PHYSICS PROJECT

TOPIC: KIRCHOFF’S LAW

BY
M. ABARNA
M.MUMTHA SHARMI
 ACKNOWLEDGEMENT
We extend our sincere gratitude to all those who contributed
to the successful completion of our group’s physics project
on KIRCHOFF’S LAW. Our heartfelt thanks go to our Physics
Teacher, Mrs.KRITHIKA, for their guidance, support, and
invaluable insights that were crucial in steering our project in
the right direction.

We would also like to express our appreciation to our group

members for their dedication and collaborative efforts. We
thank our principal Mrs. USHA RAGHAVAN for supporting us.

Furthermore, we are grateful to our parents for their

unwavering support and encouragement throughout this
endeavour. Their belief in our capabilities has been a
constant motivation.
Lastly, we acknowledge the support and resources provided
by the school administration and the Physics Department,
which significantly contributed to the success of our project.
The combined efforts of our teacher, group members,
parents, and the school community were instrumental in
achieving the goals of this project. We are genuinely thankful
for their support and involvement
 INDEX
➢INTODUCTION
➢KIRCHHOFF’S LAW
➢EXPERIMENT ON KIRCHHOFF’S
LAW
➢APPLICATION
➢WHEATSTONE BRIDGE
➢METER BRIDGE
➢POTENTIOMETER
➢BIBLIOGRAPHY
➢CONCLUSION
 INTODUCTION
In physics, it is mandatory to learn about laws of electricity
such as Kirchhoff’s laws. Using these laws, we can calculate
the amount of total current or the value of current that flows
in or out. Also, we can find the values of electronic
components such as resistor, inductor, capacitor, etc.
Kirchhoff has formulated two laws. First law is of current and
the second one is of voltage. These laws are named
as Kirchhoff’s current law and Kirchhoff’s voltage law. At
any junction, in a circuit, the sum of the currents flowing into
the circuit is equal to the sum of the currents flowing out of
the circuit. This is the same as ‘charges can neither be
created nor destroyed’. These two laws have been
formulated by Gustav Kirchhoff. It governs the conservation
of charge and energy in electric circuits. An electric circuit, as
we all know, is made up of a series of resistors and cells that
are occasionally connected in a highly intricate way. But
Kirchhoff’s law makes this problem very easy. Let’s
understand this by considering a circuit apparatus. In any
circuit the current I flows in a particular direction. If the
current is negative then the current flows in the opposite
direction. The potential difference between the positive
terminal P and the negative terminal N is determined by V =
V(P) – V(N) = e – Ir Where e is emf of battery, I is the current
passing through the circuit and r is resistance. If the current
flows in the opposite direction, from P to N, then, V = e + Ir
KIRCHHOFF’S CURRENT LAW

This rule implies that the sum of current entering the

junction is equal to the sum of current leaving the junction. In
simple words, the amount of total current entering any
junction is the same as the amount of total current leaving
the junction. This is also named as junction rule . Kirchhoff
first law. The proof of this rule is when current is steady,
there is no accumulation of charge at any point. Thus, the
total current flowing in is equal to the total current flowing
out.

Iin =Iout
For the n number of wires, the expression is, n =1kIn= 0 Now
consider an example, three wires are connected at a
common point. In two wires current I1 and I2 is coming and
from third wire, current I3 is going out so from the Kirchhoff’s
law: I1 + I2 = I3 The component of the electric circuit either
gains the electrical energy or losses.
KIRCHHOFF’S VOLTAGE LAW

The algebraic sum of voltage difference around the loop is

equal to zero. The formula for voltage rule is, V = IR Where, V
is the voltage difference I is current in the loop R is the
resistance of the circuit element in ohms.
How to apply Kirchhoff’s rule?

