This document discusses Ohm's law, Kirchhoff's laws, and nodal and mesh analysis techniques for solving circuits. It provides background on Georg Ohm and Gustav Kirchhoff, defines Ohm's law, Kirchhoff's current law, and Kirchhoff's voltage law. It then describes the steps and process for using nodal analysis and mesh analysis to solve circuits, including writing the nodal equations and mesh equations. Examples are provided for applying both techniques.

1. Sub:- Elements of Electrical Engineering (2110005)
Topic:- Ohm’s law, Kirchhoff's law, nodal & mesh analysis
Prepared by :- Kathan Patel (150120119064)
Kundariya Ankit (150120119073)
Makwana Mitesh (150120119075)
Guided by :- Prof. Abhishek Harit

2. Georg Simon Ohm
• “At Constant temperature and pressure, current
flowing through the conductor is directly
proportional to the potential difference across the
conductor and inversely proportional to the
resistance experienced by the conductor”.
• German physicist who experimentally determined
that the if the voltage across a resistor is increased,
the current through the resistor will increase.
• Ohm's work long preceded Maxwell's
equations and any understanding of frequency-
dependent effects in AC circuits.
• Modern developments in electromagnetic theory
and circuit theory do not contradict Ohm's law
when they are evaluated within the appropriate
limits.

3.  Ohm's law states that the current through
a conductor between two points is
directly proportional to the voltage across the two
points.
 Introducing the constant of proportionality,
the resistance, one arrives at the usual mathematical
equation that describes this relationship
 where I is the current through the conductor in units
of amperes, V is the voltage measured across the
conductor in units of volts, and R is the resistance of
the conductor in units of ohms.
 More specifically, Ohm's law states that the R in this
relation is constant, independent of the current.

4. • V = I * R
– For a constant resistance, if the current increases, the voltage
increases at the same rate
• I = V / R
– For a constant resistance, if the voltage increases, the current
will increase at the exact same rate
• R = V / I
– For a constant resistance, if the voltage increases, the current
must increase at the exact same rate.

5. Is ohm’s law applicable to only individual
components?
 A question arise in our mind that is this law is applicable to only
individual components or we can apply it to a complete circuit?
Ans:- ohm’s law is applicable to individual components as well as the
complete circuit.
 If it is to be applied to the complete circuit, then voltage across the
complete circuit and effective resistance of the complete circuit
should be used.
 If the law is to be applied to only a part of the circuit, then the
voltage and resistance corresponding to that part should be taken
into consideration.

6. Is ohm’s law applicable to nonlinear devices?
 The answer is No. The ohm’s law is not applicable to
any nonlinear device such as diode, transistor, zener
diodes etc. it is applicable only to the linear devices.
 A linear device exhibits a linear relation between
voltage across it and the current flowing through it
(e.g. resistor). This is the biggest limitation of ohm’s
law.

7. Examples:-
A Resistance of 15Ω carries a current of 5Amp.
Calculate the voltage developed across the
resistor.
Soln:- According to ohm’s law :
I=V/R = 50/5 = 10Amp
Calculate the resistance of an iron filament if
it operates on 230V supply and draws a
current equal to 2Amp.
Soln:- Note that the iron filament is a linear
device. Hence the ohm’s law is applicable
here even though it is an AC circuit.
Resistance of the iron filament =
R = 230/2 = 115 Ω

8. The total resistance of a circuit is dependant on the
number of resistors in the circuit and their
configuration
1 2
1 2
...
1 1 1 1
...
   
   
total
total
R R R R
R R R R
Series Circuit
Parallel Circuit

9.  Kirchhoff's circuit laws are two equalities that deal with
the current and potential difference (commonly known as
voltage) in the lumped element model of electrical
circuits.
 They were first described in 1845 by German physicist
Gustav Kirchhoff.
 This generalized the work of Georg Ohm and preceded
the work of Maxwell. Widely used in electrical
engineering, they are also called Kirchhoff's rules or
simply Kirchhoff's laws.
Kirchhoff's circuit laws

10. Gustav Kirchhoff
 Both of Kirchhoff's laws can
be understood as
corollaries of the Maxwell
equations in the low-
frequency limit.
 They are accurate for DC
circuits, and for AC circuits
at frequencies where the
wavelengths of
electromagnetic radiation
are very large compared to
the circuits.

11. Kirchhoff's current law (KCL)
This law is also called Kirchhoff's first law, Kirchhoff's point rule,
or Kirchhoff's junction rule (or nodal rule).
The principle of conservation of electric charge implies that:
At any node (junction) in an electrical circuit, the sum
of currents flowing into that node is equal to the sum of currents
flowing out of that node or equivalently
The algebraic sum of currents in a network
of conductors meeting at a point is zero.
The current entering any junction is equal to
the current leaving that
junction. i2 + i3 = i1 + i4

12. Recalling that current is a signed (positive or negative) quantity
reflecting direction towards or away from a node, this principle can be
stated as:
n is the total number of branches with currents flowing towards or
away from the node.
This formula is valid for complex currents:
The law is based on the conservation of charge whereby the charge
(measured in coulombs) is the product of the current (in amperes) and
the time (in seconds).

