Download • Electric charge is a fundamental attribute of particles

M. Electricity
1. Electric Charge
• Electric charge is a fundamental attribute of
particles.
• Electrostatics are defined as the interactions
between electric charges that are at rest (or nearly
so).
• The figure shows some experiments used to
demonstrate electrostatics.
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1. Electric Charge
Fig. 21.1
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1. Electric Charge
• Electrostatics experiments show that there are
exactly two kinds of electric charge, negative and
positive.
• Two positive charges or two negative charges
repel each other. A positive charge and a
negative charge attract each other.
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1. Electric Charge
• CAUTION
– “Like charges” only mean that two charges have
the same algebraic sign (both positive or both
negative).
– “Opposite charges” means that the electric
charges on both objects have different signs
(one positive and the other negative).
• A technological application is in a laser printer; the
figure shows a schematic diagram of such a printer
in operation.
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Fig. 21.2
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1. Electric Charge
Electric Charge and the Structure of Matter
• The atomic structure consists of three particles: the
negatively charged electron, the positively charged
proton, and the uncharged neutron.
• Protons and neutrons make up the nucleus while
electrons orbit it from a distance.
• The figure shows how changes in the atomic
structure of lithium determines its net electric
charge.
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1. Electric Charge
Electric Charge and the Structure of Matter
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Fig. 21.4
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1. Electric Charge
Electric Charge and the Structure of Matter
• Atomic number is defined as the number of
protons or electrons in a neutral atom of an
element.
• A positive ion is formed by removing one or more
electrons from an atom; a negative ion is one that
has gained one or more electrons. This process is
called ionization.
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1. Electric Charge
Electric Charge and the Structure of Matter
• When the total number of protons equals the total
number of electrons in a macroscopic body, its total
charge is zero and the body as a whole is
electrically neutral.
• When we speak of the charge of a body, we always
mean its net charge.
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1. Electric Charge
Electric Charge and the Structure of Matter
• The Principle of Conservation of Charge: The
algebraic sum of all the electric charges in any
closed system is constant.
• In any charging process, charge is not created or
destroyed but merely transferred from one body to
another.
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1. Electric Charge
Electric Charge and the Structure of Matter
• The magnitude of charge of the electron or
proton is a natural unit of charge.
• Every observable amount of electric charge on any
macroscopic body is always either zero or an
integer multiple (positive or negative) of this basic
unit, the electron charge – quantization of charge.
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2. Conductors, Insulators, and Induced Charges
• Conductors of electricity are materials that permit
electric charge to move easily through them;
Insulators do not.
• Most metals are good conductors while most nonmetals are insulators. Semiconductors are
intermediate in their properties between good
conductors and good insulators.
• The figure shows the use of copper as a good
conductor, and glass and nylon as good insulators.
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2. Conductors, Insulators, and Induced Charges
• In a metallic conductor, the mobile charges are
always negative electrons.
• In ionic solutions and ionized gases, both positive
and negative charges are mobile.
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3. Coulomb’s Law
• Coulomb’s Law states that:
The magnitude of the electric force between
two point charges is directly proportional to the
product of the charges and inversely
proportional to the square of the distance
between them.
• The directions of the forces the two charges exert
on each other are always along the line joining
them, as shown in the figure.
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3. Coulomb’s Law
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Fig. 21.9
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3. Coulomb’s Law
• Coulomb’s Law is usually written as:
where
∈ 0 = 8 . 854 × 10
− 12
C
2
/ N • m2
1
= 9 . 0 × 10 9 N • m 2 / C
4π ∈0
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2
M. Electricity
3. Coulomb’s Law
• The most fundamental unit of charge is the
magnitude of the charge of an electron or proton,
denoted by e, where
e = 1.602176462(63) x 10-19 C
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Example 21.4 Vector addition of electric forces in a plane
In Fig. 21.12, two equal
positive point charges q1
= q2 = 2.0 µC interact with
a third point charge Q =
4.0 µC. Find the
magnitude and direction
of the total (net) force on
Q.
