lecture 1a [compatibility mode]
DESCRIPTION
Basic Circuit Theory ConceptTRANSCRIPT
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Circuit Theory (EE102)
Lecture 1(a)
Basic Concepts & Basic Laws
Text Book:Fundamentals of Electric Circuits (4th Ed/3rd Ed) By Alexander & Sadiku. McGraw-Hill [CH1]
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Basic Concepts
1.1 Systems of Units.
1.2 Electric Charge.
1.3 Current.
1.4 Voltage.
1.5 Power and Energy.
1.6 Circuit Elements.
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1.1 System of Units (1)
Quantity Basic unit Symbol
Length meter m
Mass kilogram Kg
Time second s
Electric current ampere A
Thermodynamic
temperature
kelvin K
Luminous intensity candela cd
Six basic units
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1.1 System of Units (2)
The derived units commonly used in electric circuit theory
Decimal multiples and
submultiples of SI units
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1.2 Electric Charges
• Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C).
• The charge e on one electron is negative and equal in magnitude to 1.602 × 10-19 C which is called as electronic charge. The charges that occur in nature are integral multiples of the electronic charge.
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1.3 Current (1)
• Electric current i = dq/dt. The unit of ampere can be derived as 1 A = 1C/s.
• A direct current (dc) is a current that remains constant with time.
• An alternating current (ac) is a current that varies sinusoidally with time. (reverse direction)
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1.3 Current (2)
• The direction of current flow
Positive ions Negative ions
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1.3 Current (3)
Example 1
A conductor has a constant current of 5 A. How many electrons pass a fixed point on the conductor in one minute?
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1.3 Current (4)
Solution
1 A = 1C/s, 1e=1.602 × 10-19 C /electron
Total no. of charges pass in 1 min is given by
5 A = (5 C/s)(60 s/min) = 300 C/min.
Total no. of electronics pass in 1 min is given
minelectrons/ 1087.1C/electron 10602.1
C/min 300 21
19x
x=
−
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1.4 Voltage (1)• Voltage (or potential difference) is the energy
required to move a unit charge through an element, measured in volts (V).
• Mathematically, (volt)
– w is energy in joules (J) and q is charge in coulomb (C).
• Electric voltage, vab, is always across the circuit
element or between two points in a circuit.
– vab > 0 means the potential of a is higher than potential of b.
– vab < 0 means the potential of a is lower than potential of b.
dqdwvab /=
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1.5 Power and Energy (1)
• Power is the time rate of expending or absorbing energy, measured in watts (W).
• Mathematical expression: vidt
dq
dq
dw
dt
dwp =⋅==
i
+
–
v
i
+
–
v
Passive sign conventionP = +vi p = –vi
absorbing power supplying power
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1.5 Power and Energy (2)
• The law of conservation of energy
∑ = 0p
• Energy is the capacity to do work, measured in joules (J).
• Mathematical expression ∫ ∫==t
t
t
tvidtpdtw
0 0
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1.6 Circuit Elements (1)
Active Elements Passive Elements
Independentsources
Dependantsources
• A dependent source is an active element in which the source quantity is controlled by another voltage or current.
• They have four different types: VCVS, CCVS, VCCS, CCCS. Keep in minds the signs of dependent sources.
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1.6 Circuit Elements (2)
Example 2
Obtain the voltage v in the branch shown in Figure 2.1.1P for i2= 1A.
Figure 2.1.1P
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1.6 Circuit Elements (3)
Solution
Voltage v is the sum of the current-independent 10-V source and the current-dependent voltage source vx.
Note that the factor 15 multiplying the control current carries the units Ω.
Therefore, v = 10 + vx = 10 + 15(1) = 25 V
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Text Book:Fundamentals of Electric Circuits (4th Ed/3rd Ed) By Alexander & Sadiku. McGraw-Hill [CH2]
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Basic Laws
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Basic Laws
2.1 Ohm’s Law.
2.2 Nodes, Branches, and Loops.
2.3 Kirchhoff’s Laws.
2.4 Series Resistors and Voltage Division.
2.5 Parallel Resistors and Current Division.
2.6 Wye-Delta Transformations.
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2.1 Ohms Law (1)
• Ohm’s law states that the voltage across a resistor is directly proportional to the current I flowing through the resistor.
• Mathematical expression for Ohm’s Law is as follows:
• Two extreme possible values of R: 0 (zero) and ∞∞∞∞ (infinite) are related with two basic circuit concepts: short circuit and open circuit.
iRv =
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2.1 Ohms Law (2)• Conductance is the ability of an element to
conduct electric current; it is the reciprocal of resistance R and is measured in mhos or siemens.
• The power dissipated by a resistor:
v
i
RG ==
1
R
vRivip
22 ===
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2.2 Nodes, Branches and Loops (1)
• A branch represents a single element such as a voltage source or a resistor.
• A node is the point of connection between two or more branches.
• A loop is any closed path in a circuit.
• A network with b branches, n nodes, and l independent loops will satisfy the fundamental
theorem of network topology:
1−+= nlb
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2.2 Nodes, Branches and Loops (2)
Example 1
How many branches, nodes and loops are there?
Original circuit
Equivalent circuit
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2.2 Nodes, Branches and Loops (3)
Example 2
How many branches, nodes and loops are there?
Should we consider it as one branch or two branches?
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2.3 Kirchhoff’s Laws (1)
• Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.
01
=∑=
N
n
niMathematically,
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2.3 Kirchhoff’s Laws (2)
Example 3
• Determine the current I for the circuit shown in the figure below.
I + 4-(-3)-2 = 0
⇒I = -5A
This indicates that the actual current for I is flowing in the opposite
direction.We can consider the whole enclosed area as one “node”.
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2.3 Kirchhoff’s Laws (3)
• Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed
path (or loop) is zero.
Mathematically, 01
=∑=
M
m
nv
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2.3 Kirchhoff’s Laws (4)
Example 4
• Applying the KVL equation for the circuit of the figure below.
va-v1-vb-v2-v3 = 0
V1 = IR1 v2 = IR2 v3 = IR3
⇒ va-vb = I(R1 + R2 + R3)
321 RRR
vvI ba
++
−=
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2.4 Series Resistors and Voltage Division (1)
• Series: Two or more elements are in series if they are cascaded or connected sequentially and consequently carry the same current.
• The equivalent resistance of any number of resistors connected in a series is the sum of the individual resistances.
• The voltage divider can be expressed as
∑=
=+⋅⋅⋅++=N
n
nNeq RRRRR1
21
vRRR
Rv
N
n
n+⋅⋅⋅++
=21
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Example 5
10V and 5ΩΩΩΩare in series
2.4 Series Resistors and Voltage Division (2)
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2.5 Parallel Resistors and Current Division (1)
• Parallel: Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.
• The equivalent resistance of a circuit with N resistors in parallel is:
• The total current i is shared by the resistors in inverse proportion to their resistances. The current divider can be expressed as:
Neq RRRR
1111
21
+⋅⋅⋅++=
n
eq
n
nR
iR
R
vi ==
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Example 6
2ΩΩΩΩ, 3ΩΩΩΩ and 2A are in parallel
2.5 Parallel Resistors and Current Division (2)
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2.6 Wye-Delta Transformations
)(1
cba
cb
RRR
RRR
++=
)(2
cba
ac
RRR
RRR
++=
)(3
cba
ba
RRR
RRR
++=
1
133221
R
RRRRRRRa
++=
2
133221
R
RRRRRRRb
++=
3
133221
R
RRRRRRRc
++=
Delta -> Wye Wye -> Delta
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Example 7
Transform the wye network to a delta network
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Solution