node&mesh analysis for first year students

1. Node & Mesh AnalysisNode & Mesh Analysis

2. OutlineOutline
 Nodal AnalysisNodal Analysis
• Define a symbol for all unknown node voltages.Define a symbol for all unknown node voltages.
• Write KCL at each node where variables occurWrite KCL at each node where variables occur
• Using Ohm’s Law, solve resulting equations.Using Ohm’s Law, solve resulting equations.
 Mesh CurrentsMesh Currents
• Set up the currentsSet up the currents
• Use KVLUse KVL
 Methods to solve linear equationsMethods to solve linear equations
• SubstitutionSubstitution
• DeterminantsDeterminants
• CalculatorCalculator
• Method from Numerical MethodsMethod from Numerical Methods

3. Node analysis:Node analysis:
 Node analysis is more powerful method thanNode analysis is more powerful method than
mesh analysis.mesh analysis.
 This method is based on the application of KCL onThis method is based on the application of KCL on
different nodes of the circuit.different nodes of the circuit.
 In this metode,instead of assuming the meshIn this metode,instead of assuming the mesh
current,we assume node volteges with respect tocurrent,we assume node volteges with respect to
some reference node and write KCL equations forsome reference node and write KCL equations for
all the nodes.all the nodes.

4. Definition of node:Definition of node:
 The point at which two or more elements are connectedThe point at which two or more elements are connected
together is called node.together is called node.
Two types of nodeTwo types of node
1. Principal node:1. Principal node:
o If three or more elements are common to a node,that nodeIf three or more elements are common to a node,that node
is called principle node.is called principle node.
2. Reference node:2. Reference node:
o The node , we assume to zero potential is called referenceThe node , we assume to zero potential is called reference
node.node.

5. stepssteps
 Step 1 : identify a reference node .Step 1 : identify a reference node .
 Step 2 : “kill” sources and identify independent nodes.Step 2 : “kill” sources and identify independent nodes.
 Step 3 : replace sources and label “ constrained “ voltages .Step 3 : replace sources and label “ constrained “ voltages .
 Step 4 : apply KCL at each independent node .Step 4 : apply KCL at each independent node .
 step 5 : use ohms law to write the KCL equations in tremsstep 5 : use ohms law to write the KCL equations in trems
of node voltages .of node voltages .
 Step 6 : solve the system of equations to determine theStep 6 : solve the system of equations to determine the
node voltages .node voltages .

6. Nodal Analysis Example 1Nodal Analysis Example 1
Find all voltages and currents.

7. Nodal Analysis Example 2Nodal Analysis Example 2
Find Vo
+ Vo -

8. Mesh analysisMesh analysis
Definition of meshDefinition of mesh
““Mesh is defined as a loop which is not contain any otherMesh is defined as a loop which is not contain any other
loops with in it .”loops with in it .”
 Mesh analysis is important techniques which are useful toMesh analysis is important techniques which are useful to
find solution of network.find solution of network.
 If network has large number of voltage sources , it is usefulIf network has large number of voltage sources , it is useful
to use mesh analysis.to use mesh analysis.

9. Sign:Sign:
+ve sign :+ve sign :
 Both current pass through commonBoth current pass through common
resistance in the same direction.resistance in the same direction.
-ve sign:-ve sign:
 Both the current pass through theBoth the current pass through the
common resistance in oppositecommon resistance in opposite
direction.direction.

10. Mesh CurrentsMesh Currents
 Steps:Steps:
• Label each unknown current in each mesh, goingLabel each unknown current in each mesh, going
clockwise.clockwise.
 A mesh is a loop which does not contain any other loopsA mesh is a loop which does not contain any other loops
within it.within it.
 Also, write down the polarities of the currents as they goAlso, write down the polarities of the currents as they go
through each resistor.through each resistor.
• Write KVL equations for each mesh. In this case, useWrite KVL equations for each mesh. In this case, use
V=I*R. When resistors are in both meshes, I=(IV=I*R. When resistors are in both meshes, I=(I11-I-I22).).
• Use Ohm’s Law to express the voltages in terms of theUse Ohm’s Law to express the voltages in terms of the
mesh currents.mesh currents.
• Again, you may need extra equations if there are otherAgain, you may need extra equations if there are other
current/voltage sources.current/voltage sources.
• Solve for the unknown currents.Solve for the unknown currents.

11. Mesh Current Example - 1Mesh Current Example - 1
Calculate the mesh currents.

12. Mesh Current Example - 2Mesh Current Example - 2
Find the current through the 1 ohm R

13. Methods of Solving Sets ofMethods of Solving Sets of
EquationsEquations
 CalculatorCalculator
• rref functionrref function
• solve functionsolve function
 Linear AlgebraLinear Algebra
 SubstitutionSubstitution
 GraphingGraphing
 Euclid’s MethodEuclid’s Method

14. Thank YouThank You
made by :made by :
DHRUV PANCHAL.HDHRUV PANCHAL.H