Chapter 2
Fundamentals of electric circuits
Jaesung Jang
Electricity and Current
KCL and KVL
Resistance and Ohm’s law
Voltage and Current Dividers
Practical Voltage and Current Sources
1
Electrons and Protons in the Atom
• Example: A hydrogen atom contains one proton (양성자) in its nucleus. This is
balanced by one orbiting electron (전자). A hydrogen atom contains no neutrons in its
nucleus.
• Electrons are distributed in orbital rings around the nucleus.
• Charge of an electron and proton
– The charge of a single electron, or qe, is 0.16 × 10−18 C (coulomb) -> qe = - 0.16 × 10−18 C
where “-” indicates the charge is negative.
– The charge of a single proton, qP, = + 0.16 × 10−18 C (->positive charge).
– 1 coulomb (C) is equal to the charge quantity (전하량) (Q) of 6.25 × 1018 electrons or
protons.
2
Structure of the Atom
• Atomic Number
– The atomic number (원자번호) of an element is the number of protons
in the nucleus of the atom balanced by an equal number of orbiting
electrons.
– The number of electrons in orbit around the nucleus of a neutral atom is
equal to the number of protons in the nucleus. (-> electrically neutral)
• Orbital Rings
– Electrons are contained in successive rings beyond the nucleus. The
rings are called K, L, M, N, O, P, and Q, respectively.
– Each ring has a maximum number of electrons for stability. They are:
K ring = 2 electrons.
L ring = 8 electrons.
M ring = 8 or 18 electrons.
N ring = 8,18, or 32 electrons.
O ring = 8 or 18 electrons
P ring = 8 or 18 electrons
Q ring = 8 electrons
3
Structure of the Atom (Cont.)
• The electron valence of an atom is the number of electrons in the
incomplete outermost shell. The valence indicates how easily the atom can
gain or lose electrons to make a complete (stable) outermost ring.
• The valence electrons below are weakly bound to the nucleus (unstable).
The electrons in the outermost ring can escape freely from the atom due to
a certain force (e.g. electric fields). That is, they become free electrons
(자유전자).
• Free electrons can move from one atom to the next and are the basis of
electric current.
electric fields
29 protons
atomic number = 29
+
free electrons
29 electrons
(net charge = 0)
1 valence electron
positive charge
4
Current
• The charge in motion due to
electric fields is an electric
current.
• Current is defined as the time
rate of change of electric
charges (here positive charge is
considered.)
• The current is I = dq/dt.
– The unit of electric current is the
ampere (A).
– 1 A = 6.25 × 1018 electrons
(1C)/sec.
5
Conductor, Insulator, & Semiconductor
• Conductor (도체) has a great number of free electrons
• Examples of conductors include:
– Silver, copper, aluminum
• Insulator (Dielectric) (부도체) only a few free electrons (자유전자가 거의 없다)
• 정전기 (Static electricity)
• Examples of insulators include:
– Glass, plastic, rubber.
• Semiconductors (반도체) are materials that are neither good conductors nor
good insulators. (도체와 부도체의 중간 -> 반도체)
• Examples of semiconductors include:
– Carbon, silicon, germanium
6
Mechanical & Electrical Analogy
Positive charge
Stone
Gravitational field g
Distance
Ground
Gravitational field
F/a = m
Move the stone
Potential
Difference
(volt)
E
Electric field
Electric ground
Move the electron
Electric field
V/i = R
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Potential difference
• Two unlike charges generate the electric field
where potential difference is a measure of strength
of the electric field. (Imagine a battery!)
– The volt is the unit of potential difference.
+
• The potential difference (or voltage) between two
points equals 1 volt when 1 J of energy is
expended in moving 1 C of charge between those
two points.
+
Battery
-
E
– 1V=1J/1C
-
• Analogy: A 1 kg stone falling from 10 m height is
faster at the ground than from 1 m height (중력
[위치에너지] 에 의한 물체의 떨어짐). Height ~
Voltage.
8
The Closed Circuit
• A circuit can be defined as a path
for current flow. Any circuit has
three key elements:
1. There must be a source of
potential difference. Without
the applied voltage, current
cannot flow.