Fig. 21.12
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21.4 Electric Field and Electric Forces
r
E at a point is defined as the
• The electric field
r
electric force F0 experienced by a test charge q0 at
the point, divided by the charge q0.
• That is, the electric field at a certain point is equal
to the electric force per unit charge experienced by
a charge at that point:
• SI unit is 1 newton per coulomb (1 N/C).
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21.4 Electric Field and Electric Forces
• The figure shows how a charged body creates an
electric field in the space around it.
Fig. 21.13
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21.4 Electric Field and Electric Forces
• The electric field that a charged body produces
exists at all points in the region around itself.
• The electric force is an “action-at-a-distance” force
that acts across empty space without needing any
matter to transmit it through the intervening space.
• The electric force on a charged body is exerted
by the electric field created by other charged
bodies.
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21.4 Electric Field and Electric Forces
• The figure shows the
electric force exerted
by an electric field on a
point charge.
r
r
F0 = q0 E
(21.4
)
Fig. 21.14
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21.4 Electric Field and Electric Forces
r
• The electric field E, or electric force per unit charge,
is useful because it does not depend on the charge
of the body on which the electric force is exerted.
• CAUTION
The electric force experienced by a test charge q0
can vary from point to point, so the electric field can
also be different at different points. For this reason,
Eq. (21.4) can be used only to find the electric force
on a point charge, not on large bodies where the
electric field may vary with different locations on the
body.
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21.4 Electric Field and Electric Forces
• The source point S is the location of the point
charge that is producing the electric field we are
investigating.
• The field point P is the location where we are
determining the field.
• The unit vector r̂ denotes the direction along the
line from source point to field point.
• The figure illustrates these terms.
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21.4 Electric Field and Electric Forces
Fig. 21.15
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21.4 Electric Field and Electric Forces
r
• The magnitude and direction of the electric field E
can be given by the vector equation:
• The vector field is thus the infinite set of vectors
associated with every point in space in an electric
field.
• The figure shows how a point charge produces an
electric field at all points in space.
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21.4 Electric Field and Electric Forces
Fig. 21.16
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21.4 Electric Field and Electric Forces
• The field vectors point outwards from the charge for
positive charges, and inward for negative charges.
• When the magnitude and direction of the field (and
hence its vector components) are the same
everywhere throughout an electric field, the field is
uniform.
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Example 21.7 Electron in a uniform field
Fig. 21.18
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Example 21.8 An electron trajectory
If we launch an electron
into the electric field of
Example 21.7 with an
initial horizontal velocity
v0 (Fig. 21.19), what is the
equation of its trajectory?
Fig. 21.19
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21.5 Electric-Field Calculations
• In most realistic situations that involve electric fields
and forces, charge is distributed over space.
• Thus, the principle of superposition of electric
fields is used to find the total electric field at a
given point P, set up by the individual electric fields
produced by each point charge in the field:
r
r F0
r
r
r
E =
= E1 + E 2 + E 3 + L
q0
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Example 21.9 Field of an electric dipole
Fig. 21.20
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Example 21.10 Field of a ring of charge
A ring-shaped conductor
with a radius a carries a
total charge Q uniformly
distributed around it (Fig.
21.21). Find the electric
field at a point P that lies
on the axis of the ring at
a distance x from its
center.
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Fig. 21.21
M. Electricity
Example 21.11 Field of a line of charge
Positive electric charge Q
is distributed uniformly
along a line with length
2a, lying along the y-axis
between y = -a and y =
+a. (This might represent
one of the charged rods
in Fig. 21.1.) Find the
electric field at point P on
the x-axis at a distance x
from the origin.
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Fig. 21.22
M. Electricity
Example 21.12 Field of a uniformly charged disk
Find the electric field
caused by a disk of
radius R with a uniform
positive surface charge
density (charge per unit
area) σ, at a point along
the axis of the disk a
distance x from its center.
