GROUP NO.07
HAJRA AHMED (CS-107)
HAFIZA RIDA RAO (CS-110)
ALISHBA ALI (CS-073)
TOPIC:
KVL, KCL, MESH AND NODAL ANALYSIS
INTRODUCTION OF SCIENTIST:
GUSTAV ROBERT KIRCHHOFF (1824-1887) , A German physicist, stated
two basic laws in 1847 concerning the relationship between the current
and voltage in an electrical network . Kirchhoff's laws along with Ohm's
law form the basis of circuit theory.
He put forward two important laws that make circuit analysis easy.
1) Kirchhoff’s current law. 2) Kirchhoff’s voltage law
KCL
"The algebraic sum of all the currents entering or leaving the node is
equal to zero”
"The sum of currents entering or leaving the node must be equal"
EXPLANATIONS:
-i1 + i2 + i3 = 0
i1 = i2 + i3
Current entering = current leaving
KVL
"The algebraic sum of all the voltages around a close path is equal to
zero” OR
"Sum of voltage drop is equal to the sum of voltage rise in each circuit
element"
EXPLANATIONS:
-V1 + V2 +V3-V4 +V5=0
V2+V3+V5=V1+V4
Sum of voltage drop = sum of voltage
rise
MESH ANALYSIS:
The application of KVL is mesh analysis. By applying mesh analysis the
circuit becomes more easy and convenient to solve.
MESH
A mesh is a loop which does not contain any other loop within formed
it.
LOOP
A loop is closed path formed by starting at a node and then passing
through different nodes without passing through any node more than
once.
INDEPENDENT LOOP
A loop is said to be independent f it contains at least one branch which
not part of any other branch.
PLANER AND NON PLANER CIRCUITS
It is a circuit which can be drawn in plane (two-dimension) which will
not pass or cross each other’s branches and otherwise it is non planer.
PLANER CIRCUIT DIAGRAM
NON PLANER CIRCUIT DIAGRAM
MESH WITH CURRENT SOURCE(SUPER MESH)
A super mesh results when two meshes have ( dependent or
independent) current sources in common.
Numerical of super mesh.
NODAL ANALYSIS:
The example of KCL is nodal analysis. By applying nodal analysis the
circuit becomes more easy and convenient.
NODES:
Node is the point that interconnects two or more elements in a circuit.
TYPES OF NODES:
There are mainly two types of nodes
1) Reference node
2) Non reference node
REFERENCE NODE:
Ground node is known as reference node. It has a potential of 0 volts.
NON REFERNCE NODES:
They are placed between circuit elements they have assigned voltages
that have to be found.
FORMULA FOR FINDING NO. OF NODES:
The formula for finding the nodes is;
b=l+n-1
Where;
n= no. of nodes
l= no. of loop
b= no. of branches
SUPERNODE:
If a voltage source is placed between two nodes having an element
connected in parallel with it then it is called as super node.
Some of the properties of super nodes are:
1) A super node has no voltage of its own.
2) It requires the application of both KVL & KCL.
Numerical of super node.
Reference : Charles K.Alexander