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University Physics: Waves and Electricity. Ch26. Ohm’s Law. Lecture 9. Dr.-Ing. Erwin Sitompul. http://zitompul.wordpress.com. Homework 7. The rectangular ABCD is defined by its corner points of A (2,0,0), B (0,3,0), C (0,3,2.5), and D (2,0,2.5). Draw a sketch of the rectangular. - PowerPoint PPT Presentation
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University Physics: Waves and Electricity
Ch26. Ohm’s LawLecture 9
Dr.-Ing. Erwin Sitompulhttp://zitompul.wordpress.com
9/2Erwin Sitompul University Physics: Wave and Electricity
Homework 7(a) The rectangular ABCD is defined by its corner points of
A(2,0,0), B(0,3,0), C(0,3,2.5), and D(2,0,2.5). Draw a sketch of the rectangular.
(b) Given an electric field of E = –2i + 6j N/C, draw the electric field on the sketch from part (a).
(c) Determine the number of flux crossing the area of the rectangular ABCD.
→ ^ ^
9/3Erwin Sitompul University Physics: Wave and Electricity
Solution of Homework 7
x
y
z
0 1 2 3
1
2
3
1
2
3
D
A
C
B
ˆ ˆ2i 6 j N CE
2ABCD
ˆ ˆ7.5i 5j mA
ABCD ABCDE A
ˆ ˆ ˆ ˆ( 2i 6 j) (7.5i 5j ) 215 N m C
• Projection of ABCD on the yz plane
• Projection of ABCD on the xz plane
9/4Erwin Sitompul University Physics: Wave and Electricity
Electric Current Previously we have discussed electrostatics – the physics of
stationary charges. From this point onward, we will discuss the physics of
charges in motion –that is, electric currents. Electric currents involve many professions, especially
engineers. Electrical engineers are concerned with countless electrical
systems such as power systems, lightning systems, and information storage systems.
9/5Erwin Sitompul University Physics: Wave and Electricity
Electric Current As we know, there are two kinds of electric charge carriers:
the positive charge carrier (hole) and the negative charge carrier (electron).
In a conducting material, a number of electrons are not bounded to the atom and can freely move across the material. This electron is called conduction electron.
A hole is actually the empty state left by a freely moving electron. We define a hole to have a positive charge, in opposite to the electron.
• Current is defined as the rate of movement of charge passing a given reference point (or crossing a given reference plane)
• Through convention, the direction of hole movement is defined as the direction of current
QIt
9/6Erwin Sitompul University Physics: Wave and Electricity
Consider positive and negative charges moving horizontally through four different pieces of a conductor. (a) Determine the current
direction of each piece.(b) Rank the current from
highest to lowest.
(a) and (c) rightward, (b) and (d) leftward
Checkpoint
a, b and c tie, d
• Can you determine the direction of the fields E? →
9/7Erwin Sitompul University Physics: Wave and Electricity
Electric Current
If an electric field exists, the charge carriers (conducting electrons and holes) will move under the influence of the field.
Flow of carriers will stop when the electric field is zero or the potential difference is zero.
Although an electric current is a stream of moving charges, not all moving charges constitute an electric current.
An electric current through a given surface exist only when there is a net flow of charge through that surface.
0I
0E 0E
9/8Erwin Sitompul University Physics: Wave and Electricity
Electric Current The SI unit for current is the coulomb per second (C/s) or the
ampere (A).qit
1C1A1s
Current is a scalar quantity. We do not need direction to define it.
Yet, we know that current will flow in the same direction as the electric field, or from higher potential to lower potential.
We often represent the current direction with an arrow near a conductor (wire, cable, etc).
0 1 2i i i
9/9Erwin Sitompul University Physics: Wave and Electricity
CheckpointThe figure below shows a portion of a circuit. What are the magnitude and direction of the current I in the lower right-hand wire?