Assume that x is positive.
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Fig. 21.23
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21.6 Electric Field Lines
• An electric field line is an imaginary line or curve
drawn through a region of space so that its tangent
at any point is in the direction of the electric-field
vector at that point.
• This is illustrated by the following figure.
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21.6 Electric Field Lines
Fig. 21.25
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21.6 Electric Field Lines
r
• They show the direction of E at each point, and
their spacing indicates the corresponding
magnitude.
• At any particular point, the electric field has a
unique direction, so field lines never intersect.
• The figure shows the field maps of the electric field
lines for three different charge distributions.
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21.6 Electric Field Lines
Fig. 21.26
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23.1 Electric Potential Energy
• Potential Energy U is the work done when a
conservative force acts on a particle to move it from
one point to another.
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23.1 Electric Potential Energy
Electric Potential Energy in a Uniform Field
• The force on a test charge that moves from one
point to another is constant and independent of its
location.
• The work done by this force is also independent of
the particle’s path, as shown in Fig. 23.1.
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23.1 Electric Potential Energy
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Fig. 23.1
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23.1 Electric Potential Energy
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Fig. 23.2
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23.1 Electric Potential Energy
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Fig. 23.3
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23.1 Electric Potential Energy
Electric Potential Energy of Two Point Charges
• The concept of electric potential energy can also be
applied to a point charge in any electric field
caused by a static charge distribution.
• This is shown in Fig. 23.4 where displacement is
along a radial line in the electric field set up by a
single, stationary charge.
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23.1 Electric Potential Energy
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Fig. 23.4
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23.1 Electric Potential Energy
• The potential energy U when the test charge q0 is at
any distance r from charge q is thus
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23.1 Electric Potential Energy
• Potential energy is always defined relative to some
reference point where U = 0.
• It is a shared property of the two charges q and q0
because it is a consequence of the interactions
(attractive or repulsive) between these two bodies.
• Fig. 23.6 is the graphical illustration of how U varies
with these interactions.
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23.1 Electric Potential Energy
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Fig. 23.6
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23.1 Electric Potential Energy
The total electric field at
each point is the vector
sum of the fields due to
the individual charges,
and the total work done
on the charge q0 during
any displacement is the
sum of the contributions
from the individual
charges.
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Fig. 23.7
M. Electricity
23.1 Electric Potential Energy
• For every electric field due to a static charge
distribution, the force exerted by that field is
conservative.
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23.2 Electric Potential
• Generally, potential is potential energy per unit
charge.
• SI units: volt (1 V).
• Vab, the potential of a with respect to b, is the work
done by the electric force when a UNIT charge
moves from a to b. In other words, it is also the
work that must be done against the electric force to
move a UNIT charge slowly from b to a.
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23.2 Electric Potential
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25.2 Resistivity
• Resistivity ρ is described by Ohm’s law:
• SI units: ohm-meter, Ω·m.
• Conductivity – the reciprocal of resistivity, with
units as (Ω·m)-1.
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25.2 Resistivity
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25.2 Resistivity
• Over a small temperature range (up to 100°C or
so), the resistivity of a metal can be represented
approximately by the equation
• Fig. 25.6 illustrates this relationship graphically.
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25.2 Resistivity
Fig. 25.6
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25.3 Resistance
• In a conductor with
resistivity ρ, the
direction of the current
is always from the
higher-potential end to
the lower-potential end.
Fig. 25.7
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25.3 Resistance
• The resistance R of a particular conductor is
related to the resistivity ρ of its material by
• Generally,
• SI units: ohm, Ω
1 Ω = 1 V/A
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25.3 Resistance
• A circuit device made
to have a specific value
of resistance between
its ends is called a
resistor.
