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Ch25-26:
Current, power, circuits, resistance, capacitance
• Resistance and resistivity
• Resistance in series and parallel
• Circuits with power supply
• Circuits with capacitors
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Current
• A current is any motion of charge
from one region to another. Current
is defined as I = dQ/dt.
• An electric field in a conductor
causes charges to flow. (See Figure
25.1 at the right.)
• Speed of charges: small, E field
onset: near speed of light.
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Direction of current flow
•
A current can be produced by positive or negative charge flow.
•
Conventional current is treated as a flow of positive charges (example: in some
solutions H+ ions).
•
The moving charges in metals are electrons (see figure below).
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Current, drift velocity, and current density
• Current is related to current
density, charge density, and
drift velocity
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Resistivity
• The ratio of the DRIVING ELECTRIC FIELD to current
density is called resistivity ,  = E/J.
• The conductivity is the reciprocal of the resistivity.
• Table 25.1 shows the resistivity of various types of materials.
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Resistivity and temperature
• Resistivity depends on temperature. See
Figure 25.6 at the left.
• Table 25.2 shows some temperature
coefficients of resistivity.
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Resistance
• The resistance of a conductor is R = L/A (see Figure 25.7 below).
• The potential across a conductor is V = IR.
• If V is directly proportional to I (that is, if R is constant), the
equation V = IR is called Ohm’s law.
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Resistors are color-coded for easy identification
•
This resistor has a resistance of 5.7 kΩ with a tolerance of ±10%.
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Ohmic and nonohmic resistors
• Only the resistor in Figure 25.10(a) below obeys Ohm’s law.
• Follow Example 25.2.
• Follow Example 25.3.
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Resistors in series and parallel
•
Resistors are in series if they are connected one after the other so the
current is the same in all of them (see left figure below).
•
The equivalent resistance of a series combination is the sum of the
individual resistances: Req = R1 + R2 + R3 + …
•
Resistors are in parallel if they are connected so that the potential
difference must be the same across all of them (see right figure below).
•
The equivalent resistance of a parallel combinaton is given by
1/Req = 1/R1 + 1/R2 + 1/R3 + …
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Q26.1
Which of the two
arrangements shown has
the smaller equivalent
resistance between points
a and b?
A. the series arrangement
B. the parallel arrangement
C. The equivalent resistance is
the same for both
arrangements.
D. The answer depends on the
values of the individual
resistances R1, R2, and R3.
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A26.1
Which of the two
arrangements shown has
the smaller equivalent
resistance between points
a and b?
A. the series arrangement
B. the parallel arrangement
C. The equivalent resistance is
the same for both
arrangements.
D. The answer depends on the
values of the individual
resistances R1, R2, and R3.
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(LEGO BLOCKS) If you have material of resistivity , get
it’s resistance using rules of resistance in series and
parallel:
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Q26.2
Three identical resistors,
each of resistance R, are
connected as shown.
What is the equivalent
resistance of this
arrangement of three
resistors?
A. 3R
B. 2R
C. 3R/2
D. 2R/3
E. R/3
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A26.2
Three identical resistors,
each of resistance R, are
connected as shown.
What is the equivalent
resistance of this
arrangement of three
resistors?
A. 3R
B. 2R
C. 3R/2
D. 2R/3
E. R/3
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Electromotive force and circuits
•
An electromotive force (emf) makes current flow. In spite of the name, an emf
is not a force.
•
The figures below show a source of emf in an open circuit (left) and in a
complete circuit (right). ON WB, electric circuit equivalent
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Internal resistance
• Real sources of emf actually
contain some internal
resistance r.
• The terminal voltage of an
emf source is Vab =  – Ir.
• The terminal voltage of the
12-V battery shown at the
right is less than 12 V when
it is connected to the light
bulb.
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Q26.7
Three identical light bulbs are
connected to a source of emf
as shown. Which bulb is
brightest?
A. light bulb A
B. light bulb B
C. light bulb C
D. both light bulbs B and C
(Both are equally bright and
are brighter than light bulb
A.)
E. All bulbs are equally
bright.
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A26.7
Three identical light bulbs are
connected to a source of emf
as shown. Which bulb is
brightest?
A. light bulb A
B. light bulb B
C. light bulb C
D. both light bulbs B and C
(Both are equally bright and
are brighter than light bulb
A.)
E. All bulbs are equally
bright.
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Q26.3
A 120-V, 60-W light bulb, a 120V, 120-W light bulb, and a 120V, 240-W light bulb are
connected in parallel as shown.
120 V
60 W
The voltage between points a
120 V
and b is 120 V. Through which
a
120 W
bulb is there the greatest
voltage drop?
A. the 120-V, 60-W light bulb
120 V
B. the 120-V, 120-W light bulb
240 W
C. the 120-V, 240-W light bulb
D. All three light bulbs have the same voltage
drop.
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b
A26.3
A 120-V, 60-W light bulb, a 120V, 120-W light bulb, and a 120V, 240-W light bulb are
connected in parallel as shown.
