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Circuit Elements and Variables
What is Electric Circuit?
 An electric circuit is an interconnection of electrical
elements
 Example: Consists of 3 basic elements: battery, lamp,
connecting wires.
 When the wires are connected properly, the circuit is
said to be closed and the lamp will light. When the
wires are disconnected, the circuit is said to be
open.
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Circuit Diagram
3
Basic Electric Concept
1. Review SI unit (International Systems of Unit)
2. Know the definition of basic electrical quantities :
charge, current, voltage, power & energy
3. Know the symbols and definition of the elements of the
circuit:
passive and active elements & independent and
dependent sources
4. To understand some fundamentals laws and basic
network to determine the values of electric circuit
variables:
Ohm’s Law, nodes, branches, loops & Kirchoff’s Law
4
Review SI Units (1)
SI: International System of Unit is used by all the major
engineering societies and most engineers throughout the
world.
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Review SI Units(2)
Standardized prefixes to signify powers of 10
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Basic Electric Concept
1.
Review SI unit (International Systems of Unit)
2. Know the definition of basic electrical
quantities :
charge, current, voltage, power & energy
Know the symbols and definition of the elements of the
circuit:
passive and active elements & independent and
dependent sources
4. To understand some fundamentals laws and basic network to
determine the values of electric circuit variables:
Ohm’s Law, nodes, branches, loops & Kirchoff’s Law
3.
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Unit, Symbol and Definition
Quantity
Unit
Symbol
Charge, Q
Coulomb
C
Current, I
Ampere
A
Voltage, V
Volt
V
Power, P
Watt
W
Energy, W
Joule
J
Quantity
Definition
Charge, Q
Electric charge is a property of the atomic particles
possessed by both electrons and protons.
Current, I
Current is the movement of charge in a specified direction.
Voltage, V Voltage (or potential difference) is the energy required to move
a unit charge through an element
Power, P
Power is the time rate of expending or absorbing energy.
Energy, W Energy is the capacity to do work
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Charge, Q (C)
The charge on one electron is called
electronic charge and equivalent to
Q of e = - 1.602  10-19 C
How many electrons in 1 C?
1 C = 1 / 1.602  10-19
= 6.24 x 1018 electrons
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Current, I (A)
Current is the movement of charge in a specified direction.
Charge
Current =
Time
2 common types of current:
dQ
I (A) = dt
C/s
i
t
Direct current (DC)
Alternating current (AC)
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Voltage, V (v)
Voltage (or potential difference) is the energy required to
move a unit charge through an element
Energy
Voltage =
Charge
dW
vab = dQ
It is a potential energy difference between two points, a and
b
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Power, P (W)
Power is the time rate of expending or absorbing
energy.
Energy
Power =
Time
i
dW
P = dt
i
+
+
v
v
–
–
P = +vi
absorbing power
P = –vi
supplying power
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Energy, W (J)
• Energy is the capacity to do work, measured in joules
(J).
t
t
t0
t0
w   pdt   vidt
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Basic Electric Concept
1. Review SI unit (International Systems of Unit)
2. Know the definition of basic electrical quantities :
charge, current, voltage, power & energy
3. Know the symbols and definition of the
elements of the circuit:
passive and active elements & independent
and dependent sources
4. To understand some fundamentals laws and basic
network to determine the values of electric circuit
variables:
Ohm’s Law, nodes, branches, loops & Kirchoff’s Law
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Active and Passive Elements
Circuit
Elements
Active elements
•capable of generating
electric energy
•Example : generators,
batteries, operational
amplifier, voltage and
current sources
Passive elements
•incapable of generating
electric energy
•Example : resistor,
inductor, capacitor
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Independent Source
AC
Voltage
(+/- sign)
DC
Current
(arrow)
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Dependent Source
• A dependent source is an active element in which the
source quantity is controlled by another voltage or
current.
• They have four different types:
1. VCVS: Voltage-controlled voltage source
2. CCVS: Current-controlled voltage source
3. VCCS: Voltage-controlled current source
4. CCCS: Current-controlled current source
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Dependent Source (Diamond shape)
Voltage
(+/- sign)
Current
(arrow)
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Example of sources
Current
controlled
voltage
source,
V =10 i
Independent
voltage
source
V =20 V
Current
controlled
current
source,
Is =10.2 I
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Basic Electric Concept
1.