13. Kirchhoff's voltage law (KVL)
 This law is also called Kirchhoff's second law, Kirchhoff's loop (or
mesh) rule, and Kirchhoff's second rule.
 The directed sum of the electrical potential differences (voltage)
around any closed network is zero, or:
 The algebraic sum of the products of the resistances of the
conductors and the currents in them in a
closed loop is equal to the total emf
available in that loop.
The sum of all the voltages around a loop is
equal to zero.
v1 + v2 + v3 - v4 = 0

14. Similarly to KCL, it can be stated as:
Here, n is the total number of voltages measured. The
voltages may also be complex:
This law is based on the conservation of energy whereby voltage is
defined as the energy per unit charge. The total amount of energy
gained per unit charge must be equal to the amount of energy lost per
unit charge, as energy and charge are both conserved.
Kirchhoff’s Current Law
KCL
Conservation of charge
The algebraic sum of all the currents at
any node in a circuit equals zero.
Kirchhoff’s Voltage Law
KVL
Conservation of energy
The algebraic sum of all the voltages
around any closed path in a circuit equals
zero.

15. Definition of Nodal Analysis
Nodal analysis is a method that provides a general procedure for
analysing circuits using node voltages as the circuit variables. Nodal
Analysis is also called the Node –Voltage Method.
In analysing a circuit using Kirchhoff's circuit laws, one can either do
nodal analysis using Kirchhoff's current law (KCL) or mesh analysis
using Kirchhoff's voltage law (KVL)
Nodal analysis writes an equation at each
Electrical node, requiring that the branch
currents incident at a node must sum
to zero.
NODAL ANALYSIS

16. Types of Nodes in Nodal Analysis
• Non Reference Node - It is a node which has a
definite Node Voltage. e.g. Here Node 1 and Node 2 are
the Non Reference nodes
• Reference Node - It is a node which acts a
reference point to all the other node. It is also called the
Datum Node.

17. Steps Taken While Solving Problem By Nodal Analysis:
1) Mark all nodes. Normally there is a return path which is datum node D. All voltages
are to be determined w.r.t . node D.
2) Certain nodes are super nodes whose potential are already known.
3) At each node, find the currents through various branches and equate the algebraic
sum to 0
4) If a branch consists only one resistance, then normally current is assumed to flow
away from node, such as VA/R4 or VB/R5.
5) For a common branch between two nodes, one of the node voltage is assumed to
be of higher value and other of lower value. then difference of voltages will make
the current to flow from higher node voltage to lower node voltage.
For example
current through branch AB is (VA - VB)/R2.
But the same current can be written as (VB - VA)/R1. Flowing from B to A.
6) Write down all such equation on node basis.
For node A it is , (VA – E1)/R1 + (VA/R4) + (VA –VB)/R2 = 0
For node B it is , (VB –VA )/R2 + (VB/R5) + (VB + E2 )/R3 = 0
7) Solve these equations & also current in different branches can also calculated.

18. Examples of nodal analysis
1) Calculate the value of branch for network
shown in fig.

19. 2) Calculate the node voltage VB using the
nodal analysis

20. 3)Using nodal voltage method find current
in the 3 resistance

21. Mesh analysis (or the mesh current method) is a method that is used
to solve planar circuits for the currents (and indirectly the voltages) at
any place in the circuit.
Planar circuits are circuits that can be drawn on a plane surface with
no wires crossing each other.
A more general technique, called loop analysis (with the
corresponding network variables called loop currents) can be applied
to any circuit, planar or not.
Mesh analysis and loop analysis both make use of Kirchhoff’s voltage
law to arrive at a set of equations guaranteed to be solvable if the
circuit has a solution.
Mesh Analysis

22. The following is the same circuit from above with the equations
needed to solve for all the currents in the circuit.

23. Potential rise and potential drop for a Resistor:
Potential rise : If we trace the path along a closed loop from negatively
marked terminal of a resistor, then the associated potential change is
called as the potential rise.
Potential drop : If we trace the path along the closed loop from the
positive marked terminal to negative marked terminal, then the
associated potential change is called as the potential drop.

25. 1) Determine the current and power
consumed in the 3 resistance of the circuit
shown in fig

26. 2) Using Kirchhoff's law calculate
the current delivered by the
battery

27. 3) In fig (a) determine V2 which results
in zero current in the branch containing
v1 , using mesh analysis.