2. There must be a complete path
for current flow.
3. The current path normally has
resistance, either to generate
heat or limit the amount of
current.
Circuit diagram
A closed circuit
(current is flowing)
9
The Open and Short Circuit
An open circuit
(no current is flowing)
• Open and Short Circuits
– When a current path is broken
(incomplete) the circuit is said
to be open. The resistance of
an open circuit is infinitely high.
There is no current in an open
circuit.
– When the current path is
closed but has no resistance,
the result is a short circuit.
Short circuits can result in too
much current due to no
resistance.
10
Ideal Voltage Source
•
•
Ideal voltage source: it provides a
prescribed voltage (fixed) across its
terminals irrespective of the current
flowing through it.
Note that by convention, current is
considered as the motion of positive
charges. (load ~ resistance)
Voltage
Current
11
Ideal Current Source
•
Ideal current source: it provides a
prescribed current to any circuit
connected to it irrespective of the
voltage flowing through it.
Current
Voltage
12
Dependent (Controlled) Source
•
Dependent (controlled sources): Current or voltage output is a function of
some other voltage or current in a circuit
Current or voltage source
13
Branch and Node
•
•
Branch is any portion of a circuit with two terminals connected to it.
Node is the junction of two or more branches. (two branches -> trivial node)
14
Loop and Mesh
•
•
Loop is any closed connection of branches.
Mesh is a loop that does not contain other loops.
15
Kirchhoff’s Current Law (KCL)
• Charge cannot be created but must be
conserved. -> For any nodes of an
electric circuit, the (algebraic) sum of
all branch currents leaving the nodes is
zero at any time.
• Plus sign: current direction points away
from a node.
IA
+
IC
P
+
_
IB
• Kirchhoff’s Current Law (KCL) on a
node may also be stated as
∑ IP = 0
For node P, IA+IB-IC=0
16
Kirchhoff’s Voltage Law (KVL)
• A loop is any closed path in a circuit.
• KVL: For any loops of an electric circuit, the algebraic sum of the branch
voltages around the loop is zero at any time. -> ΣV = 0 on a loop.
• Plus sign: voltage directions (Not the current direction) agree with “loop
direction”.
a
Loop direction
Loop direction
+ i
Generalized representation of
circuit elements
V
Resistors, Inductors,
Capacitors, or Transformers
_
What about voltage source?
V=Vab
b
Loop = Voltage
Voltage sign:
positive +
Loop ≠ Voltage
Voltage sign:
negative -
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Example
Loop B
For clockwise loops
−VS1 + V1 + V2 + V3 = 0
− V2 + V S 2 − V4 = 0
− V3 + V4 + V5 = 0
Loop A
Loop C
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Resistance and Ohm’s Law
•
•
•
•
Resistance is the opposition to the
flow of current. For example, atoms
can obstruct the path of electrons.
Voltage and current have a certain
relationship (i-v characteristic)
because of resistance.
Nonlinear resistance: i=f(v) v
Linear resistance: i=kv, where k is a
constant
l
– Ohm’s law -> v=i R or i=G v
R=ρ
A
– R (unit: Ohm) and G (unit:
Siemens) are constants.
ρ : resistivity
R : resistance
σ : conductivity
G : conductance
19
Resistor
• A component manufactured to have a specific value of resistance is called a resistor.
• The two main considerations when buying a resistor are its resistance, R, in ohms
(with tolerance) and its power rating, P, in Watts.
– The resistance, R, provides the required reduction in current or the desired drop in voltage.
– The power rating indicates the amount of maximum power the resistor can safely work. (Ex.
½ power, ¼ power, 1 power)
– Exceeding the power rating leads to overheating and burning.
20
Resistor Color Coding
x10color value
Color Code
0 Black
1 Brown
2 Red
3 Orange
4 Yellow
5 Green
6 Blue
7 Violet
8 Gray
9 White
Gold: -1
Silver: -2
21
Electric Power
• Battery generates electric power (=work or
energy per unit time).
• Resistor dissipates electric power as a form of
heat due to collision of electrons and atoms.
