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7/29/2019 Electric and Electronic Lecture Presentation - Chapter02.ppt
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Fundamentals of Electric
Circuits
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An Electrical System
Source Control Load
Transmission system
1) Source to provide energy for the electrical system
can be voltage source or current source
2) Transmission systemconducts the energy from source to load
3) Control apparatusto control the flow of energy
4) Loadto absorb electrical energy supplied by source
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Figure 2.1,2.2
2-1
Ideal voltage sources
Various representations of an electrical system
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Figure 2.3, 2.4
2-2
Symbol for ideal current source
Symbols for dependent sources
By convention : +ve current flow out of a voltage
thru +ve terminal
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Some Definitions
Electrical networka collection of elements thru which current flows
Branchany portion of a circuit with two terminals connected to it. A branch may
consist of one or more circuit elements.
Nodethe junction of two or more branches
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Figure 2.5,
2.6
2-3
Definition of a branch
Definitions of node and supernode
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Figure 2.7, 2.8
Definition of a loop
2-4
Figure 2.7
Definition of a mesh
Figure 2.8
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Figure 2.11,
2.13
2-5
Demonstration of KCLIllustration of Kirchhoffs current lawFigure 2.11
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Electric Charge and Current
- An electricsystem transmits energy due to movement of electric charge.- So fundamental electric quantity is chargesmallest amount of charge- electron
- Electrical currenttime rate of charge of charge passing a predetermined area
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Example 1
Determine current given charge suppose that charge is given by
For current to flow, there must exist a closed circuit.
i = current flowing in closed circuit
Note : Current flowing from source to load is the same as current flowing from load to source- No current is lost around closed circuit
- This principle is known as Kirchhoffs Current Law (KCL)
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KCL state that the sum of current at a node must equal to zero, or
For node 1
Define : current entering a node asve
current leaving a node as +ve
Node 1KCL :
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Exercise
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Voltage and Kirchhoffs Voltage Law- change moving in an electric circuit given rise to a current.
- So it must take some work, or energy for the charge to move between two points in a circuit.
- Total work per unit charge associated with the motion of charge between two points is calledVOLTAGE
- Definition :
- The voltage, or potential difference, between two points in a circuit indicates the energy
required to move charge from one point to the other
- The direction or polarity of the voltage related to whether energy is being dissipated orgenerated
- as in case of current, energy in the system is not lost or the sum of
voltages associated with sources must equal the sum of the load voltages
The net voltage around a closed circuit is zero
KIRCHHOFFS VOLTAGE LAW (KVL)
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- Introduce reference (ground) voltage
- Voltage V2 is the difference between two node voltages Va and
V2 = VaVb
- Select any mode as the reference node, so all node voltages may be referenced to this
reference voltage.
- In figure, select node b as reference (normally assign 0V at reference)
So, Vb = 0V
V1 = 1.5V
V2 = Vab = VaVb = Va0 = Va
but Va and V1 are the same so V1 = V2
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Exercise 1Determine unknown voltage V2
Vs = 12V
V1 = 6V
V3 = 1V
KVL: -Vs + V1 + V2 + V3 = 0
V2 = 5V
V4 = 5V
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Exercise 2
Vs1 = 12V, Vs2 = -4V
V2 = 2V , V3 = 6V
V5 = 12V
Find V1 and V4 ?
KVL : - V2 + Vs2V4 = 0V4 = -V2 +Vs2
- Vs1 - V1 +V2 +V3 = 0
1
1
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Electrical Power
- Power is defined as work per unit time
- P = work = work x charge
time charge time
= voltage x current
P = VI Watts (W)
- Power is a signal signed quantitypositive power
negative power
- Positive Power = power dissipated P = vi (power dissipated)
- Negative Power = power generated P = vi (power generated)
i
+
v
i
+
v
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Resistance and Ohms Law
- When current flows thru a wire/other circuit elements, it encounters resistance
- This causes energy to be dissipated (heat)
- According to Ohms Law
V = IR
- Voltage is proportional to the current flowing thru it
R Ohms () 1 = 1 V
A
- The resistance of a material depends on Resistivity () ; the inverse called conductivity ()
- For a cylindrical resistance element, resistance is proportional to length of sample, l , and
inversely proportional to its crosssectional area A and conductivity
A
lR = l A
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- Convenient to define conductance of circuit element as the inverse of its resistance, used
symbol G
G = I Siemen (S)
RThus ohms law can be written as
I = GV (V = IR = I )
G
- For resistors, in addition to resistance in ohm, the max allowable power dissipation (power
rating) is specified. Exceeding this power rating could cause overheating and burn out.
