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Electric Circuit Theory
Lecture 03:
Basic Nodal and Mesh Analysis
Week #3 : Dejwoot KHAWPARISUTH
http://webstaff.kmutt.ac.th/~dejwoot.kha/
Objectives :
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• Implementation of the nodal analysis
• Implementation of the mesh analysis
• Supernodes and Supermeshes
• Basic computer-aided circuit analysis
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Basic Nodal and Mesh Analysis
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Example: 4.2
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find the nodes voltages:
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Basic Nodal and Mesh Analysis
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Practice: 4.2
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Basic Nodal and Mesh Analysis
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Week #3
Practice: 4.2
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v1
Node 1:
Node 2:
Node 3:
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v2
v3
v1  v3 v1  v2
3

0
2
1
v2  v1 v2 v2  v3


0
1
3
4
v3  v1 v3  v2 v3
7


0
2
4
5
Basic Nodal and Mesh Analysis
Week #3
The Supernode:
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find the nodes voltages:
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Basic Nodal and Mesh Analysis
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The Supernode:
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find the nodes voltages:
i
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Basic Nodal and Mesh Analysis
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The Supernode:
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find the nodes voltages:
i
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Basic Nodal and Mesh Analysis
Week #3
Practice: 4.3
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Compute the voltage across each current source
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Basic Nodal and Mesh Analysis
Week #3
Practice: 4.3
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v1
v2
Node 1:
v1  v2
v1
4
i 
0
1 
1 
3
2
Node 2:
v2  v1
v2
i 
9  0
1 
1 
3
6
Supernode 1-2:  4 
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v1  v2
v1
v2  v1 v2



9  0
1 
1 
1 
1 
3
2
3
6
Basic Nodal and Mesh Analysis
Week #3
Example: 4.4
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Determine the node-to-reference voltages in the circuit below.
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Basic Nodal and Mesh Analysis
Week #3
Example:
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Determine the node-to-reference voltages in the circuit below.
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Basic Nodal and Mesh Analysis
Week #3
Practice: 4.4
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Use nodal analysis to find vx, if element A is (a)
a 25 Ω; (b) a 5-A current source, arrow pointing
right; (c) a 10-V voltage source, positive
terminal on the right; (d) a short circuit
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Basic Nodal and Mesh Analysis
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Practice:
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Use nodal analysis to determine the nodal
voltage in the circuit.
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Basic Nodal and Mesh Analysis
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Mesh Analysis:
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Mesh analysis is applicable only to those
networks which are planar.
Examples of planar and nonplanar networks
Mesh is a loop that doesn’t contain any other loops.
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Basic Nodal and Mesh Analysis
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Path, Closed path, and Loop:
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(a) The set of branches identified by the heavy lines is neither a path nor a
loop. (b) The set of branches here is not a path, since it can be traversed
only by passing through the central node twice. (c) This path is a loop but
not a mesh, since it encloses other loops. (d) This path is also a loop but
not a mesh. (e, f) Each of these paths is both a loop and a mesh.
Basic Nodal and Mesh Analysis
Week #3
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Example: 4.6
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Determine the two mesh currents, i1 and i2, in the circuit below.
For the left-hand mesh,
-42 + 6 i1 + 3 ( i1 - i2 ) = 0
For the right-hand mesh,
3 ( i2 - i1 ) + 4 i2 - 10 = 0
Solving, we find that i1 = 6 A and i2 = 4 A.
(The current flowing downward through
the 3- resistor is therefore i1 - i2 = 2 A. )
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Basic Nodal and Mesh Analysis
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Practice: 4.5
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Determine i1 and i2
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Basic Nodal and Mesh Analysis
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Practice: 4.5
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Mesh 1:
 6  14i1  10i1  i2   0
Mesh 2:
10i2  i1   10i2  5  0
Basic Nodal and Mesh Analysis
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Example: 4.7
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determine the three mesh currents
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Basic Nodal and Mesh Analysis
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Example:
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determine the three mesh currents
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Basic Nodal and Mesh Analysis
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Practice: 4.6
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Determine i1 and i2
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Basic Nodal and Mesh Analysis
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Practice: 4.6
Mesh 1:
 10  4i1  i2   3  0
Mesh 2:
4i2  i1   5i2  9i2  10i2  i3   0
Mesh 3:
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 3  10i3  i2   8i3  0
Basic Nodal and Mesh Analysis
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The Supermesh:
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Find the three mesh currents in the circuit below.
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Basic Nodal and Mesh Analysis
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The Supermesh:
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Find the three mesh currents in the circuit below.
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Basic Nodal and Mesh Analysis
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The Supermesh:
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Basic Nodal and Mesh Analysis
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The Supermesh:
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Find the three mesh currents in the circuit below.
Creating a “supermesh” from meshes 1 and 3:
-7 + 1 ( i1 - i2 ) + 3 ( i3 - i2 ) + 1 i3 = 0
[1]
Around mesh 2:
1 ( i2 - i1 ) + 2 i2 + 3 ( i2 - i3 ) = 0
[2]
Finally, we relate the currents in meshes 1 and 3:
i1 - i3 = 7
[3]
Rearranging,
i1 - 4 i 2 + 4 i3 = 7
[1]
-i1 + 6 i2 - 3 i3 = 0
[2]
i1
[3]
- i3 = 7
Solving,
i1 = 9 A, i2 = 2.5 A, and i3 = 2 A.
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Basic Nodal and Mesh Analysis
Week #3
Practice: 4.8
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Find the voltage v3 in the circuit below.
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Basic Nodal and Mesh Analysis
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Practice: 4.8
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Find the voltage v3 in the circuit below.
iB
iA
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Basic Nodal and Mesh Analysis
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Practice: 4.8
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Find the voltage v3 in the circuit below.
iB
iA
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Basic Nodal and Mesh Analysis
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A comparison:
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Basic Nodal and Mesh Analysis
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Week #3
A comparison:
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Basic Nodal and Mesh Analysis
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Week #3
A comparison:
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Basic Nodal and Mesh Analysis
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Week #3
A comparison:
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Basic Nodal and Mesh Analysis
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Week #3
Ex:
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Ch4-26 p.94 Determine each mesh current in the circuit
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Basic Nodal and Mesh Analysis
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Computer-Aided:
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Basic Nodal and Mesh Analysis
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Computer-Aided:
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Basic Nodal and Mesh Analysis
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Example:
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Ch4.58 p.100 Write an appropriate input deck
for SPICE to find v5 in the circuit. Submit a
printout of the output file, with the solution
highlight
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Basic Nodal and Mesh Analysis
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Homework:
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Circuit Analysis and Electrical Engineering
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Week #3
Reference:
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W.H. Hayt, Jr., J.E. Kemmerly, S.M. Durbin, Engineering Circuit Analysis, Sixth Edition.
Copyright ©2002 McGraw-Hill. All rights reserved.
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Basic Nodal and Mesh Analysis
Week #3