methods of analysis of resistive circutis
DESCRIPTION
Methods of Analysis of Resistive Circuits(c) credits to the ownerTRANSCRIPT
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EE101 EE CIRCUITS 1
1T SY 2014-2015
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Methods of Analysis of Resistive
Networks
Week 3
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LEARNING OUTCOME
Solve for resistance, current, voltage, and
power in a dc resistive network using
mesh (loop) analysis and nodal analysis.
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Two (2) Powerful Techniques for Circuit
Analysis
NODAL ANALYSIS MESH ANALYSIS
Based on a systematic
application of Kirchhoffs
current law
Finding the node voltages
Based on a systematic
application of Kirchhoffs
voltage law
Finding the mesh currents
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MESH ANALYSIS
Applicable only to planar circuits
Planar circuit: one that can be drawn in a plane with no
branches crossing one another
When
redrawn
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MESH ANALYSIS
Is this a planar circuit?
There is no way to redraw it and avoid the branches crossing
(Alexander, et. al, 2011).
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MESH ANALYSIS
Mesh is a loop which does not contain any other loops
within it.
How many meshes? What are those?
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MESH ANALYSIS
Steps to determine the mesh currents:
1. Assign mesh currents , , , to the n meshes.
Note:
i1 and i2 are mesh currents
(imaginative, not
measurable directly)
I1, I2 and I3 are branch
currents (real, measurable
directly)
Direction of mesh current is arbitrary, but it is conventional to
assume that mesh current flows clockwise MCBLOYOLA
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MESH ANALYSIS
Steps to determine the mesh currents:
2. Apply KVL to each of the n meshes. Use Ohms law to
express the voltages in terms of the mesh currents.
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MESH ANALYSIS
KVL at mesh 1: 1 + 11 + 3 1 2 = 0
1 + 3 1 32 = 1 ---Eqn. 1
KVL at mesh 2: 22 + 2 + 3 2 1 = 0
-31 + 2 + 3 2 = 2 ---Eqn. 2
Notice the coefficients of 1 and 2.
Coefficient of 1 : sum of the resistances in the first mesh
Coefficient of 2 : negative of the resistance common to meshes 1 and
2
The same is true in Eqn. 2. Thus, this is a shortcut! MCBLOYOLA
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MESH ANALYSIS
Steps to determine the mesh currents:
3. Solve the resulting n simultaneous equations to get the mesh
currents.
I1 = i1; I2 = i2; I3 = i1 - i2
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ILLUSTRATIVE PROBLEM 1
Using mesh analysis, find 1, 2, and 3 in the circuit below.
= . , = . , = . MCBLOYOLA
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ILLUSTRATIVE PROBLEM 2
Apply mesh analysis to find i.
= . MCBLOYOLA
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ILLUSTRATIVE PROBLEM 3
Using mesh analysis, find in the circuit below.
= MCBLOYOLA
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ILLUSTRATIVE PROBLEM 4
Using mesh analysis, find in the circuit below.
= MCBLOYOLA
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How should we apply KVL to mesh 2?
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MESH ANALYSIS WITH CURRENT
SOURCES
Case 1: When a current source exists only in one mesh, set
mesh current equal to the current source.
2 = 5 A
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How should we apply KVL to these meshes?
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MESH ANALYSIS WITH CURRENT
SOURCES
Case 2: When a current source exists between two meshes,
create a supermesh by excluding the current source and any
element connected in series with it.
A supermesh results
when two meshes have
a (dependent or
independent) current
source in common.
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MESH ANALYSIS WITH CURRENT
SOURCES
Exclude current source and
elements in series, and apply KVL to
the supermesh.
+ + + =
Apply KCL to a node in the branch
where the two meshes intersect.
= +
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ILLUSTRATIVE PROBLEM 5
Apply mesh analysis to the circuit below to obtain .
MCBLOYOLA = .
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ILLUSTRATIVE PROBLEM 6
Apply mesh analysis to find 1, 2, and 3.
