Circuit Theory 1 Midterm
Circuit Theory 1 Midterm
Circuit Theory 1 Midterm
CIRCUIT THEORY 1
Clark Darwin M. Gozon, RV. Morcilla
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CHAPTER 1
BASIC CONCEPTS
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ELECTRIC CIRCUIT
An interconnection of electrical elements.
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SYSTEMS OF UNITS
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1 ampere = 1 coulomb/second
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VOLTAGE
Voltage (or potential difference) is the energy
required to move a unit charge through an element,
measured in volts (V).
Voltage vab between two points a and b in an electric
circuit is the energy (or work) needed to move a unit
charge from a to b; mathematically,
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VOLTAGE
The plus (+) and minus () signs are used to define
reference direction or voltage polarity.
(1) point a is at a potential of vab volts higher than point b
(2) the potential at point a with respect to point b is vab
vab = vba
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CIRCUIT ELEMENTS
Two types of elements found in electric circuits:
Passive element not capable of generating energy
(resistors, capacitors, and inductors)
Active element - capable of generating energy (generators,
batteries, and operational amplifiers)
Two kinds of sources:
Independent Sources - an active element that provides a
specified voltage or current that is completely independent
of other circuit variables
Dependent Sources - an active element in which the source
quantity is controlled by another voltage or current.
(transistors, operational amplifiers and integrated circuits)
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CIRCUIT ELEMENTS
Ideal Independent Voltage Source delivers to the
circuit whatever current is necessary to maintain its
terminal voltage (batteries and generators).
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CIRCUIT ELEMENTS
Ideal Independent Current Source is an active
element that provides a specified current
completely independent of the voltage across the
source.
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CIRCUIT ELEMENTS
Four possible types of dependent sources:
Voltage-Controlled Voltage Source (VCVS).
Current-Controlled Voltage Source (CCVS).
Voltage-Controlled Current Source (VCCS).
Current-Controlled Current Source (CCCS).
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CIRCUIT ELEMENTS
1. Calculate the power supplied or absorbed by
each element
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CHAPTER 2
BASIC LAWS
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OHMS LAW
Resistance (R) of an element denotes its ability to resist
the flow of electric current; it is measured in ohms ().
The resistance of any material with a uniform cross-
sectional area (A) depends on A and its length (l)
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OHMS LAW
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OHMS LAW
Ohms law states that the voltage v across a
resistor is directly proportional to the current i
flowing through the resistor.
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OHMS LAW
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OHMS LAW
Conductance is the ability of an element to conduct
electric current; it is measured in mhos ( ) or siemens (S).
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OHMS LAW
1. An electric iron draws 2 A at 120 V. Find its
resistance.
2. In the circuit shown, calculate the current i, the
conductance G, and the power p.
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KIRCHHOFFS LAWS
Kirchhoffs current law (KCL) states that the
algebraic sum of currents entering a node (or a
closed boundary) is zero.
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KIRCHHOFFS LAWS
The sum of the currents entering a node is equal to
the sum of the currents leaving the node.
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KIRCHHOFFS LAWS
Kirchhoffs voltage law (KVL) states that the
algebraic sum of all voltages around a closed
path(or loop) is zero.
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KIRCHHOFFS LAWS
By KVL:
v1 + v2 + v3 v4 + v5 = 0
v2 + v3 + v5 = v1 + v4
Sum of voltage drops = Sum of voltage rises
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KIRCHHOFFS LAWS
1. For the circuit, find voltages v1 and v2.
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KIRCHHOFFS LAWS
3. Find current io and voltage vo in the circuit shown
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By Ohms Law
By KCL @ Node a
Then:
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Example
1. Find Req for the circuit shown in Fig. A.
2. Calculate the equivalent resistance Rab in the circuit
shown in Fig. B
3. Find the equivalent conductance Geq for the circuit
in Fig. C.
Fig. A
Fig. C
Fig. B
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Example
4. Find io and vo in the circuit shown in Fig. D. Calculate
the power dissipated in the 3- resistor.