• Power “dissipated”= voltage x current ->
positive values for power consumption
elements (e.g. resistor, inductor, conductor,
etc.)
• P=Vi = i2R = v2/R
• The generated power is equal to the sum of the
power dissipated by each resistance.
22
Series Circuit and Voltage Dividers
Series circuit
• Characteristics of a Series
Circuit
– The current is the same
everywhere in a series circuit.
– The total (equivalent) resistance is
equal to the sum of the individual
resistance values.
– The total voltage is equal to the
sum of the IR voltage drops across
the individual resistances.
I1= I2 = I3
I1
V1
R1
I2
VT V2
R2
I3
V3
R3
RT = R1+ R2 + R3
V1: V2 :V3 = R1: R2: R3
R1
V1=
V
R1+ R2 + R3 T
R2
VT
V2=
R1+ R2 + R3
R3
VT
V3=
R1+ R2 + R3
VT = V1+ V2 +V3
23
Parallel Circuit and Current Dividers
Parallel circuit
• Characteristics of a Parallel
Circuit
– Voltage is the same across each
branch.
– The total current is equal to the
sum of the individual branch
currents.
– The reciprocal of total
(equivalent) resistance is equal
to the sum of the reciprocal of
individual resistance values.
– The equivalent resistance (total
resistance) (REQ=RT) is less
than the smallest branch
resistance. The term equivalent
resistance refers to a single
resistance that would draw the
same amount of current as all of
the parallel connected branches.
V1= V2 = V3
IT
I1
R1
V1
I2
R2
V2
I1:I2:I3 = 1/R1: 1/R2 :1/R3
I3
R3
V3
1/R1
I
1/R1+ 1/R2 +1/R3 T`
1/R2
I2=
I
1/R1+ 1/R2 +1/R3 T
1/R3
I2=
IT
1/R1+ 1/R2 +1/R3
I1=
IT = I1+ I2 + I3
1/RT = 1/R1+ 1/R2 +1/R3
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Voltage Dividers & Current Dividers
Series circuit
Parallel circuit
I1
V1
R1
I2
VT V2
R2
I3
V3
R3
RT = R1+ R2 + R3
V1: V2 :V3 = R1: R2: R3
R1
V1=
V
R1+ R2 + R3 T
R2
VT
V2=
R1+ R2 + R3
R3
VT
V3=
R1+ R2 + R3
VT = V1+ V2 +V3
V1= V2 = V3
IT
I1= I2 = I3
I1:I2:I3 = 1/R1: 1/R2 :1/R3
I1
I2
I3
R1
R2
R3
V1
V2
V3
1/R1
I1=
I
1/R1+ 1/R2 +1/R3 T`
1/R2
I2=
I
1/R1+ 1/R2 +1/R3 T
1/R3
I2=
IT
1/R1+ 1/R2 +1/R3
IT = I1+ I2 + I3
1/RT = 1/R1+ 1/R2 +1/R3
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Practical Voltage & Current Source
•
Real voltage source has the
internal resistance inside.
•
The internal resistance
poses a limit to the
maximum current in a
practical voltage source and
maximum voltage in a
practical current source.
In the practical current source
iL =
rS
iS
RL + rS
→ υ S = iL R L =
rS
RL
i S RL =
iS rS
RL + rS
RL + rS
26
Ohmmeter & Ammeter
•
Ohmmeter:
– The resistance of an element can
be measured only when the
element is disconnected from any
other circuit.
•
Ammeter
– The ammeter must be placed in
series with the element to be
measured.
– The ammeter should not restrict
the flow of current (induce
another voltage drops) or else it
will not be measuring the true
current flowing in the circuit. An
ideal ammeter has zero internal
resistance.
27
Voltmeter
•
Voltmeter
– The voltmeter must be
placed in parallel with
the element to be
measured.
– The voltmeter should
not draw any current or
else it will not be
measuring the true
current flowing in the
circuit. An ideal
voltmeter has infinite
internal resistance.
•
Wattmeter
– Combination of
voltmeter and ammeter.
Read conclusion at pp. 48!!!!
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