Download Chapter 18 - Purdue Physics

Summary
Force: (N)
Vector
Scalar
Potential Energy: (J)
2-particle
1-particle
Electric Field: (N/C)
Potential: (V)
Example:
 At which position (A, B, or C)
Equipotential
Surfaces
C
•
B•
•
A
does the electric field have
the greatest magnitude?
Example:
 A charge Q is placed inside
a metal cavity.
 What is the electric field at the
dashed Gaussian surface?
Q
 What is the flux through the
Gaussian surface?
 What is the net charge on the
inner surface of the cavity?
Example:
 What is the electric field
between two (large) charged
sheets?
Electric Potential Energy
Revisited
 One way to view electric potential energy is that the
potential energy is stored in the electric field itself
 Whenever an electric field is present in a region of
space, potential energy is located in that region
 Implications for electromagnetic waves (optics)
Section 18.8
Electric Potential Energy, final
 The energy density of the electric field can be
defined as the energy per volume:
uelec
1
  oE 2
2
 These results give the energy density for any
arrangement of charges
Section 18.8
Chapter 19
Electric Currents and Circuits
Why doesn’t the bird fry?
Electric Current
 The magnitude of the
current is measured by
the amount of charge
that moves along the
wire
 Current, I, is defined as
q
I
t
Section 19.1
Movement of Charges
 The definition of current uses the net
charge, Δq, that passes a particular
point during a time interval, Δt
 The amount of charge could be the
result of many possible configurations,
including
 A few particles each with a large charge
 Many particles each with a small charge
 A combination of positive and negative
charges
Section 19.1
Movement of Charges, final
 A positive electric current can be
produced by
 Positive charges moving in one direction
 Negative charges moving in the opposite
direction
 Current is carried by different particles
 Carried by electrons in a metal
 Generally carried by + and/or - ions in a
liquid or gas
Section 19.1
Current and Potential Energy
 For charge to move along a wire, there must be a change
in the electric potential energy between the ends.
 V = PEelec / q
 The potential is referred to simply as “voltage”
Section 19.2
Current and Voltage
 The current flows from higher
potential to lower potential
 regardless if the current is carried
by positive or negative charges
 The potential difference may be
supplied by a battery
Section 19.2
EMF
 Batteries convert chemical energy to electrical
energy
 The potential difference between a battery’s
terminals is called an electromotive force, or emf
 Emf is not a force
 The emf is denoted with ε and referred to as voltage
 The value of the emf depends on the particular
chemical reactions it employs and how the
electrodes are arranged
Section 19.2
Simple Circuit
 If the battery terminals are
connected to two ends of a wire, a
current is produced
 The charge moves from one
terminal to the other through a
circuit
 No net charge accumulates on
the battery terminals while the
current is present
Section 19.2
Ideal vs. Real Batteries
 An ideal battery has two important properties
 It always maintains a fixed potential difference
between its terminals
 This emf is maintained no matter how much current
flows from the battery
 Real batteries have two practical limitations
 The emf decreases when the current is very high

The electrochemical reactions do not happen
instantaneously
 The battery will “run down”
 It will not work forever
Section 19.2
Current
 The electrons moving in a
wire collide frequently with
one another and with the
atoms of the wire
 When there is no electric
field present, the average
displacement is zero
 There is no net
movement of charge
 There is no current
Section 19.3
Current, cont.
 With a battery connected,
an electric potential is
established
 There is an electric field in
the wire: E = V / L
 The electric field produces
a force that gives the
electrons a net motion
 The velocity of this motion
is the drift velocity
Section 19.3
Current and Drift Velocity
 The current is equal to
the amount of charge
that passes out the end
of the wire per unit time
q
I
t
 In time ∆t, electrons in
the wire will move a
distance, vd ∆t
Section 19.3
Current and Drift Velocity
 Let n be the density of
electrons per unit
volume
 Let A be the crosssectional area of the
wire
 I = - n e A vd
Section 19.3
Ohm’s Law

