ene 104 electric circuit theory -...

ENE 104

Electric Circuit Theory

Lecture 03:

Basic Nodal and Mesh Analysis

http://webstaff.kmutt.ac.th/~dejwoot.kha/

Week #3 : Dejwoot KHAWPARISUTH



Objectives :

Week #3

ENE 104

• Implementation of the nodal analysis

• Implementation of the mesh analysis

• Supernodes and Supermeshes

• Basic computer-aided circuit analysis


Example: 4.2

Week #3

ENE 104 Basic Nodal and Mesh Analysis

find the nodes voltages:

Practice: 4.2

Week #3


Practice: 4.2

Week #3

ENE 104

012

3 2131

vvvvNode 1:

Node 2:

Node 3:

0431

32212

vvvvv

0542

7 32313

vvvvv

1v 2v3v


The Supernode:



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The Supernode:



i

Week #3

Practice: 4.3

Week #3


Compute the voltage across each current source

Practice: 4.3

Week #3

ENE 104

042

1

1

31

21

vi

vvNode 1:

Node 2:

Supernode 1-2:

096

1

2

31

12

vi

vv

0946

1

2

31

12

21

1

31

21

vvvvvv

1v 2v


Example: 4.4


Determine the node-to-reference voltages in the circuit below.

Week #3

Example:


Determine the node-to-reference voltages in the circuit below.

Week #3

Practice: 4.4

Week #3


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

Practice:

Week #3


Use nodal analysis to determine the nodal

voltage in the circuit.

Mesh Analysis:


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.

Week #3

Path, Closed path, and Loop:


(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.

Week #3

Example: 4.6


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. )

Week #3

Practice: 4.5

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Determine i1 and i2

Practice: 4.5

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ENE 104

010146 211 iiiMesh 1:

Mesh 2:

051010 212 iii


Example: 4.7


determine the three mesh currents

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Example:


determine the three mesh currents

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Practice: 4.6

Week #3


Determine i1 and i2

Practice: 4.6

Week #3

ENE 104

03410 21 iiMesh 1:

Mesh 2:

Mesh 3:

010954 322212 iiiiii

08103 323 iii


The Supermesh:


Find the three mesh currents in the circuit below.

Week #3

The Supermesh:

ENE 104 Basic Nodal and Mesh Analysis Week #3

The Supermesh:


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]

Rearranging,

i1 - 4 i2 + 4 i3 = 7 [1]

-i1 + 6 i2 - 3 i3 = 0 [2]

i1 - i3 = 7 [3]

Solving,

i1 = 9 A, i2 = 2.5 A, and i3 = 2 A.

Finally, we relate the currents in meshes 1 and 3:

i1 - i3 = 7 [3]

Week #3

Practice: 4.8


Find the voltage v3 in the circuit below.

Week #3

Practice: 4.8


Find the voltage v3 in the circuit below.

Week #3

Ai

Bi

A comparison:


Ex:

ENE 104 Week #3

Ch4-26 p.94 Determine each mesh current in the circuit


Computer-Aided:


Example:


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

Homework:

ENE 104 Circuit Analysis and Electrical Engineering Week #3

ene 104 electric circuit theory -...

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