Fig. 25.8
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25.3 Resistance
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25.3 Resistance
Fig. 25.9
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25.4 Electromotive Force and Circuits
• For a conductor to
have a steady current,
it must be part of a path
that forms a closed
loop or complete
circuit.
• If the circuit is
incomplete, the current
flows for only a very
short time.
Fig. 25.11
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25.4 Electromotive Force and Circuits
• Fig. 25.13 is a
schematic diagram of
an ideal source of emf
that maintains a
potential difference
between conductors a
and b, called the
terminals of the device.
Fig. 25.13
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25.4 Electromotive Force and Circuits
• Fig. 25.14 is the
schematic diagram of
the same ideal source
of emf in a complete
circuit.
Fig. 25.14
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25.4 Electromotive Force and Circuits
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Example 25.5 A source on open circuit
Figure 25.16 shows a source (a battery) with an emf ξ
of 12 V and an internal resistance r of 2 Ω. (For
comparison, the internal resistance of a commercial
12-V lead storage battery is only a few thousandths of
an ohm.) The wires to the left of a and to the right of
the ammeter A are not connected to anything.
Determine the readings of the idealized voltmeter V
and the idealized ammeter A.
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Example 25.5 A source on open circuit
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Fig. 25.16
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Example 25.6 A source in a complete circuit
Using the battery in
Conceptual Example
25.5, we add a 4-Ω
resistor to form the
complete circuit shown in
Fig. 25.17. What are the
voltmeter and ammeter
readings now?
Fig. 23.17
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Example 25.7 Using voltmeters and ammeters
The voltmeter and ammeter in Example 25.6 are
moved to different positions in the circuit. What are
the voltmeter and ammeter readings in the situations
shown in a) Fig. 25.18a and b) Fig. 25.18b?
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Example 25.7 Using voltmeters and ammeters
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Fig. 23.18
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Example 25.8 A source with a short circuit
Using the same battery
as in the preceding three
examples, we now
replace the 4-Ω resistor
with a zero-resistance
conductor, as shown in
Fig. 25.19. What are the
meter readings now?
Fig. 25.19
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25.4 Electromotive Force and Circuits
• The net change in potential energy for a charge q
making a round trip around a complete circuit must
be zero.
• Hence the net change in potential around the circuit
must also be zero.
• Fig. 25.20 is a graph showing how the potential
varies as we go around the complete circuit of Fig.
25.17.
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25.4 Electromotive Force and Circuits
Fig. 25.20
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25.5 Energy and Power in Electric Circuits
• In electric circuits we are most often interested in
the rate at which energy is either delivered to or
extracted from a circuit element.
• The time rate of energy transfer is power, denoted
by P:
• Units: watt, W
1 W = 1 J/s
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25.5 Energy and Power in Electric Circuits
• The power input to the
circuit element
between a and b is
P = (Va – Vb)I = VabI.
Fig. 25.21
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25.5 Energy and Power in Electric Circuits
• If the circuit element is a resistor, the rate of
transfer of electric potential energy into it is
• The internal energy of the material will increase
and energy (heat) will be dissipated in the resistor
at a rate I2R.
• Every resistor has a power rating, the maximum
power the device can dissipate without becoming
overheated and damaged.
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25.5 Energy and Power in Electric Circuits
Power Output of a Source
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Fig. 25.22
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25.5 Energy and Power in Electric Circuits
Power Input to a Source
Fig. 25.23
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26.1 Resistors in Series and Parallel
Fig. 26.1 Four different ways of connecting
three resistors
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26.1 Resistors in Series and Parallel
• When several resistors R1, R2, R3,…are connected
in series, the equivalent resistance Req is the sum
of the individual resistances.
• The same current flows through all the resistors in
a series connection.
• In general:
• The equivalent resistance of any number of
resistors in series equals the sum of their
individual resistances and is greater than any
individual resistance.