5. For the circuit shown in Fig. E, determine: (a) the
voltage vo, (b)the power supplied by the current
source, (c) the power absorbed by each resistor.
Fig. E
Fig. D
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WYE-DELTA TRANSFORMATIONS
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WYE-DELTA TRANSFORMATIONS
Delta to Wye Conversion
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WYE-DELTA TRANSFORMATIONS
Wye to Delta Conversion
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WYE-DELTA TRANSFORMATIONS
The Y and networks are said to be balanced when
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Example
1. Convert the network in Fig. A to an equivalent Y
network.
2. Obtain the equivalent resistance Rab for the circuit
in Fig. B and use it to find current i.
Fig. A Fig. B
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CHAPTER 3
METHODS OF ANALYSIS
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NODAL ANALYSIS
Nodal analysis provides a general procedure for
analyzing circuits using node voltages as the circuit
variables
Steps to Determine Node Voltages:
1. Select a node as the reference node. Assign voltages v1,
v2, . . . , vn1 to the remaining n 1 nodes. The voltages are
referenced with respect to the reference node.
2. Apply KCL to each of the n 1 nonreference nodes. Use
Ohms law to express the branch currents in terms of node
voltages.
3. Solve the resulting simultaneous equations to obtain the
unknown node voltages.
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NODAL ANALYSIS
Current flows from a higher potential to a lower
potential in a resistor.
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NODAL ANALYSIS
@ Node 1
@ Node 2
Then;
In Terms of Conductance:
So;
In Matrix Form:
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MESH ANALYSIS
Mesh analysis provides another general procedure for
analyzing circuits, using mesh currents as the circuit
variables
A mesh is a loop that does not contain any other loop
within it
Nodal analysis applies KCL to find unknown voltages in a
given circuit, while mesh analysis applies KVL to find
unknown currents
only applicable to a circuit that is planar
Planar circuit is one that can be drawn in a plane with no
branches crossing one another; otherwise it is nonplanar.
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MESH ANALYSIS
(c)
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MESH ANALYSIS
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CHAPTER 4
CIRCUIT THEOREMS
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LINEARITY PROPERTY
Linearity is the property of an element describing a
linear relationship between cause and effect
The property is a combination of both the
homogeneity (scaling) property and the additivity
property
Homogeneity property requires that if the input
(also called the excitation) is multiplied by a
constant, then the output (also called the response) is
multiplied by the same constant.
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LINEARITY PROPERTY
For example, Ohms law relates the input i to the output v,
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LINEARITY PROPERTY
In general, a circuit is linear if it is both additive
and homogeneous. A linear circuit consists of only
linear elements, linear dependent sources, and
independent sources
A linear circuit is one whose output is linearly
related (or directly proportional) to its input
Relationship between power and voltage (or
current) is nonlinear linearity theorems are not
applicable to power
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LINEARITY PROPERTY
Consider the linear circuit shown
linear circuit has no independent sources inside it
Excited by a voltage source vs
Terminated by a load R
Current i through R as the output
Suppose vs = 10 V gives i = 2 A. According to the
linearity principle, vs = 1 V will give i = 0.2 A. By
the same token, i = 1 mA must be due to vs =5 mV.
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LINEARITY PROPERTY
1. For the circuit, find io when vs = 12 V and vs = 24
V.
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LINEARITY PROPERTY
3. Assume Io = 1 A and use linearity to find the actual
value of Io in the circuit.
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SUPERPOSITION
The superposition principle states that the voltage across
(or current through) element in a linear circuit is the
algebraic sum of the voltages across (or currents through)
that element due to each independent source acting
alone.
To apply the superposition principle, we must keep two
things in mind:
1. We consider one independent source at a time while all
other independent sources are turned off. This implies that
we replace every voltage source by 0 V (or a short circuit),
and every current source by 0 A (or an open circuit). This
way we obtain a simpler and more manageable circuit.