Review SI unit (International Systems of Unit)
2. Know the definition of basic electrical quantities :
charge, current, voltage, power & energy
3. Know the symbols and definition of the elements of the
circuit:
passive and active elements & independent and
dependent sources
4. To understand some fundamentals laws
and basic network to determine the
values of electric circuit variables:
Ohm’s Law, nodes, branches, loops & Kirchoff’s Law
20
Ohms Law
 Ohm’s law states that the voltage across a resistor
is directly proportional to the current I flowing
through the resistor.
V  IR
 Two extreme possible values of R:
R = 0 : short circuit
R =  : open circuit.
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Short Circuit
R = 0 , no voltage difference exists,
thus V = 0 V, but current still can
flow.
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Open circuit
R =  , no current flows .Voltage
difference can exist, as determined by
the circuit
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Conductance & Power
 Conductance is a measure of the ability of an element
to conduct electric current
 Inverse of resistance
 The units is Siemens (S) or mhos
1 i
G 
R v
 Power dissipated by resistor:
2
v
p  vi  i R 
R
2
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Example 1
 In the circuit, calculate the current I, the conductance
G, and the power P.
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Example 2
 In the circuit, calculate the voltage V, the conductance
G, and the power P.
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Branches
 A branch represents a single element such as a voltage
source or a resistor.
 In other words, a branch represents any elements
which has two terminals.
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1
2
3
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Exercise
Should we consider it as one
branch or two branches?
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Nodes
 A node is the point of connection between two or more
branches.
 A node usually indicated by a dot in a circuit.
 If a short circuit (no element between dots), the multiple
dots constitute as a single nodes.
 How many branches connected to node a, b and c?
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2
1
3
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1
2
3
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Loops
 A loop is any closed path in a circuit.
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Relation of branches, nodes and
loops
 A network with b branches, n nodes, and l
independent loops will satisfy the
fundamental theorem of network topology:
b  l  n 1
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Example 3
How many branches, nodes and loops are there?
Does it satisfy b = l + n -1?
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Kirchhoff Law
 Gustav Robert Kirchhoff (1824–1887)
 Models relationship between:
 circuit element currents (KCL)
 circuit element voltages (KVL)
 Introduce two laws:
 Kirchhoff Current Law (KCL)
 Kirchhoff Voltage Law (KVL)
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Kirchhoff’s Current Laws (KCL)
 Kirchhoff’s current law (KCL) states that the algebraic
sum of currents entering a node (or a closed boundary) is
zero.
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Kirchhoff’s Current Laws (KCL)
 Convention sign for current entering and leaving node:
current entering node = + i
current leaving node = - i
 According to KCL, for any node:
N
i
n 1
n
0
N = number of branches connected to the nodes
in = nth current entering (+ i) or leaving (- i) the
node
 Without the sign (+Ve or -Ve), the formula of KCL can be
written as:
Current entering node = current leaving node
(What goes in, must comes out)
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Example of KCL (1)
Node A
Current leaving node, (-i)
Current entering node, (+i)
 2 options:
N
i
n 1
n
 5mA  10mA  15mA  (30mA)  0
Current entering = current leaving
5mA  10mA  15mA  30mA
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Example of KCL (2)
Node a
IT : Leaving node a (-Ve)
I1 : Entering node a (+Ve)
I2: Leaving node a (-Ve)
I3: Entering node a (+Ve)
N
i
n 1
n
 (  I T )  I1  (  I 2 )  I 3  0
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Kirchhoff’s Voltage Laws (KVL)
 Kirchhoff’s voltage law (KVL) states that the algebraic sum
of all voltages around a closed path (or loop) is zero.
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Kirchhoff ’s Voltage Law (KVL)
For any circuit loop:
M
v
m 1
m
0
M = number of voltages in the loop
vm = mth voltage
Convention sign for voltage inside loop (clockwise or
anticlockwise direction):
 If the positive terminal of voltage is met first: +V
 If the negative terminal of voltage is met first: -V
Without the +/- sign, KVL formula can be written as
Sum of voltage drops = sum of voltage rises
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Example of KVL
+V
+V
Voltage drop
Voltage drop
-V
-V
Voltage
rise
Voltage
rise
+V
Voltage drop
M
v
m 1
m
 v1  v2  v3  v4  v5  0
v2  v3  v5  v1  v4
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KVL in parallel circuit
 voltage in parallel circuit is equal across all
components in the circuit
 V1 = V2 = V3 =V4 = 9V
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Example 4
 Find v1 and v2 using KVL and Ohm’s Law.
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Example 5
 Find v1, v2 and v3 using Ohm’s Law KCL and KVL.
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Example 6
 Determine vo and I in the circuit
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