120 V
60 W
The voltage between points a
120 V
and b is 120 V. Through which
a
120 W
bulb is there the greatest
voltage drop?
A. the 120-V, 60-W light bulb
120 V
B. the 120-V, 120-W light bulb
240 W
C. the 120-V, 240-W light bulb
D. All three light bulbs have the same voltage
drop.
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b
Q26.4
A 120-V, 60-W light bulb, a 120V, 120-W light bulb, and a 120V, 240-W light bulb are
connected in parallel as shown.
120 V
60 W
The voltage between points a
and b is 120 V. Which bulb
glows the brightest?
120 V
120 W
a
A. the 120-V, 60-W light bulb
120 V
B. the 120-V, 120-W light bulb
240 W
C. the 120-V, 240-W light bulb
D. All three light bulbs glow with equal
brightness.
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b
A26.4
A 120-V, 60-W light bulb, a 120V, 120-W light bulb, and a 120V, 240-W light bulb are
connected in parallel as shown.
120 V
60 W
The voltage between points a
and b is 120 V. Which bulb
glows the brightest?
120 V
120 W
a
A. the 120-V, 60-W light bulb
120 V
B. the 120-V, 120-W light bulb
240 W
C. the 120-V, 240-W light bulb
D. All three light bulbs glow with equal
brightness.
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b
Symbols for circuit diagrams
• Table 25.4 shows the usual symbols used in circuit diagrams.
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A source in an open circuit
• What’s the voltmeter reading? If circuit closed, the
Ammeter?
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Source in a complete circuit
• Same here:
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Potential changes around a circuit
• The net change in
potential must be zero
for a round trip in a
circuit.
• Follow Figure 25.20 at
the right.
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Energy and power in electric circuits
• The rate at which energy is
delivered to (or extracted from) a
circuit element is P = VabI.
• The power delivered to a pure
OHMIC resistor is P = I2R =
Vab2/R.
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Power input and output
•
On WB
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Power in a short circuit
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Next:
• How can we apply
series/parallel combinations of
resistors to a complex circuit
board?
• In this chapter, we will learn
general methods for analyzing
more complex networks.
• We shall look at various
instruments for measuring
electrical quantities in circuits.
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Equivalent resistance
•
Techniques: “COMBINE”
resistance
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Series versus parallel combinations
• Try here:
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Kirchhoff’s Rules I (or while you’ll need Linear Algebra)
• A junction is a point where
three or more conductors
meet.
• A loop is any closed
conducting path.
• See Figure 26.6 at the
right.
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Kirchoff’s Rules II
• Kirchhoff’s junction rule: The algebraic sum of the currents into
any junction is zero: I = 0. (See Figure 26.7 below.)
• Kirchhoff’s loop rule: The algebraic sum of the potential
differences in any loop must equal zero: V = 0.
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Sign convention for the loop rule
• Figure 26.8 below shows the sign convention for emfs
and resistors.
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Reducing the number of unknown currents
• Read Problem-Solving Strategy 26.2.
• Figure 26.9 below shows how to use the junction rule to reduce the
number of unknown currents.
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A single-loop circuit
• Start up your engines…
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Charging a battery
• Follow Example 26.4, which shows how to charge a battery.
Use Figure 26.11 below.
• Follow Example 26.5, which looks at the power delivered in the
same circuit as in the previous example.
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A complex network
• Follow Example 26.6, using Figure 26.12 below.
• Follow Example 26.7 which looks at the same circuit
as above.
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Charging a capacitor
• Read the discussion of charging a capacitor in the text, using
Figures 26.20 and 26.21 below.
• The time constant is  = RC.
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Discharging a capacitor
• Read the discussion of discharging a capacitor in the text, using
Figures 26.22 and 26.23 below.
• Follow Examples 26.12 and 26.13.
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D’Arsonval galvanometer
• A d’Arsonval galvanometer measures the current through it (see
Figures 26.13 and 26.14 below).
• Many electrical instruments, such as ammeters and voltmeters,
use a galvanometer in their design.
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Ammeters and voltmeters
• An ammeter measures the
current passing through it.
• A voltmeter measures the
potential difference between
two points.
• Figure 26.15 at the right
shows how to use a
galvanometer to make an
ammeter and a voltmeter.
• Follow Examples 26.8
(ammeter) and 26.9
(ammeter).
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Ammeters and voltmeters in combination
• An ammeter and a voltmeter may be used together to measure
resistance and power. Figure 26.16 below illustrates how this can
be done.
• Follow Example 26.10 using Figure 26.16(a).
• Follow Example 26.11 using Figure 26.16(b).
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Ohmmeters and potentiometers
• An ohmmeter is designed to measure resistance. (See Figure
26.17 below left.)
• A potentiometer measures the emf of a source without drawing
any current from the source. (See Figure 26.19 below right.)
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Power distribution systems
• Follow the text discussion using Figure 26.24 below.
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Household wiring
• Figure 26.26 at the right
shows why it is safer to
use a three-prong plug for
electrical appliances.
• Follow Example 26.14.
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