The magnitude of the current is 8 A, flowing from left to right
5 A6 A
8 A
9/10Erwin Sitompul University Physics: Wave and Electricity
Resistance and Resistivity One of the characteristics of a conductor is the electrical
resistance. We determine the resistance between any two points of a
conductor by applying a potential difference V between those points and measuring the current i that results.
VRi
The SI unit for resistance is the volt per ampere. This combination, however, occurs so often that it is given a special name ohm (symbol Ω).1ohm 1 1volt per ampere 1V A
9/11Erwin Sitompul University Physics: Wave and Electricity
Resistance and Resistivity A conductor whose function in an electric
circuit is to provide a specified resistance is called a resistor.
In a circuit diagram, the resistor is represented by the symbols:
ViR
We can rewrite the last equation to become:
For a given V,• The greater the resistance, the smaller the current• The smaller the resistance, the greater the current
9/12Erwin Sitompul University Physics: Wave and Electricity
Resistance and Resistivity The resistivity is
characteristic for each material. It depends on the properties of the material and on temperature.
The next table lists the resistivities of some materials at 20°C.
9/13Erwin Sitompul University Physics: Wave and Electricity
Resistance and Resistivity The resistivity is denoted with ρ. The SI unit of resistivity is
ohm-meter (Ωm). We can also speak of the conductivity σ of a material. This is
simply the reciprocal of its resistivity, so:
1
The SI unit of conductivity is (Ωm)–1. Sometimes the unit mhos per meter is used.
1 1( m)m
mhosm m
9/14Erwin Sitompul University Physics: Wave and Electricity
Calculating Resistance from Resistivity Distinction:
Resistance is a property of an object.Resistivity is a property of a material
Let A be the cross-sectional area of the wire of length L, and let a potential difference V exist between its ends.
The resistance of the wire is given by:
LRA
9/15Erwin Sitompul University Physics: Wave and Electricity
CheckpointThe figure here shows three cylindrical copper conductors along with their face areas and lengths.Rank them according to the current through them, greatest first, when the same potential difference V is placed across their lengths. (a) and (c) tie,
then (b)
LRA
For the same potential difference V,• The resistance >>, the current <<• The resistance <<, the current >>
aLRA
1.52bLR
A
3 LA
22c
LRA
LA
9/16Erwin Sitompul University Physics: Wave and Electricity
0 01 ( )T T
Variation with Temperature The values of resistivity varies
with temperature. The next figure shows the
variation of this property for copper over temperature.
The relation between temperature and resistivity for copper –and for metal in general– is fairly linear.
For such linear relations, the following empirical approximation is good enough for most engineering purposes:
• T0 = 20°C = 293 K (room temperature)
• α is the temperature coefficient, (°C)–1, (see table)
9/17Erwin Sitompul University Physics: Wave and Electricity
Color-Coding of Resistor Identification
1 0 4410 10 10%R
100 k 10%
1 2 6±5%
±10%
162 10 5%R 620 5%
3 3 9 ±1%00339 10 1%R
339 1%
9/18Erwin Sitompul University Physics: Wave and Electricity
Homework 8A rectangular block of iron has dimensions 1.2 cm 1.2 cm 15 cm. The temperature of the surrounding air is 20 °C. A potential difference is to be applied to the block between parallel sides. (a) What is the resistance of the block if the two parallel sides
are the square ends (with dimensions 1.2 cm 1.2 cm)?(b) The temperature of the iron block increases up to 35 °C due
to the flowing current. What is the resistance of the block now?
9/19Erwin Sitompul University Physics: Wave and Electricity
Homework 8
A rectangular block of copper has dimensions 1.2 cm 1.2 cm 15 cm. The temperature of the surrounding air is 25 °C. A potential difference of 60 V is to be applied to the block between parallel sides. (a) What is the resistance of the block if the two parallel sides
are the two rectangular sides (with dimensions 1.2 cm 15 cm)?
(b) The temperature of the copper block increases up to 35 °C due to the flowing current. What is the magnitude of the current now?
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