Electrical Circuits (EEE/ETE-141)
Chapter-2 & 3: Voltage, Current and Resistance
Book: Robert L Boylestad, 12th Edition
Prof. K. M. A. Salam (KAS)
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Atoms and Their structure:
• All atoms made up of two basic particles,
the proton and the electron,
• The nucleus of the hydrogen atom is the
proton, a positively charged particle
• The orbiting electron carries a negative
charge equal in magnitude to the positive
charge
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Atomic structure of Copper:
• Atomic number: 29
• Number proton: 29
• Number of electron: 29
• To calculate the number of
electrons in Orbital shell: 2n2
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Charge created:
• Separated valence electron (29th) of
Cu, in fig.(a) and create region of
positive and negative charges, in
fig.(b) & (c)
• Inside dash boundary (b), protons
exceeding the electrons by 1 so that
net charge is positive. On the other
hand, free electron leaves from
parent atom established of positive
and negative charge (fig. d).
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Voltage:
• every source of voltage is established by simply creating a separation of positive and negative charges.
• a package of electrons called a coulomb (C) of charge was defined as: One coulomb of charge is the total charge
associated with 6.242 x 1018 electrons.
• In Fig. (b), if we take a coulomb of negative charge near the surface of the positive charge and move it toward the
negative charge, we must expend energy to overcome the repulsive forces of the larger negative charge and the
attractive forces of the positive charge. In the process of moving the charge from point a to point b in Fig. (b): if a
total of 1 joule (J) of energy is used to move the negative charge of 1 coulomb (C), there is a difference of 1 volt
(V) between the two points.The defining equation is V=W/Q where, V volts (V), W joules (J), Q coulombs
(C)
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Voltage is the difference in charge between two points.
Also called electromotive force, is the potential difference in charge
between two points in an electrical field.
• Example-1: Find the voltage between two points if 60 J of energy are required to move
a charge of 20 C between the two points.
Solution: V=W/Q = 60/20= 3V
• Prob#1: Determine the energy expended moving a charge of 50 μC between two points
if the voltage between the points is 6 V.
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Current:
• The applied voltage is the starting
mechanism—the current is a
reaction to the applied voltage.
I=Q/t where, I ampere (A), Q
coulombs (C), t time (s)
Current is the rate at which electric
charge flows past a point in a
circuit. In other words, current is
the rate of flow of electric charge.
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Current:
• Example-1: The charge flowing through the imaginary surface is 0.16 C every 64 ms.
Determine the current in amperes.
Solution: I=Q/t = 0.16 C/64x0.001s= 2.5A
• Prob#1: Determine how long it will take 4x1016 electrons to pass through the imaginary
surface if the current is 5 mA.
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Voltage source:
• The DC (Direct Current) is a unidirectional (one
direction) flow of charge and its a fixed voltage.
• The long bar represents the positive side; the short
bar, the negative. It also the use of the letter E to
denote voltage source. It comes from the fact that
an electromotive force (emf) is a force that
establishes the flow of charge (or current) in a
system due to the application of a difference in
potential.
Standard symbol for a dc voltage source
Types of DC Voltage source:
(1) Batteries (chemical action or solar energy)
(2) Generators (electromechanical) and
(3) Power supplies
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Ampere-hour (Ah) rating:
• The ampere-hour (Ah) rating provides an indication of how long a battery of fixed
voltage will be able to supply a particular current.
Say, a battery with an ampere-hour rating of 100 will theoretically provide a current of 1 A for 100
hours, 10 A for 10 hours, or 100 A for 1 hour. Obviously, the greater the current, the shorter is the
time.
Example: How long will a 9 V transistor battery with an ampere-hour
rating of 520 mAh provide a current of 20 mA?
Solution: Life = 520mAh/20mA = 26 h
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Battery Life Factors:
• The capacity of a battery (in ampere-hours) will change with change in current demand.
• The ampere-hour rating of a battery will decrease from the room temperature level with very cold
and very warm temperatures.
Ampere-hour rating (capacity) versus drain current
Ampere-hour rating (capacity) versus temperature
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Resistance:
• Resistance is a material's tendency to resist the flow of charge (current), has the
units of ohms and uses the Greek letter omega (Ω) as its symbol.
Types of Resistors:
(1) Fixed Resistor
(2) Variable Resistor (also called Potentiometer)
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Temperature effect on Resistance:
• Temperature has a significant effect on the resistance of conductors, semiconductors, and
insulators.
• For good conductors, an increase in temperature results in an increase in the resistance level.
Consequently, conductors have a positive temperature coefficient [fig (a)].
• For semiconductor and insulator materials, an increase in temperature results in a decrease
in the resistance level because an increase in the number of free carriers in the material for
conduction. Consequently, semiconductors and insulators have negative temperature
coefficients [fig (b)].
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Inferred Absolute Temperature:
• Effect of temperature on the resistance of different materials.
Effect of temperature on the resistance of copper
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Where, |T1| indicates that the inferred absolute temperature of the material
involved is inserted as a positive value in the equation.
Example: If the resistance of a copper wire is 50 at 20°C, what is its resistance at 100°C (boiling
point of water)?
Solution: From the above equation,
Problem: If the resistance of an aluminum wire at room temperature (20°C) is 100 m Ω (measured
by a milliohmmeter), at what temperature will its resistance increase to 120 m Ω?
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Temperature Coefficient of Resistance:
Where, α20 is the temperature coefficient of resistance at a temperature of 20°C and R20
is the resistance of the sample at 20°C, we determine the resistance R1 at a temperature T1 by
Since ΔR/ΔT is the slope, the higher the temperature
coefficient of resistance for a material, the more sensitive
is the resistance level to changes in temperature.
If, T1-20°C is the change in temperature from 20°C then
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PPM/°C (Parts per million):
• Since, resistance changes with a change in temperature. parts per million per degree Celsius (PPM/°C),
providing an immediate indication of the sensitivity level of the resistor to temperature. For resistors, a
5000 PPM level is considered high, whereas 20 PPM is quite low.
• A 1000 PPM/°C characteristic reveals that a 1° change in temperature results in a change in resistance
equal to 1000 PPM, or 1000/1,000,000 1/1000 of its nameplate value—not a significant change for most
applications. However, a 10° change results in a change equal to 1/100 (1%) of its nameplate value, which
is becoming significant.
Where, Rnominal is the nameplate value of the resistor at room
temperature and ΔT is the change in temperature from the
reference level of 20°C.
Example: For a 1 k carbon composition resistor with a PPM of 2500, determine the resistance at 60°C.
Solution:
and
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Color Coding and standard resistor values:
• Resistor Color Coding uses colored bands to quickly identify a resistors resistive value and its
percentage of tolerance with the physical size of the resistor
Band count
Usually first band will be closest to the
end. Also the tolerance band on the end
will be silver or gold which is not in the
normal sequence so you can tell its the
tolerance band - the first digit is on the
opposite end.
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How to read Resistor color code:
If the fourth band is omitted, the tolerance
is assumed to be 20%.
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