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26.1 Resistors in Series and Parallel
• When several resistors are connected in parallel,
the reciprocal of the equivalent resistance Req is the
sum of the reciprocals of the individual resistances.
• All resistors in a parallel connection have the same
potential difference between their terminals.
• In general:
• The equivalent resistance is always less than any
individual resistance.
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26.1 Resistors in Series and Parallel
• For the special case of two resistors in parallel:
R1R2
Req =
(two resistors in parallel)
(26.3)
R1 + R2
• Because Vab = I1R1 = I 2 R2 , it follows that
I1 I 2
=
(two resistors in parallel)
(26.4)
R1 R2
• Currents carried by two resistors in parallel are
inversely proportional to their resistances. More
current goes through the path of least
resistance.
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Example 26.1 Equivalent resistance
Compute the equivalent resistance of the network in Fig.
26.3a, and find the current in each resistor. The source
of emf has negligible internal resistance.
Fig. (26.3)
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Example 26.1 (SOLN)
• The 6-Ω and 3-Ω resistors are in parallel with
an equivalent resistance of 2Ω. The remaining
series combination of the 2-Ω resistor with the
4-Ω resistor is reduced to 6Ω.
• To find the current, reverse the steps used to
reduce the network. (Fig. 26.3)
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Example 26.2 Series versus parallel combinations
Two identical light bulbs are connected to a source
with ε=8V and negligible internal resistance. Each
light bulb has a resistance R=2Ω. Find the current
through each bulb, the potential difference across
each bulb and the power delivered to each bulb
and to the entire network if the bulbs are
connected a) in series, b) in parallel c) Suppose
one of the bulbs burns out (filament breaks and no
current can flow through it) What happens to the
other bulb in the series case? Parallel case?
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Example 26.2 Series versus parallel combinations
Fig. 26.4 Circuit diagrams for two light bulbs
(a) in series and (b) in parallel
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Example 26.2 (SOLN)
Identify and Set up
• Simple series and parallel connections are
involved. Use Eq.(25.18) to find the power
2
2
delivered to each resistor: P = I R = V / R
Execute
• (a) Potential difference across each of the
identical bulbs is the same:
Vab = Vbc = IR = (2 A)(2Ω) = 4V
P = I 2 R = (2 A) 2 (2Ω) = 8W
•
Ptotal = 2 P = 16W
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Example 26.2 (SOLN)
Execute
• (b) Similarly,
Vde 8V
=
= 4A
I=
R 2Ω
2
2
Vde
(8V )
P=
=
= 32W
R
2Ω
2
Ω
• For the parallel case, the value of Req is less, thus
Ptotal = V 2 / Req is greater.
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Example 26.2 (SOLN)
Execute
• (c) In the series case there will be no current at
all in the circuit and neither bulbs will glow.
• In the parallel case the potential difference
across either bulb remains equal to 8V even if
one of the bulbs burns out.
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26.2 Kirchhoff’s Rules
• Kirchhoff’s junction rule is based on conservation
of charge. This states that the algebraic sum of
the currents into any junction must be zero.
• Kirchhoff’s loop rule is based on conservation of
energy and the conservative nature of
electrostatic fields. It states that the algebraic
sum of potential differences around any loop
must be zero
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26.2 Kirchhoff’s Rules
• Kirchhoff’s loop rule is based on conservation of
energy and the conservative nature of
electrostatic fields. It states that the algebraic
sum of potential differences around any loop
must be zero.
• Careful use of consistent sign rules is essential
in applying Kirchoff’s rules.
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26.2 Kirchhoff’s Rules
• A junction in a circuit is a point where three or
more conductors meet. Junctions are also called
nodes or branch points.
• A loop is any closed conducting path.
Fig. 26.7 Kirchhoff’s
junction rule states
that as much
current flows into
a junction as flows
out of it
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26.2 Kirchhoff’s Rules
Fig. 26.6 Two networks that cannot be reduced to
simple series-parallel combinations of resistors
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