Transcript Phys132 Lecture 5 - Welcome to the Department of Physics

Physics 1502: Lecture 12
Today’s Agenda
• Announcements:
– Lectures posted on:
www.phys.uconn.edu/~rcote/
– HW assignments, solutions etc.
• Homework #4:
– On Masterphysics : due next Friday at 8:00 AM
– Go to masteringphysics.com
• Midterm 1: next week (Oct. 5)
– Covers Ch. 20-25
Summary
R1
• Resistors in series
– the current is the same in
both R1 and R2
– the voltage drops add
V
R2
• Resistors in parallel
– the voltage drop is the same
in both R1 and R2
– the currents add
V
R1
R2
e1
R
I1
I2
e2
R
•
I3
e3
R
RC Circuits
R
•
a
Consider the circuit shown:
– What will happen when we close the
switch ?
– Add the voltage drops going around the
circuit, starting at point a.
b
V
C
IR + Q/C – V = 0
– In this case neither I nor Q are known or
constant. But they are related,
•This is a simple, linear differential equation.
c
RC Circuits
R
a
• Case 1: Charging
b
Q1 = 0, Q2 = Q and t1 = 0, t2 = t
V
C
c
•To get Current, I = dQ/dt
I
Q
t
t
RC Circuits
R
a
• Case 2: Discharging
• To discharge the capacitor we have to
take the battery out of the circuit
b
C
c
•To get Current, I = dQ/dt
I
t
Q
t
2
Chapter 12, ACT 1
Consider the circuit at right
after the switch is closed
6W
i) What is the initial current
12 V
I?
A) 0
B) 1 A C) 2 A
D) 3 A
E) 4 A
6W
I
ii) What is the current I after 2 minutes?
A) 0
B) 1 A C) 2 A
D) 3 A
E) 4 A
12 mF
Lecture 12, ACT 2
If R = 3.0 kΩ, C = 6.0 nF,
e2 = 6.0 V,
e1 = 10.0 V,
Q = 18 nC,
and I = 5.0 mA, what is the potential
difference Vb –Va ?
a.
b.
c.
d.
e.
–13 V
+28 V
+13 V
–28 V
+2.0V
Electrical Instruments
The Ammeter
The device that measures current is called an ammeter.
R2
R1
-
A
+
I
e
Ideally, an ammeter should have zero resistance so that
the measured current is not altered.
Electrical Instruments
The Voltmeter
The device that measures potential difference
is called a voltmeter.
I2 R
R1
2
I
Iv
V
e
An ideal voltmeter should have infinite resistance so that
no current passes through it.
Problem Solution
Method:
Five Steps:
1) Focus on the Problem
-
draw a picture – what are we asking for?
2) Describe the physics
-
what physics ideas are applicable
what are the relevant variables known and unknown
3) Plan the solution
-
what are the relevant physics equations
4) Execute the plan
-
solve in terms of variables
solve in terms of numbers
5) Evaluate the answer
-
are the dimensions and units correct?
do the numbers make sense?
Example: Power in Resistive
Electric Circuits
A circuit consists of a 12 V battery with internal
resistance of 2 Wconnected to a resistance of
10 W. The current in the resistor is I, and the
voltage across it is V. The voltmeter and the
ammeter can be considered ideal; that is, their
resistances are infinity and zero, respectively.
What is the current I and voltage V measured by
those two instruments ? What is the power
dissipated by the battery ? By the resistance ?
What is the total power dissipated in the circuit ?
Comment on these various powers.
Step 1: Focus on the problem
• Drawing with relevant parameters
– Voltmeter can be put a two places
• What is the question ?
–
–
–
–
–
–
What is I ?
What is V ?
What is Pbattery ?
What is PR ?
What is Ptotal ?
Comment on the various P’s
V
I
I
R
V
r 2W
e 12 V
10 W
A
Step 2: describe the physics
• What concepts are relevant ?
– Potential difference in a loop is zero
– Energy is dissipated by resistance
• What are the known and unknown quantities ?
– Known: R = 10 W,r = 2 We = 12 V
– Unknown: I, V, P’s
Step 3: plan the solution
• What are the relevant physics equations ?
• Kirchoff’s first law:
• Power dissipated:
For a resistance
Step 4: solve with symbols
• Find I:
e - Ir - IR = 0
I
I
R
• Find V:
r
e
• Find the P’s:
A
Step 4: solve numerically
• Putting in the numbers
Step 5: Evaluate the answers
• Are units OK ?
– [ I ] = Amperes
– [ V ] = Volts
– [ P ] = Watts
• Do they make sense ?
– the values are not too big, not too small …
– total power is larger than power dissipated in R
» Normal: battery is not ideal: it dissipates energy
Magnetism
The Magnetic Force
B
x x x x x x
x x x x x x
v
x x x x x x
F q
B
B

v

 q
F
x x x x x x x x x x x x
x x x x x x x x x x x v
x B
x x x x x x x x x x x x
v
F
F q
v
q
F=0
Magnetism
•
Magnetic effects from natural magnets have been known for a
long time. Recorded observations from the Greeks more than
2500 years ago.
•
The word magnetism comes from the Greek word for a certain
type of stone (lodestone) containing iron oxide found in
Magnesia, a district in northern Greece – or maybe it comes
from a shepherd named Magnes who got the stuff stuck to the
nails in his shoes
•
Properties of lodestones: could exert forces on similar stones
and could impart this property (magnetize) to a piece of iron it
touched.
•
Small sliver of lodestone suspended with a string will always
align itself in a north-south direction. ie can detect the
magnetic field produced by the earth itself. This is a compass.
Bar Magnet
• Bar magnet ... two poles: N and S
Like poles repel; Unlike poles attract.
• Magnetic Field lines: (defined in same way as electric
field lines, direction and density)
S
N
You can see this
field by bringing
a magnet near a
sheet covered
with iron filings
• Does this remind you of a similar case in electrostatics?
Electric Field Lines
of an Electric Dipole
Magnetic Field Lines of
a bar magnet
S
N
Magnetic Monopoles
• One explanation: there exists magnetic charge, just like
electric charge. An entity which carried this magnetic
charge would be called a magnetic monopole (having + or magnetic charge).
• How can you isolate this magnetic charge?
Try cutting a bar magnet in half:
S
N
S
N
S
N
• In fact no attempt yet has been successful in finding
magnetic monopoles in nature.
• Many searches have been made
• The existence of a magnetic monopole could give an
explanation (within framework of QM) for the quantization of
electric charge (argument of P.A.M.Dirac)
Source of Magnetic Fields?
• What is the source of magnetic fields, if not magnetic
charge?
• Answer: electric charge in motion!
– eg current in wire surrounding cylinder (solenoid)
produces very similar field to that of bar magnet.
• Therefore, understanding source of field generated by bar
magnet lies in understanding currents at atomic level
within bulk matter.
Orbits of electrons about nuclei
Intrinsic “spin” of
electrons (more
important effect)
Forces due to Magnetic Fields?
•
Electrically charged particles come under various sorts of forces.
•
As we have already seen, an electric field provides a force to a
charged particle, F = qE.
•
Magnets exert forces on other magnets.
•
Also, a magnetic field provides a force to a charged particle, but
this force is in a direction perpendicular to the direction of the
magnetic field.
Definition of Magnetic Field
Magnetic field B is defined operationally by the magnetic
force on a test charge.
(We did this to talk about the electric field too)
• What is "magnetic force"? How is it distinguished from
"electric" force?
Start with some observations: CRT deflection
• Empirical facts: a) magnitude:  to velocity of q
b) direction: ^ to direction of q
q
v
F mag