The direction of current must be in a circular loop. And the

sum of the loop of voltage difference must be zero. Assume
all the voltage source and resistance. Label each branch with
the branch current. Apply junction rule at each node. Apply
loop rule for each loop. This rule implies the second rule and
is termed as Kirchhoff’s voltage rule. This is also termed as
loop rule. Potential difference in a close loop = 0 .
NOTE: In general, there will be no such simplification due to
symmetry and only by the application of Kirchhoff’s law can
we solve the problem.
 EXPERIMENT ON KIRCHHOFF’S LAW

AIM:
To verify Kirchhoff’s law by comparing resistance obtained
from a circuit to those predicted by Kirchhoff’s Law
APPARATUS REQUIRED:

• Digital multimeter
• 1 Ω resistors
• Soldering iron
• Wax
• Soldering wire
• Stand for soldering iron
• Key
• Battery
THEORY:
JUNCTION RULE:
The algebraic sum of all the current meeting at a point is
zero. It obeys law of conservation of charge
VOLTAGE LAW:
It states that the sum of changes in potential around any
closed path of electric circuit (or closed loop) involving
resistors and cells in the loop is zero.
COLOUR CODE RESISTANCE
FIGURE 1
A 10V Battery connected in a cubical consist of 1 Ω resistance

FIGURE 2:
Find the currents I1, I2 and I3 from the electrical network given below
PROCEDURE
1. First we have to connect the same resistors in series and
parallel to get the desired shape of circuit.

2. We can connect the resistors by the use of soldering iron,

resistors can be connected by putting the melted wire pieces
over the connections with the help of soldering iron.

3. Once all the resistors are connected, leave .The circuit as it

takes a few seconds for it to become solid at all its ends.

4. Take a digital multimeter and connect it across the

terminals of the prepared circuit.

5. Set the multimeter over the resistance option so as to

obtain the value of the associated resistance of the circuit.

6.Keep the multimeter at same terminals for a while so the

précised value is observed
7.Once value of resistance obtained on multimeter, compare
it with the theoretically calculated value.
CALCULATION
For Figure 1 :
The network is not reducible to a simple series and parallel
combinations of resistors. There is however , a clear
symmetry in the problem which we can exploit to obtain the
equivalent resistance of the network.
AA', AD and AB are symmetric hence the current in each is
equal. Taking a closed-loop ABCC'EA, we apply the loop rule:

-IR-(1/2)IR -IR+ε=0
ε = (5/2)IR
Req=ε/3I=(5/6)R
R=1Ω, therefore Req=(5/6)Ω
For ε=10V, 3I=10/(5/6)=12A
Thus, I=4A.
The current in each edge is determined from the diagram. In
this manner the current in all 12 edges of the cube is easily
written down in terms of I ,using Kirchhoff’s 1st law and the
symmetry in the problem.
For Figure 2:
First we apply KCL at every junction to mark the unknown
current. Then we apply KVL to determine the values of
current.
For loop ADCA,
10-4(I1-I2)+2(I2+I3-I1)-I1=0
i.e, 7I1-6I2-2I3=10
For loop ABCA,
10-4I2-2(I2+I3)-I1=0
i.e, I1+6I2+2I3=10
For loop BCDEB,
5-2(I2+I3)-2(I,+I3-I1)=0
i.e, 2I1-4I2-4I3=-5
From these three equations we get,
I 1 =2.5A ,
I 2 =5/8A,
I 3 =15/8A.
The distribution of current in the various arms of the
skeleton cube is shown according to Kirchhoff’s first law and
second law.
It is easily verified that Kirchhoff’s second rule applied to the
remaining closed loops does not provide any additional
independent equation ,i.e, the above values of currents
satisfy the second rule for every closed loop for the network.
For example, the total voltage drop over the closed loop
BADEB
5V +[5/8 ×4]V – [15/8]V
Equal to zero, as required by Kirchhoff’s second law
RESULT
1 . The net equivalent resistance is 0.83Ω
2. The voltage in a closed loop is 0
PRECAUTION
• All the connections should be neat and tight
• Never apply power to the circuit while measuring
resistance with a multimeter
• Solder the corners of the cube used under the guidance
 APPLICATION OF KIRCHHOFF’S LAW

