⋅meter[ ]

€

ρ ≡ Ωm[ ] = Ohm⋅meter[ ]

Resistivity and Resistivity and TemperatureTemperature

• At what temperature would the resistance of a copper conductor be double its resistance at 20.0°C? • Does this same "doubling temperature" hold for all copper conductors, regardless of shape or size?

Resistivity depends on temperature:

ρ = ρ0(1+ (T-T0) )

b

a

Power in electrical Power in electrical circuitscircuitsA battery “pumps” charges through the resistor (or any device), by producing a potential difference V between points a and b. How much work does the battery do to move a small amount of charge dq from b to a?

dW = –dU = -dq•V = (dq/dt)•dt•V= iV•dt

The battery “power” is the work it does per unit time:

P = dW/dt = iVP=iV is true for the battery pumping charges through any device. If the device follows Ohm’s law (i.e., it is a resistor), then V=iR and

P = iV = i2R = V2/R