methods of analysis of resistive circutis

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EE101 EE CIRCUITS 1 1T SY 2014-2015 MCBLOYOLA

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  • EE101 EE CIRCUITS 1

    1T SY 2014-2015

    MCBLOYOLA

  • Methods of Analysis of Resistive

    Networks

    Week 3

    MCBLOYOLA

  • LEARNING OUTCOME

    Solve for resistance, current, voltage, and

    power in a dc resistive network using

    mesh (loop) analysis and nodal analysis.

    MCBLOYOLA

  • 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

    MCBLOYOLA

  • 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

    MCBLOYOLA

  • MESH ANALYSIS

    Is this a planar circuit?

    There is no way to redraw it and avoid the branches crossing

    (Alexander, et. al, 2011).

    MCBLOYOLA

  • MESH ANALYSIS

    Mesh is a loop which does not contain any other loops

    within it.

    How many meshes? What are those?

    MCBLOYOLA

  • 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

  • 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.

    MCBLOYOLA

  • 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

  • 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

    MCBLOYOLA

  • ILLUSTRATIVE PROBLEM 1

    Using mesh analysis, find 1, 2, and 3 in the circuit below.

    = . , = . , = . MCBLOYOLA

  • ILLUSTRATIVE PROBLEM 2

    Apply mesh analysis to find i.

    = . MCBLOYOLA

  • ILLUSTRATIVE PROBLEM 3

    Using mesh analysis, find in the circuit below.

    = MCBLOYOLA

  • ILLUSTRATIVE PROBLEM 4

    Using mesh analysis, find in the circuit below.

    = MCBLOYOLA

  • How should we apply KVL to mesh 2?

    MCBLOYOLA

  • 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

    MCBLOYOLA

  • How should we apply KVL to these meshes?

    MCBLOYOLA

  • 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.

    MCBLOYOLA

  • 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.

    = +

    MCBLOYOLA

  • ILLUSTRATIVE PROBLEM 5

    Apply mesh analysis to the circuit below to obtain .

    MCBLOYOLA = .

  • ILLUSTRATIVE PROBLEM 6

    Apply mesh analysis to find 1, 2, and 3.

    MCBLOYOLA = , = , =

  • 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

  • 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

  • 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

  • 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 =

  • 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

  • ILLUSTRATIVE PROBLEM 7

    Find the node voltages in the circuit shown below.

    V1 = 80 V V2 = -64 V V3 = 156 V

  • ILLUSTRATIVE PROBLEM 8

    Determine the power supplied by the dependent source

    of the figure below using nodal analysis.

    4.5 kW

  • 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

  • How should we handle the 2-V voltage source?

  • 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

  • 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.

  • 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.

    + + =

  • ILLUSTRATIVE PROBLEM 10

    Find and in the circuit below.

    0.6 4.2

  • 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

  • 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.

  • REFERENCES

    Please refer to course syllabus.

    MCBLOYOLA