Section 19.3
Ohm’s Law, cont.
 The constant of proportionality between I and V is
the electrical resistance, R
V
I
R
 This relationship is called Ohm’s Law
 The unit of resistance is an Ohm, Ω
 Ω = Volt / Ampere
 The value of the resistance of a wire depends on its
composition, size, and shape
Section 19.3
Resistivity
 The resistivity, ρ, depends
only on the material used
to make the wire
 The resistance of a wire of
length L and crosssectional area A is given
by
L
R
A
 The resistivities of some
materials are given in
table 19.1
Section 19.3
Ohm’s Law: Final Notes
 Ohm’s Law predicts a linear relationship between
current and voltage
 Ohm’s Law is not a fundamental law of nature
 Many, but not all, materials and devices obey Ohm’s
Law
 Resistors do obey Ohm’s Law (mostly)
 Resistors will be used as the basis of circuit ideas
Section 19.3
Resistive Circuit Applet
 http://phet.colorado.edu/en/simulation/circuit-
construction-kit-dc
Capacitors
 A capacitor uses potential
difference to store charge and
energy
 Applying a potential difference
between the plates induces
opposite charges on the plates
 Example:


parallel-plate capacitor
clouds
Section 18.4
Capacitance Defined
 Capacitance is the amount of charge that can be
stored per unit potential difference
 The capacitance is dependent on the geometry of
the capacitor
 For a parallel-plate capacitor with plate area A and
separation distance d, the capacitance is
 Unit is farad, F
 1 F = 1 C/V
Section 18.4
Energy in a Capacitor, cont.
 Storing charge on a
capacitor requires energy
 Requires energy to move a
charge ΔQ through a
potential difference ΔV

The energy corresponds to the
shaded area in the graph
 The total energy stored is
equal to the energy
required to move all the
packets of charge from
one plate to the other
Section 18.4
Energy in a Capacitor, cont.
 The total energy
corresponds to the area
under the ΔV – Q graph
 Energy = Area = PEcap
Q
is the final charge
ΔV is the final potential
difference
Section 18.4
Energy in a Capacitor, Final
 From the definition of
capacitance, the energy can be
expressed in different forms
PEcap
1
1
1 Q2
2
 QV  C  V  
2
2
2 C
 These expressions are valid for
all capacitors
Section 18.4
Dielectrics
 Most real capacitors
contain two metal
“plates” separated by a
thin insulating region
 Many times these
plates are rolled into
cylinders
 The region between the
plates typically contains
a material called a
dielectric
Section 18.5
Dielectrics, cont.
 Inserting the dielectric material between the plates
changes the value of the capacitance
 The change is proportional to the dielectric
constant, κ
 Cvac is the capacitance without the dielectric and Cd is
with the dielectric
 κ is a dimensionless factor
 Generally, κ > 1, so inserting a dielectric increases
the capacitance
Section 18.5
Dielectrics, final
 When the plates of a
capacitor are charged, the
electric field established
extends into the dielectric
material
 Most good dielectrics are
highly ionic and lead to a
slight change in the
charge in the dielectric
 Since the field decreases,
the potential difference
decreases and the
capacitance increases
Section 18.5
Equivalent Capacitance: Series
 In series:
 ΔVtotal = ΔVtop (1) + ΔVbottom (2)
1
Cequiv
1
1


C1 C2
Section 18.4
Equivalent Capacitance: Parallel
 In parallel:
 Qtotal = Q1 + Q2
Section 18.4
Combinations of Three or More
Capacitors
 For capacitors in parallel: Cequiv = C1 + C2 + C3 + …
 For capacitors in series:
1
Cequiv
1
1
1




C1 C2 C3
 These results apply to all types of capacitors
 When a circuit contains capacitors in both series and
parallel, the above rules apply to the appropriate
combinations
Section 18.4
Uses of Capacitance
Circuit Symbols
Section 19.3