Download Physics 2102 Spring 2002 Lecture 8

Physics 2102
We Are Borg.
Resistance Is
Futile!
Jonathan Dowling
Physics 2102
Lecture 13: WED 11 FEB
Capacitors III / Current & Resistance
Ch25.6–7
QuickTime™ and a
decompressor
are needed to see this picture.
Ch26.1–3
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d eco mpres sor
are nee ded to s ee this picture.
Georg Simon Ohm
(1789-1854)
Exam 01:
Sec. 2 (Dowling) Average: 67/100
A: 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 PM
Q3/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!
This problem from our slides first week of class.
F
(ii) (4 pts) What is the direction of the net electrostatic force
on the central particle due to the other particles?
F≠E!
F≠E! Units!
Most common mistake
to Compute Magnitude
and Direction of
Electric Field instead of
Electric Force at
Central Point.
This is Sample Problem from Book We worked on Board
x
F32
F13
q3
x–L
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: Wrong x.
r
r
k q3 q1 k q3 q2
F31  F32 

2
r31
r312
4kQ2
kQ2
4
1

 2
2
2
2
x
x
x  L
x  L
Common mistake: To put
q3 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!
4 x  L  x 2   2x  L  x
2
2x  L  x or  2x  L  x
x  2L or x  2L /3 Not to right.
Dielectric Constant
• If the space between capacitor
DIELECTRIC
plates is filled by a dielectric, the
capacitance INCREASES by a
factor 
• This is a useful, working definition
+Q –Q
C =  A/d
for dielectric constant.
• Typical values of  are 10–200
The  and the constant
o are both called
dielectric constants. The 
has no units (dimensionless).
Atomic View
Emol
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.
Ecap
Hence the bigger the
dielectric constant the
more charge you can
store on the capacitor.
Example
• Capacitor has charge Q, voltage V
• Battery remains connected while
dielectric slab is inserted.
dielectric
• Do the following increase,
slab
decrease or stay the same:
– Potential difference?
– Capacitance?
– Charge?
– Electric field?
Example
• Initial values:
capacitance = C; charge = Q; potential
difference = V;
electric field = E;
• Battery remains connected
• V is FIXED; Vnew = V (same)
• Cnew = C (increases)
dielectric
slab
• Qnew = (C)V = Q (increases).
• Since Vnew = V, Enew = V/d=E (same)
Energy stored?
u=0E2/2 => u=0E2/2 = E2/2
Summary
• 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 learn?
A 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)
Resistance is NOT Futile!
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”.
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.
Ohm’s laws
V
R
i
Units : [R] 
V
and therefore : i 
and V  iR
R
Volt
 Ohm (abbr. )
Ampere
Georg Simon Ohm
(1789-1854)
"a professor who preaches such heresies
is unworthy to teach science.” Prussian
minister of education 1830
Devices specifically designed to have a constant value of R are called
resistors, and symbolized by
dq C
i
   Ampere   A
s 
dt
Current density and drift speed
Vector :

Same direction as E

J
such that
 
i   J  dA
The current is the flux of the current density!
If surface is perpendicular to a constant electric
field, then i=JA, or J=i/A
[J ] 
Units:
dA
J
Ampere
m2
E
i
Drift speed: vd :Velocity at which electrons move in order to establish a current.
Charge q in the length L of conductor: q  (n A L) e
L
n =density of electrons, e =electric charge
A
t
E
i
L
vd
i
q n ALe

 n A e vd
L
t
vd
i
J

n Ae n e


J  n e vd
vd 
Resistivity and resistance
Metal
“field lines”
These two devices could have the same resistance
R, when measured on the outgoing metal leads.
However, it is obvious that inside of them different
things go on.


E
resistivity:   or, as vectors, E   J
J
Resistivity is associated
( resistance: R=V/I )
  m  Ohm  meter 
with a material, resistance
with respect to a device
1
Conductivi
ty
:


constructed with the material.


Example:
A
-
L
V
+
V
E ,
L
i
J
A

Makes sense!
For a given material:
V
LRA
i
L
A
R
L
A
Longer  More resistance
Thicker  Less resistance
Resistivity and Temperature
Resistivity depends on
temperature:
 = 0(1+a(T-T0) )
• 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?
b
Power in electrical circuits
A 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?
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 = iV
P=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