2. Dependent sources are left intact because they are
controlled by circuit variables.
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SUPERPOSITION
Steps to Apply Superposition Principle :
Turn off all independent sources except one source.
Find the output (voltage or current) due to that active
source using nodal or mesh analysis.
Repeat step 1 for each of the other independent
sources.
Find the total contribution by adding algebraically all
the contributions due to the independent sources.
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SUPERPOSITION
1. Use the superposition theorem to find v in the
circuit
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SUPERPOSITION
3. Find io in the circuit using superposition.
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SUPERPOSITION
5. For the circuit, use the superposition theorem to
find i.
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SOURCE TRANSFORMATION
A source transformation is the process of replacing
a voltage source vs in series with a resistor R by a
current source is in parallel with a resistor R, or vice
versa.
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SOURCE TRANSFORMATION
Points to be mind when dealing with source
transformation:
The arrow of the current source is directed toward the
positive terminal of the voltage source.
Source transformation is not possible when R = 0, which is
the case with an ideal voltage source. However, for a
practical, nonideal voltage source, R = 0. Similarly, an
ideal current source with R =cannot be replaced by a
finite voltage source.
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SOURCE TRANSFORMATION
1. Use source transformation to find vo in the circuit
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SOURCE TRANSFORMATION
3. Find vx using source transformation.
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THEVENINS THEOREM
Developed in 1883 by M. Leon Thevenin (18571926), a
French telegraph engineer
Thevenins theorem states that a linear two-terminal circuit
can be replaced by an equivalent circuit consisting of a
voltage source VTh in series with a resistor RTh, where VTh is
the open-circuit voltage at the terminals and RTh is the input
or equivalent resistance at the terminals when the
independent sources are turned off.
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THEVENINS THEOREM
CASE 1: If the network has no dependent sources,
we turn off all independent sources. RTh is the input
resistance of the network looking between terminals
a and b, as shown
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THEVENINS THEOREM
CASE 2: If the network has dependent sources, we turn off all
independent sources. As with superposition, dependent sources
are not to be turned off because they are controlled by circuit
variables. We apply a voltage source vo at terminals a and b
and determine the resulting current io. Then RTh = vo/io, as shown.
Alternatively, we may insert a current source io at terminals a-b
as shown in and find the terminal voltage vo. Again RTh = vo/io.
Either of the two approaches will give the same result.
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THEVENINS THEOREM
It often occurs that RTh takes a negative value. In this
case, the negative resistance (v = iR) implies that
the circuit is supplying power.
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THEVENINS THEOREM
1. Find the Thevenin equivalent circuit of the circuit
shown, to the left of the terminals a-b. Then find the
current through RL = 6, 16, and 36 .
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THEVENINS THEOREM
3. Find the Thevenin equivalent of the circuit shown.
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THEVENINS THEOREM
5. Determine the Thevenin equivalent of the circuit
shown.
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NORTONS THEOREM
Developed by E. L. Norton, an American engineer at Bell
Telephone Laboratories in 1926, about 43 years after
Thevenin published his theorem.
Nortons theorem states that a linear two-terminal circuit
can be replaced by an equivalent circuit consisting of a
current source IN in parallel with a resistor RN, where IN is
the short-circuit current through the terminals and RN is the
input or equivalent resistance at the terminals when the
independent sources are turned off.
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NORTONS THEOREM
By Source transformation, the Thevenin and Norton
resistances are equal
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NORTONS THEOREM
Since VTh, IN, and RTh are related, to determine the
Thevenin or Norton equivalent circuit requires that
we find:
The open-circuit voltage voc across terminals a and b.
The short-circuit current isc at terminals a and b.
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NORTONS THEOREM
1. Find the Norton equivalent circuit of the circuits
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NORTONS THEOREM
3. Find the Norton equivalent circuit of the circuit.
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Maximum power is
transferred to the load
when the load resistance
equals the Thevenin Maximum power transferred is obtained by:
resistance as seen from
the load (RL = RTh).
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