MCBLOYOLA = , = , =
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NODAL ANALYSIS
Steps to determine the node voltages: 1. Select a node as the reference node.
Commonly called the ground since it is
assumed to have zero potential
Reference node
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NODAL ANALYSIS
Steps to determine the node voltages:
2. Assign voltages , , , to the remaining n-1 nodes. The voltages are referenced with respect to the reference node.
Each node is the voltage rise from the reference node
to the corresponding non-reference node.
V1 V2
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NODAL ANALYSIS Steps to determine the node voltages:
3. Apply KCL to each of the n-1 non-reference nodes. Use Ohms law to express the branch currents in terms of node voltages.
KCL at node 1:
KCL at node 2:
V1 V2
I1 I3
I2
1 = 1 + 2
2 = 3 + 4
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NODAL ANALYSIS
Steps to determine the node voltages:
3. Apply KCL to each of the n-1 non-reference nodes. Use Ohms law to
express the branch currents in terms of node voltages.
KCL at node 1: KCL at node 2:
By Ohms law: By Ohms law:
1 = 1 + 2 2 = 3 + 4
1 = 1 0
2+
1 26
1 2
6=
2 0
7+ 4
Key idea: current flows from a higher potential to a
lower potential in a resistor =
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NODAL ANALYSIS
Steps to determine the node voltages:
4. Solve the resulting simultaneous equations to obtain the unknown
node voltages.
1 = 1 0
2+
1 26
1 26
= 2 0
7+ 4
V1 = -2 V, V2 = -14 V, I1 = -1 A, I2 = 2 A, I3 = -2 A
--- Eqn. 1
--- Eqn. 2
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ILLUSTRATIVE PROBLEM 7
Find the node voltages in the circuit shown below.
V1 = 80 V V2 = -64 V V3 = 156 V
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ILLUSTRATIVE PROBLEM 8
Determine the power supplied by the dependent source
of the figure below using nodal analysis.
4.5 kW
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ILLUSTRATIVE PROBLEM 9
For the circuit below, use nodal analysis to determine 1 and 2. Likewise, compute the power absorbed by the 6- resistor.
1 = 58.54 2 = 64.39 6 = 542.83
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How should we handle the 2-V voltage source?
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NODAL ANALYSIS WITH VOLTAGE
SOURCES
Case 1: If the voltage source is connected between the reference node
and a non-reference node, set the voltage at the non-reference node equal
to the voltage source.
1 = 10
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NODAL ANALYSIS WITH VOLTAGE
SOURCES
Case 2: If the voltage source (dependent or independent) is connected
between two non-reference nodes, the two non-reference nodes form a
generalized node, or supernode; apply both KCL and KVL to determine the
node voltages.
A supernode is formed by
enclosing a (dependent or
independent) voltage source
connected between two non-
reference nodes and any elements
connected in parallel with it.
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NODAL ANALYSIS WITH VOLTAGE
SOURCES
Take off all voltage sources in
supernodes and apply KCL to
supernodes.
+ = +
Put voltage sources back to the
nodes and apply KVL to relative
loops.
+ + =
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ILLUSTRATIVE PROBLEM 10
Find and in the circuit below.
0.6 4.2
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ILLUSTRATIVE PROBLEM 11
With the help of nodal analysis, find and the power dissipated in the 2.5- resistor.
= 25.91 2.5 = 82.66
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To select the method that results in the smaller number of equations:
1. Choose nodal analysis for circuit with fewer nodes than meshes.
2. Choose mesh analysis for circuit with fewer meshes than nodes.
3. Networks that contain many series connected elements, voltage sources, or supermeshes are more suitable for mesh analysis.
4. Networks with parallel-connected elements, current sources, or supernodes are more suitable for nodal analysis.
5. If node voltages are required, it may be expedient to apply nodal analysis. If branch or mesh currents are required, it may be better to use mesh analysis.
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REFERENCES
Please refer to course syllabus.
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