Download A d f T d A d f T d Agenda for Today

Physics
ys cs 132:
3 Lecture
ectu e 15
5
Elements of Physics II
A
Agenda
d for
f T
Today
d


Resistance
 Resistors
 Series
 Parallel
 Ohm’s law
Electric Circuits
 Current
 Kirchhoff
Kirchhoff’s
s laws
Physics 202: Lecture 5, Pg 1
Electric Current

H
How
d
does a capacitor
it gett di
discharged?
h
d?

Figure (a) shows a charged capacitor in equilibrium.

Figure (b) shows a wire discharging the capacitor
capacitor.

As the capacitor is discharging, there is a current in the
wire.
Physics 202: Lecture 5, Pg 2
Charge Carriers

The outer
Th
t electrons
l t
off metal
t l
atoms are only weakly bound
to the nuclei.

In a metal, the outer
electrons become detached
from their parent nuclei to
form a fluid-like sea of
electrons that can move
through the solid.
solid

Electrons are the charge
carriers in metals.
Physics 202: Lecture 5, Pg 3
A Model of Conduction
 Within a conductor in
electrostatic
equilibrium, there is no
electric field.
 In this case, an electron
bounces back and forth
between collisions, but
its average velocity is
zero.
zero
Physics 202: Lecture 5, Pg 4
A Model of Conduction
• In the presence of an
electric field, the
electric
l t i fforce causes
electrons to move
along parabolic
trajectories between
collisions.
• Because of the
curvature of the
t j t i
trajectories,
there
th
is
i a
slow net motion in the
“downhill”
downhill direction.
Physics 202: Lecture 5, Pg 5
Plinko




Disks = electrons
Disk bounces through atoms on it’s
way down the incline
Angle of incline = emf (potential
difference))
Youtube demo
Physics 202: Lecture 5, Pg 6
Discharging a Capacitor

How long should it take
to discharge this
capacitor?

A typical drift speed of
electron current
through
h
h a wire
i iis
vd  104 m/s.

At this rate
rate, it would
take an electron about
2000 s (over half an
hour) to travel 20 cm.
cm
Physics 202: Lecture 5, Pg 7
Discharging a Capacitor

The wire is already full
of electrons!

We don’t have to wait
for electrons to move all
the way through the wire
from one plate to
another.

We just need to slightly
rearrange the charges
on the plates and in the
wire.
Physics 202: Lecture 5, Pg 8
Creating a Current

A book on a table will
slow
l
d
down and
d stop
t
unless you continue
pushing.

Analogously, the sea of
electrons will slow down
and stop unless you
continue pushing with
an electric field.
Physics 202: Lecture 5, Pg 9
Electromotive force




Electromotive force (emf) is the maximum
potential difference a battery or power source
can give a circuit.
A car b
battery h
has an emff off 12 V
Sometimes shown as a script (E)
Symbol for emf
+
Physics 202: Lecture 5, Pg 10
Electrical Current
When we connect the two terminals of an emf to
a circuit ( a continuous conducting path), charge
will move continuously through the circuit.


Since there is a potential difference electrons in
circuit will feel a force

emf

Electrons will flow
in direction of
positive terminal
Battery “pushes”
electrons
Physics 202: Lecture 5, Pg 11
Electrical Current

This flow is called electric current

Net amount of charge through a point in
the circuit per unit time.

Units Ampere = Coulomb/second
Q
I
t
Physics 202: Lecture 5, Pg 12
Electric Current

The direction of current flow – from the positive terminal to
the negative one – was decided before it was realized that
electrons are negatively charged
charged. Therefore
Therefore, current flows
around a circuit in the direction a positive charge would
move; electrons move the other way. However, this does
not matter in most circuits.
circuits
Physics 202: Lecture 5, Pg 13
Establishing
g the Electric Field in a Wire

The figure shows two
metal wires attached to
th plates
the
l t off a charged
h
d
capacitor.

This is an electrostatic
situation.

What will happen if we
connect the bottom
ends of the wires
together?
Physics 202: Lecture 5, Pg 14
Establishing the Electric Field in a Wire
Establishing the Electric Field in a Wire

Within a very brief
interval of time
(109 s) of connecting
the wires
wires, the sea of
electrons shifts
slightly.

The surface charge is
rearranged into a
nonuniform
distribution, as shown
in the figure
Physics 202: Lecture 5, Pg 15
Establishing the Electric Field in a Wire

The nonuniform distribution of surface
charges along a wire creates a net electric
field inside the wire that points from the more
positive end toward the more negative end of
the wire.

This is the internal electric field that pushes
the electron current through the wire.
Physics 202: Lecture 5, Pg 16
Give it a try:
Surface charge is distributed on a wire as shown. Electrons
in the wire
A. Drift to the right.
g
B. Drift to the left.
C. Move upward.
p
D. Move downward.
E. On average, remain at rest.
Physics 202: Lecture 5, Pg 17
Resistance

Resistance: Traveling through a conductor, electrons
b
bump
iinto
t thi
things which
hi h slows
l
th
them d
down.
 : Resistivity: Density of bumps
L
 L: Length of conductor
A
 A: Cross sectional area of conductor
R ρ

A
All electrical devices will resist
the flow of electrical current
L
Physics 202: Lecture 5, Pg 18
R ρ
L
A
Plinko
Physics 202: Lecture 5, Pg 19
Ohm’s law

Rule for current flow in most conductors:
 Higher resistance leads to lower current
 Higher potential difference leads to higher current

Ohm’s
Ohm
s law
V  IR
• Higher
Hi h resistance
i t
llower currentt

Units are Ohms ()
V
I 
R
Physics 202: Lecture 5, Pg 20
Ohm’s law

Ohm’s law
V  IR
V
I 
R
Physics 202: Lecture 5, Pg 21
Resistor

A device that resists current

Used to
o co
control
o cu
current
e flow
o in a ccircuit
cu

Resistor in a circuit:

Generally in a circuit the resistance of the
connecting wires are very small and we can
neglect them.

Wires will resist current, but we will assume
they have zero resistance!!
Physics 202: Lecture 5, Pg 22
Battery-Wire-Resistor-Wire
y
Circuit

The figure shows a
resistor connected to a
battery with currentcarrying wires
wires.

Current must be
conserved; hence the
current I through the
resistor is the same as the
current in each wire.
Physics 202: Lecture 5, Pg 23
Kirchhoff’s Junction Law
For a junction, the law of
conservation of current
requires that
where the  symbol
y
means summation.
This basic conservation
statement is called
Kirchhoff’s junction
law
law.
Physics 202: Lecture 5, Pg 24
Give it a try:
The current in the fourth wire is
A.
16 A to the right.
B.
4 A to the left.
C. 2 A to the right.
D. 2 A to the left.
E.
Not enough information to tell.
Physics 202: Lecture 5, Pg 25