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Chapter 23
Circuits
Topics:
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Circuits containing
multiple elements
Series and parallel
combinations
Complex Multi-loop
Circuits
RC circuits
Sample question:
An electric eel can develop a potential difference of over 600 V. How do the
cells of the electric eel s body generate such a large potential difference?
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Slide 23-1
RC Circuits
•  RC circuits are circuits containing resistors and
capacitors.
•  In RC circuits, the current varies with time.
•  The values of the resistance and the capacitance in
an RC circuit determine the time it takes the
capacitor to charge or discharge. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
RC Circuits
The current and the
capacitor voltage decay to
zero after the switch closes,
but not linearly. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
RC Circuits
The decays of the voltage and the current are
exponential decays:
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RC Circuits
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QuickCheck
• The following circuits contain capacitors that
are charged to 5.0 V. All of the switches are
closed at the same time. After 1 second has
passed, which capacitor is charged to the
highest voltage? Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
QuickCheck
Which capacitor discharges more quickly after the
switch is closed?
A.  Capacitor A
B.  Capacitor B
C.  They discharge at the same rate.
D.  We can’t say without knowing the initial amount of charge.
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Charging a Capacitor
•  In a circuit that charges a capacitor, once the switch is closed, the potential difference of the battery causes a current in the circuit, and the capacitor begins to charge.
•  As the capacitor charges, it develops a potential
difference that opposes the current, so the current
decreases, and so does the rate of charging.
•  The capacitor charges until ΔV
C
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= ℇ.
Charging a Capacitor
• The equations that describe the capacitor
voltage and the current as a function of time
are
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Tau = RC
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Slide 23-29
Capacitor behavior while charging
Before Switch is thrown
After Capacitor is charged
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Additional Clicker Questions
2.  In the circuit shown below, the switch is initially closed and the bulb
glows brightly. When the switch is opened, what happens to the
brightness of the bulb? A.  The brightness of the bulb is not affected.
B. The bulb gets dimmer.
C. The bulb gets brighter.
D.  The bulb initially brightens, then dims.
E. The bulb initially dims, then brightens.
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Slide 23-39
Answer
2.  In the circuit shown below, the switch is initially closed and the bulb
glows brightly. When the switch is opened, what happens to the
brightness of the bulb? B. The bulb gets dimmer.
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Slide 23-40
QuickCheck 23.26
•  The red curve shows how the capacitor charges
after the switch is closed at t = 0. Which curve
shows the capacitor charging if the value of the
resistor is reduced?
B
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QuickCheck 23.26
•  The red curve shows how the capacitor charges
after the switch is closed at t = 0. Which curve
shows the capacitor charging if the value of the
resistor is reduced?
B
Smaller time constant.
Same ultimate amount
of charge.
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Nuclear Decay and Half-Lives
•  If you start with N
unstable nuclei, after an interval of time called the
half-life, you’ll have ½ N0 nuclei remaining.
0
•  The half-life t
decay. 1/2
is the average time required for one-half the nuclei to
•  The number of nuclei N remaining at time t is
•  No matter how many nuclei there are at any point in time,
the number decays by half during the next half-life.
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Nuclear Decay and HalfLives
• The figure shows the decay of a sample of
radioactive nuclei.
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Nuclear Decay and Half-Lives
• The number of
radioactive atoms
decreases
exponentially with
time.
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QuickCheck
A sealed box is completely evacuated (perfect vacuum), then 1,000,000 radioactive atoms are added. Their half-life is
2 days. After 4 days have passed, how many atoms are in the
box?
A.  1,000,000
B.  500,000
C.  250,000
D. 
0
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Nuclear Decay and Half-Lives
• The decay of radioactive nuclei is an
exponential decay. • The equation for the number of atoms after
a half-life can be written in terms of a time
constant τ that is related to the half-life:
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Chapter 24
Magnetic Fields and Forces
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• 
• 
• 
• 
Topics:
Magnets and the magnetic
field
Electric currents create
magnetic fields
Magnetic fields of wires,
loops, and solenoids
Magnetic forces on charges
and currents
Magnets and magnetic
materials
Sample question:
This image of a patient s knee was made with magnetic fields, not x rays.