• In the deserts, days are very hot as sand is rough; therefore,

it is a good heat absorber. Now by Kirchhoff’s Laws, a Good
absorber is a good emitter. So accordingly, the nights will be
cool. That’s why in deserts, days are hot and nights are cold.
• This law is used to calculate the unknown values of current
and voltages in the circuit.
• Kirchhoff’s law was the first law that helped the analysis and
calculation of complex circuits become manageable and easy.
• The Wheatstone bridge is an essential application of
Kirchhoff’s laws. It is also used in mesh and node analysis.
• Node analysis, Grid analysis , Power analysis
• Telecommunication networks, Fluid dynamics
• Mesh analysis , Transient analysis, signal processing
• Energy efficiency
• Meter bridge
• Potentiometer
• Audio engineering
• Electrical vehicle charging system
 WHEATSTONE BRIDGE
Wheatstone bridge, also known as the resistance bridge,
calculates the unknown resistance by balancing two legs of
the bridge circuit. One leg includes the component of
unknown resistance.
The Wheatstone Bridge Circuit comprises two known
resistors, one unknown resistor and one variable resistor
connected in the form of a bridge. This bridge is very reliable
as it gives accurate measurements.
PRINCIPLE OF WHEATSTONE BRIDGE
The Wheatstone bridge works on the principle of null deflection, i.e.
the ratio of their resistances is equal, and no current flows through
the circuit. Under normal conditions, the bridge is in an unbalanced
condition where current flows through the galvanometer. The bridge
is said to be balanced when no current flows through the
galvanometer. This condition can be achieved by adjusting the
known resistance and variable resistance.
Wheatstone Bridge Application

• The Wheatstone bridge is used for the precise

measurement of low resistance.
• Wheatstone bridge and an operational amplifier are
used to measure physical parameters such as
temperature, light, and strain.
• Quantities such as impedance, inductance, and
capacitance can be measured using variations on the
Wheatstone bridge.

Wheatstone Bridge Limitations

• For low resistance measurement, the resistance of the

leads and contacts becomes significant and introduces
an error.
• For high resistance measurement, the measurement
presented by the bridge is so large that the
galvanometer is insensitive to imbalance.
• The other drawback is the resistance change due to the
current’s heating effect through the resistance.
Excessive current may even cause a permanent change
in the value of resistance.

METER BRIDGE
A meter bridge, also called a slide wire bridge, is an
instrument that works on the principle of a Wheatstone
bridge. A meter bridge is used to find the unknown resistance
of a conductor as that of in a Wheatstone bridge.
FORMULA FOR METER BRIDGE
S (l) = R (100-l)
S = Unknown resistance in Ω
R= Known resistance in Ω
l = Balancing length in metre
 POTENTIOMETER
The potentiometer is an instrument used to measure the
unknown voltage by comparing it with the known voltage. It
can be used to determine the emf and internal resistance of
the given cell and also used to compare the emf of different
cells. The comparative method is used by the potentiometer.
The reading is more accurate in a potentiometer.

Working Principle of Potentiometer

The basic principle of the potentiometer is that the potential
drop across any section of the wire will be directly
proportional to the length of the wire, provided the wire is of
a uniform cross-sectional area and a uniform current flows
through the wire.
APPLICATION OF POTENTIOMETER

• Comparison of emf of two cells of emf E1 AND E2

ε1 / ε2 = l1/l2
• Determination of internal resistance of a cell
r = R(L1 –L2)/ L2
 BIBLIOGRAPHY
➢ PHYSICS NCERT BOOK OF CLASS 12
➢ Unacademy
➢ Wikipedia
➢ BYJU’S
➢ Scribd
➢ Studoku
➢ Shiksha
➢ Knowledge Cycle
➢ SlideShare
➢ Shaalaa.com
 CONCLUSION
Thus, Kirchhoff’s law is a fundamental electrical law that
helps solve and analyse the electric circuit quickly. Calculating
the unknown current and voltage in an electric circuit
becomes easier. Kirchhoff’s first law is based on the
conservation of charges, and Kirchhoff’s second law is based
on energy conservation. Gustav Robert Kirchhoff described it
in 1845.

Kirchhoff’s first law is junction rule or current law, and

Kirchhoff’s second law is loop rule or voltage law. It is the
significant and fundamental law of electricity.