EE201 Circuit Theory
Ch.1. Basic Concepts
Bongjin Kim
Associate Professor
Electrical Engineering, KAIST
*Lecture materials are modified version of the contents provided by Prof. Minkyu Je (KAIST)
Outline
❑
System of Units
❑
Basic Quantities
❑
Circuit Elements
2
International System of Units (SI)
❑
SI base units (SI = Systeme Internationale)
•
•
International system of units
The SI is founded on seven base units for seven base quantities assumed
to be mutually independent
3
International System of Units (SI)
❑
SI prefixes
– The SI unit uses prefixes based on the power of 10 to relate larger and smal
ler units to the basic unit.
4
Charge
❑
Charge is an electrical property of matter that can result in electrostatic attraction or repulsion in the presence of other matter
❑
SI unit of quantity of electric charge: coulomb (C)
• [Definition] The quantity of charge that has passed through the cross
section of an electrical conductor carrying one ampere in one second.
• 1C = 1A x 1s = 1F x 1V
• -1C is equivalent to the charge carried by about 6.242 1018 electrons
• Charge of an electron (electronic charge) is approximately −1.602 10−19 C.
• The charges found in nature are integral multiples of the electronic charge.
❑
Law of conservation of charge
• Charge can neither be created nor destroyed, only transferred.
• Thus, algebraic sum of the electric charge in a system does not change.
5
Current
❑
Current is defined as the time rate of change of charge:
dq (t )
i (t ) =
dt
or
q (t ) =
t
i ( x )dx
−
where i and q represent current and charge, respectively.
❑
SI unit of quantity of current: ampere (A)
• 1 A = 1 Cs (coulomb per second)
6
Current
❑
Convention for current
• Current flow can be resulted both from positive and negative charges.
• Universally accepted conventional current flow represents the movement
of positive charges
Positive charges
Negative charges
7
Current
❑
Representation of current flow
• It is important to specify not only the magnitude but also the direction.
• A positive value for the current indicates flow in the direction of the arrow.
• A negative value indicates the flow in the direction opposite to the arrow.
2 C of charge pass
from left to right
each second.
3 C of charge pass
from right to left
each second.
8
Current
❑
Direct current (DC)
A current that flows only in one direction and can be constant or time
varying, which is used in automobiles, flashlights, and so on, being supplied
by batteries typically.
❑
Alternating current (AC)
A current that changes direction with respect to time, which is commonly
found in every household and used to run the refrigerator, stove, washing
machine, and so on, being supplied by home outlets typically.
Direct current (DC)
Alternating Current (AC)
9
Current
❑
Typical current magnitudes
10
Voltage
❑
Voltage (electric potential or electromotive force) between two points
is defined as the difference in energy level of a unit charge located
at each of the two points.
❑
SI unit of quantity of voltage: volt (V)
• 1 V = 1 JC = 1 NmC
work or energy is measured in joules (J) and 1 joule is 1 newton meter (Nm)
• If a positive charge is moved between two points, the energy required
to move it is the difference in energy level between the two points, and
is the defined voltage:
where v(t) and w(t) represent voltage and energy (or work), respectively
11
Voltage
❑
Representation of voltage
• Voltage is always measured in a relative form as the voltage difference
between two points.
• It is important to define a voltage with a reference direction so that it
can be determined which point is at the higher potential with respect to
the other.
• Hence, like in the case of current, both magnitude and direction must
be specified.
12
Voltage
❑
Examples of voltage representation
The + and − signs define a reference direction for V1. V1 is defined
with the assumption that point A is at the higher potential than point
B. Hence, V1 = 2 V means that the difference in potential of points A
and B is 2 V and point A is at the higher potential.
If a unit positive charge is moved from point A through the circuit to point B,
it will give up energy to the circuit and have 2-J less energy when it
reaches point B.
If a unit positive charge is moved from point B to point A, extra energy
must be added to the charge by the circuit, and hence the charge will end
up with 2-J more energy at point A than it started with at point B.
These two representations are equivalent to each other.
Both represent potential between points a and b is 9V and the
point a is at a higher potential.
There is a 9V voltage drop from a to b, or equivalently a 9V
voltage rise from b to a
13
Voltage
❑
Typical voltage magnitudes
14
Energy
❑
Voltage-current relationship for energy transfer
Chemical Energy
Electrical Energy
Thermal Energy
• Charges flow out of the positive terminal of the battery and light bulb and
back into the negative terminal of the battery.
• The battery supplies energy, and the charges gain energy as they pass
through the battery; the current leaves the positive terminal of the voltage.
• The bulb absorbs energy, and the charges expend energy as they move
through the bulb; the current enters the positive terminal of the voltage.