How can we use magnetic fields to visualize the inside of the body?
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Slide 24-1
3-D Arrows, Cross Products, and Right Hand Rule 1
•  Showing vectors in 3D
! ! !
•  Cross Product C = A!B
!
! "
C = A B sin !
For direction use Right-hand rule 1
! ! !
•  Right-hand rule 1 (RHR 1) C = A ! B
=> for finding direction of cross-product vector
(Cross-Product Rule)
1.  Point right hand in the direction of the first vector (vector A)
2.  Rotate your right hand until you can point your fingers in the
direction of the second vector (vector B)
3.  Thumb points in direction the cross-product vector (vector C)
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Slide 24-2
Electric vs. Magnetic Interactions
1.  Nature of Magnetic Interactions
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Slide 24-2
Discovering Magnetism
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Slide 24-6
The Magnetic Field
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Slide 24-7
Mapping Out the Field of a Bar Magnet
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Slide 24-8
Mapping Out the Magnetic Field Using Iron Filings
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Slide 24-9
Drawing Field Lines of a Bar Magnet
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Slide 24-10
Magnetic Fields Produced by Bar Magnets
A single bar magnet
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A single bar magnet
(closeup)
Slide 24-11
Magnetic Fields Produced by Bar Magnets
Two bar magnets, unlike poles facing
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Two bar magnets,
like poles facing
Slide 24-12
Checking Understanding
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Slide 24-13
Magnetic Fields from Two Magnets
Bar Magnets A and B are placed at right angles. Two compasses, X and Y are placed so
that they are equidistant from the two magnets as shown
A.) The arrow in compass X indicates the direction
in which the North pole of the compass is pointing.
Indicate the North and South ends of both magnets
in the diagram
B.) Draw an arrow in compass Y to show the direction
in which the North pole of the compass needle
would point.
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Slide 24-2
Magnetic Fields Around Us
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Slide 24-14
Key Points
•  Three types of magnetic interactions
1.  no interaction with either pole of a magnet => object is non-magnetic
2.  attracted to both poles of a magnet => object is magnetic
3.  Attracted to one pole and repelled by the other pole
=> object is a magnet
•  Magnetic field vector from a bar magnet is a super position of the
magnetic field vectors from the N and S poles:
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• 
Vector from N pole points away from N pole Vector from S pole points towards S pole
•  Field lines form complete loops inside and outside of magnet
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Field lines outside magnet go from N to S poles
Field lines inside magnet go from S to N poles
Magnetic Field vectors at a point are tangential to Magnetic Field Lines
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Electric Currents Also Create Magnetic Fields
A long, straight
wire
A current loop
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A solenoid
Slide 24-15
The Magnetic Field of a Straight Current-Carrying Wire
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Slide 24-16
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Slide 24-17
Representing Vectors and Currents That Are
Perpendicular to the Page
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Slide 24-18
Checking Understanding
Point P is 5 cm above the wire as you look straight down at it. In
which direction is the magnetic field at P?
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Slide 24-19
Answer
Point P is 5 cm above the wire as you look straight down at it. In
which direction is the magnetic field at P?
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Slide 24-20
Drawing Field Vectors and Field Lines of a Current-Carrying Wire
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Slide 24-21
Drawing a Current Loop
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Slide 24-22
The Magnetic Field of a Current Loop
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Slide 24-23
The Magnetic Field of a Solenoid
A short solenoid
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A long solenoid
Slide 24-24
The Magnitude of the Field due to a Long, Straight,
Current-Carrying Wire
µ0 I
B=
2! r
µ0 = permeability constant = 1.257 ! 10 "6 T # m/A
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Slide 24-25
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Slide 24-26
Checking Understanding
The magnetic field at point P is zero. What are the magnitude and
direction of the current in the lower wire? A.  10 A to the right.
B.  5 A to the right.
C.  2.5 A to the right. D.  10 A to the left.
E.  5 A to the left. F.  2.5 A to the left.
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Slide 24-27
Answer
The magnetic field at point P is zero. What are the magnitude and
direction of the current in the lower wire? E.  5 A to the left. Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.
Slide 24-28