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K. A. Saaifan, Jacobs University, Bremen
2. Basic Components and Electrical Circuits
2.1 Units and Scales
The International System of Units (SI) defines 6 principal units from which the
units of all other physical quantities can be derived
Table 2.1 SI base units
Basic Quantity
Length
Mass
Time
Electric current
Thermodynamic temperature
Luminous intensity
Unit
meter
kilogram
second
ampere
kelvin
candela
Symbol
m
kg
s
A
K
cd
The SI unit of work or energy is the joule (J), which equals to a kg m2 s-2 in SI
base units
The SI unit of power is equivalent to one joule per second
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K. A. Saaifan, Jacobs University, Bremen
The SI unit uses prefixes based on the power of 10 to relate larger and smaller
units to the basic unit
Table 2.2 SI prefixes
Basic
Quantity
1012
109
106
103
10-2
10-3
10-6
10-9
10-12
Name
Symbol
tera
giga
mega
kilo
centi
milli
micro
nano
pico
T
G
M
k
c
m
n
p
K. A. Saaifan, Jacobs University, Bremen
2.2 Circuit Variables
2.2.1 Charge
Electric charge is an electrical property of the atomic particles of which
matter consists, measured in coulombs (C)
The charge of an electron is -1.602 X 10-19 C
The coulomb is a large unit for charges such that in 1 C of charge, there are
1/(1.602 X 10-19)=6.24 X 1018 electrons
The realistic or laboratory values of charges are on the order pC, nC, and μC
2.2.2 Current
Electric current is a flow of electric charge measured in ampere (A)
note that 1 ampere (A) is equal to 1 coulombs per second (C/s)
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K. A. Saaifan, Jacobs University, Bremen
The total charge transferred between time t0 and t can be expressed as
There are several different types of current
Direct current (dc)
Sinusoidal current (ac)
Exponential current
Damped sinusoidal currents
Representation of current in circuit analysis
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K. A. Saaifan, Jacobs University, Bremen
Practice
In the wire of shown figure, electrons are moving left to right to
create a current of 1 mA. Determine and
Ans: the current is in the opposite direction to flow of electrons
2.2.3 Voltage
Voltage or potential difference measured in volts (V) is the energy required
to move a unit of charge through an element
note that 1 volt (V) is equal to 1 joule per coulombs (J/C)
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K. A. Saaifan, Jacobs University, Bremen
Representation of voltage in circuit analysis
The plus (+) and minus (-) signs at the points a and b are
used to define a reference direction (the voltage polarity)
Similar to the electric current, a constant voltage is called a dc voltage,
whereas a sinusoidal voltage (time-varying) is called an ac voltage
For practical purposes, the power and energy are important measures in
circuit analysis
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K. A. Saaifan, Jacobs University, Bremen
2.2.4 Power
Measured in watts (W) to indicate the average absorbing energy by a circuit
element
The sign of power
+ sign: the power is absorbed by the element (resistor)
- sign: the power is supplied by the element (?)
Since the energy can neither be created or dissipated (only transferred), the
algebraic sum of powers in a circuit, at any instant of time, must be zero
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K. A. Saaifan, Jacobs University, Bremen
Determine p1
Ans:
2.2.5 Energy
The energy absorbed or supplied by an element from time 0 to t is
Electricity bills:: The electric power utility companies measure energy in
kilowatt-hours (kWh), where 1 kWh = 3600 kJ
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K. A. Saaifan, Jacobs University, Bremen
2.3 Voltage and Current Sources
There are two types of circuit elements:
Active elements (supplying energies), e.g., electric generator, batteries
Passive elements (absorbing energy), e.g., resistors, capacitors, and
inductors
The passive elements can be classified according to the relationship of the
current through it to the voltage
Resistor,
Capacitor,
Inductor,
Voltage and current sources:
Voltage sources provides the circuit with a specified voltage
Current source provides the circuit with a specified current
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K. A. Saaifan, Jacobs University, Bremen
Independent voltage source
The source is characterized by a terminal voltage which is completely
independent of the current through it
dc voltage source
ac voltage source
Independent current source
The current through the element is completely independent of the
voltage across it
dc current source
ac current source
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K. A. Saaifan, Jacobs University, Bremen
Dependent sources
The value of dependent sources depends on a voltage or currents of
some other elements
There are 4 different types of dependent sources
current-controlled
current source
voltage-controlled
current source
Find vL
Ans:
voltage-controlled
voltage source
current-controlled
voltage source
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K. A. Saaifan, Jacobs University, Bremen
Dependent sources
The value of dependent sources depends on a voltage or currents of
some other elements
There are 4 different types of dependent sources
current-controlled
current source
voltage-controlled
current source
voltage-controlled
voltage source
current-controlled
voltage source
Find the power absorbed by each element in the circuit
Ans:
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K. A. Saaifan, Jacobs University, Bremen
2.4 Ohm's Law
Ohm's law states the voltage across conducting materials is directly
proportional to the current flowing through the material, or
where R is the resistance
slope=R (V/A)
The unit of the resistance is Ohm (Ω)
The Resistor has a linear relation between the applied voltage and
the current
The current goes from a higher potential to a lower potential
The power absorbed by the resistor can be expressed as
The resistor is a passive element that cannot deliver or store energy
Find i and R, if v=-10 V and R is absorbing 0.1 W
Ans:
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K. A. Saaifan, Jacobs University, Bremen
The resistance of any cylindrical object is given as
l
Material with resistivity ρ
A
For a linear resistor, the ratio of the current to the voltage is called the
conductance
The SI unit of the electrical conductance G is siemens (S)
Homework Assignment 1
P2.11, P2.12, P2.15, P2.17, P2.20, P2.22, P2.23, P2.26, P2.31, P2.32, P2.33,
and P2.35