15
Energy: Voltage-Current Relationship
Examples of voltage-current relationships for energy absorbed & supplied
Energy is being supplied to the element by the rest of the circuit.
2 C of charge are moving from point A to point B through the element
each second.
Each coulomb loses 3 J of energy as it passes through the element
from point A to point B.
Therefore, the element is absorbing 6 J of energy per second.
Energy is being supplied by the element to the rest of the circuit.
2 C of charge are moving from point B to point A through the element
each second.
Each coulomb gains 3 J of energy as it passes through the element
from point B to point A.
Therefore, the element is suppling 6 J of energy per second.
16
Power
❑
Power is defined as the time rate of change of energy:
p=
dw dw dq
=
= vi
dt dq dt
where p represents the power.
❑ SI unit of quantity of power: watt (W)
• 1 W = 1 Js (joule per sec)
❑
The change in energy from time t1 to time t2 can be found by
w =
t2
t2
1
1
t p dt = t vi dt .
17
Power
❑
Convention of Power: passive sign convention
• A voltage v(t) is defined as the voltage across the element with the positive
reference at a terminal where a current variable i(t) is entering.
• If the sign of the power is positive, power is being absorbed by the
element.
• If the sign of the power is negative, power is being supplied by the
element.
18
Power
❑
Examples of power calculation
P = (12 V) (−4 A) = −48 W
The element is supplying power.
P = (4 V) (2 A) = 8 W
The element is absorbing power.
19
Power
Example of Power Absorbing – Battery Jump Start
❑ Shown below is an illustration of using one car battery to “jump start”
another car battery. Calculate the power for each battery.
❑
Power is
Supplied
Power is
Absorbed
20
Conservation of Energy and Power
❑
Tellegen’s theorem (Bernard D. H. Tellegen, 1952)
• Electrical networks satisfy the principle of energy conservation, and it
implies that the power is also conserved.
• The sum of the powers absorbed by all elements in an electrical
network is zero.
• The power supplied in a network is exactly equal to the power absorbed.
• Checking if Tellegen’s theorem satisfies for a particular network is one
way for analyzing electrical networks.
21
Example
❑
Use Tellegen’s theorem to find the current IO.
P2A = (6 V) (−2 A) = −12 W
P1 = (6 V) Io = 6Io W
P2 = (12 V) (−9 A) = −108 W
P3 = (10 V) (−3 A) = −30 W
P4V = (4 V) (−8 A) = −32 W
PDS = (8Ix V) (11 A) = (16 V) (11 A) = 176 W
−12 + 6Io − 108 − 30 − 32 + 176 = 0
6Io = 12 + 108 + 30 + 32 − 176 = 6
Io = 1 A
22
Summary of Q, I, V, P, and E
23
Circuit Elements
❑
Circuit elements
• Terminal devices that are completely characterized by the current through
the element and/or the voltage across it.
• Circuit elements are employed in constructing electric circuits.
❑
Passive and Active elements
• Active elements can generate energy (e.g., batteries and generators).
• Passive elements can’t generate energy
Some passive elements dissipate energy and some can store energy (e.g.,
resistors, capacitors, and inductors)
• Independent/dependent voltage/current sources are important active
elements.
24
Independent Sources
❑
Independent voltage source
• Two-terminal element that
maintains a specified voltage
between its terminals
regardless of the current
through it
❑
Independent current source
• Two-terminal element that
maintains a specified current
regardless of the voltage
across its terminals
25
Independent Sources
❑
Limitation of the mathematical model (ideal source model)
– Mathematical models approximate actual physical systems only under a
certain range of conditions.
– Example: Car battery
• With the headlights on, turn on the radio. Do the headlights dim with
the radio on?
• If you try to crank your car with the headlights on, will the lights dim?
26
Dependent Sources
❑
Dependent sources generate a voltage or a current that is
determined by a voltage or a current at a specified location in
the circuit.
• These sources are important because they are an integral part of the
mathematical models used to describe the behavior of many electronic
circuit elements.
• For example, metal-oxide-semiconductor field-effect transistors
(MOSFETs) and bipolar transistors are modeled with dependent
sources, and therefore the analysis of electronic circuits involves the
use of these controlled elements.
27
Dependent Sources
❑
Four types of dependent sources
VCVS: voltage-controlled voltage source
CCVS: current-controlled voltage source
VCCS: voltage-controlled current source
CCCS: current-controlled current source
28
Dependent Sources
❑
Example: Determine the outputs.
29
Summary
30
Recommended Problems
❑
1.2.7, 1.2.12, 1.2.24, 1.3.3, 1.3.6, 1.3.11, 1.3.14, 1.3.15 (in textbook)
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