- Power dissipated in R
P = IV = I . IR
= IR
= VR
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ExampleDetermine the minimum resistor size that can be connected to a given battery w/o exceeding
the resistors 1/4W power rating
SolutionPower rating = 0.25W
Battery voltage = 1.5V
P = V
R0.25 (1.5)
R
R (1.5) = 9 So min R = 9
0.25
R (1/4 W)+1.5 V
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Exercise
Determine iB and power supplied by battery if: i1 = 0.2 mA
i2 = 0.4 mA
i3 = 1.2 mAVB = 3 V
VB+
iB
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Open and Short Circuit
Short circuit:- 1) R 0
2) V = 0 for any i3) Allow unimpeded current
Open Circuit :- 1) R
2) I = 0
+
V
i
8
+
V
R8
i = 0 for any V
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Series Resistors
-
Series Circuit
Def : Two or more circuit elements are said to be in series if the current flow from one
elements exclusively flows into the next element. In the example, to the battery, the
resistors appear an a single equivalent resistance,
REQ where REQ = R1 + R2
So, for series resistance
+
i R1
+V1 -
R2
+V2
-1.5 V
by KVL1.5 = V1 + V2
= iR1 + iR2
= i(R1 + R2)
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Voltage Divider- Closely tied to series resistors
- Source voltage divides among the resistors in series according to KVL
- We can write the voltage across each R
i R1
+V1 -
R2
+V2
-V
+
R3-V3 +
V = i (R1 + R2+R3)
V = i REQ
i = V
REQ
V1 = iR1 = R1 V
REQ
V2 = iR2 = R2 V
REQ
V3 = iR3 = R3 V
REQ
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Parallel Resistors
Def : Two or more circuit elements are said to be in parallel if the elements share the
same terminals. From KVL , it follows that the elements will have the samevoltage.
Ex:
KCL requires that
is = i1 + i2 + i3
ohms lawi1 = V , i2 = V, i3 = V
R1 R2 R3
so is = V 1 + 1 + 1 = V 1
R1 R2 R3 REQ
isR3
i1
R1 R2
i2 i3 +
V
-
R1 R2
i2 i3
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Where
or REQ =
- Note : for parallel combinations, normally indicate R1 // R2 // R3 .
1 = 1 + 1 + 1
REQ R1 R2 R3
1 = 1 + 1 + 1 + .... + 1REQ R1 R2 R3 RN
1 + 1 + + 1R1 R2 RN
1
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Current Divider
From circuit ,
ohms law: V = i REQ
i1 = i REQ = i
=
i1 = V, i2 = V, i3 = V
R1 R2 R3
11 + 1 + 1
R1 R2 R3
R1
R1
i1
R1
1 + 1 + 1
R1 R2 R3
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i2 = =
i3 = =
So :
i REQR2
i1
R2
1 + 1 + 1
R1 R2 R3
i REQR3
i1
R3
1 + 1 + 1
R1 R2 R3
1 + 1 +.. + 1
R1 R2 Rn
is
1
Rnin =
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Ex:
Determine i1 , R1= 10
R2= 2
R3= 20
Is = 4 A
-
V
+
R1 R2
i2 i3
R3
i1
Is
1 + 1 + 1
R1 R2 R3
Is
1
R1i1 =
1 + 1 + 1
10 2 20
(4)
1
10=
8
13= A
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Ex:
Determine V3
1 k
1 k
+V3
-5V
+
1 k
R1
R2//R3
+V3
-Vs+