MAHARASHTRA STATE BOARD
CLASS XI AND XII
CHAPTER 9
CURRENT ELECTRICTY
CONTENT
Electric Cell and its Internal resistance
Potential difference and emf of a cell
Combination of cells in series and in parallel
Kirchhoff's laws and their applications
Wheatstone bridge
Metre bridge
Potentiometer – principle and its applications
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Rotational dynamics as per class 12 Maharashtra State Board syllabusRutticka Kedare
This ppt is as per class 12 Maharashtra State Board's new syllabus w.e.f. 2020. Images are taken from Google public sources and Maharashtra state board textbook of physics. Gif(videos) from Giphy.com. Only intention behind uploading these ppts is to help state board's class 12 students understand physics concepts.
this is class 12 Maharashtra board physics subject content. this is complete content with notes with easily explaination.
for buying or neet attractive ppt in any subject contact me 8879919898. go to my site akchem.tk
blog akchem.blogspot.com
Rotational dynamics as per class 12 Maharashtra State Board syllabusRutticka Kedare
This ppt is as per class 12 Maharashtra State Board's new syllabus w.e.f. 2020. Images are taken from Google public sources and Maharashtra state board textbook of physics. Gif(videos) from Giphy.com. Only intention behind uploading these ppts is to help state board's class 12 students understand physics concepts.
Chapter 2 - Mechanical Properties of Fluids.pptxPooja M
MARASHTRA STATE BOARD
CLASS XII
PHYSICS
MECHANICAL PROPERTIES OF FLUIDS
CONTENT
Density and pressure.
Buoyant force and Archimedes' principle.
Fluid dynamics.
Viscosity.
Surface tension.
Electrostatic potential and capacitanceEdigniteNGO
Hello everyone, we are from Edignite NGO and we have come up with chapters of class 11 and 12 (CBSE).
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Lekha Periwal : +916290889619
Heer Mehta : +917984844099
JC H2 Physics Formula List/Summary (all topics)John Jon
Some of the concepts might be out of syllabus but I believe most of it is still relevant. It is a very concise summary containing mostly formulas and the Laws that govern Physics. This was done by a Raffles Institution student. I hope you will find this beneficial!
The presentation explain principal, working and construction and application of Potentiometer it is useful for senior secondary students of Indian school
Chapter 2 - Mechanical Properties of Fluids.pptxPooja M
MARASHTRA STATE BOARD
CLASS XII
PHYSICS
MECHANICAL PROPERTIES OF FLUIDS
CONTENT
Density and pressure.
Buoyant force and Archimedes' principle.
Fluid dynamics.
Viscosity.
Surface tension.
Electrostatic potential and capacitanceEdigniteNGO
Hello everyone, we are from Edignite NGO and we have come up with chapters of class 11 and 12 (CBSE).
For any queries, please contact
Lekha Periwal : +916290889619
Heer Mehta : +917984844099
JC H2 Physics Formula List/Summary (all topics)John Jon
Some of the concepts might be out of syllabus but I believe most of it is still relevant. It is a very concise summary containing mostly formulas and the Laws that govern Physics. This was done by a Raffles Institution student. I hope you will find this beneficial!
The presentation explain principal, working and construction and application of Potentiometer it is useful for senior secondary students of Indian school
Electricity and Electromagnetism (experimental study)Raboon Redar
You’ll understand the way to calculate and measure resistance in parallel and series circuits by knowing two of the three values of voltage, current, or resistance. In this experiment, there are 3 resistors, 1 power supply and wires you need for connecting resistors to each other, then to power supply. You can measure each resistor by an ohmmeter, voltages by voltmeter and currents by amperemeter (ammeter), while all of them can be measured by a multimeter. Use a multimeter for measuring resistance for better accuracy.
Current Electricity and Effects of CurrentOleepari
Electric current, potential difference and electric current. Ohm’s law; Resistance, Resistivity,
Factors on which the resistance of a conductor depends. Series combination of resistors,
parallel combination of resistors and its applications in daily life. Heating effect of electric
current and its applications in daily life. Electric power, Interrelation between P, V, I and R
Laboratory session in Physics II subject for September 2016-January 2017 semester in Yachay Tech University (Ecuador). Topic covered: electricity, magnetism
Based on Bruna Regalado's work
MAHARASHTRA STATE BOARD
CLASS XI
PHYSICS
CHAPTER 1
UNITS AND MEASUREMENT
Introduction
The international system of
units
Measurement of length
Measurement of mass
Measurement of time
Accuracy, precision of
instruments and errors in
measurement
Significant figures
Dimensions of physical
quantities
Dimensional formulae and
dimensional equations
Dimensional analysis and its
applications
MAHARASHTRA STATE BOARD
CLASS XI AND XII
CHAPTER 4
THERMODYNAMICS
CONTENT
Introduction
Thermal equilibrium
Zeroth law of
Thermodynamics
Heat, internal energy and
work
First law of
thermodynamics
Specific heat capacity
Thermodynamic state
variables and equation of
state
Thermodynamic processes
Heat engines
Refrigerators and heat
pumps
Second law of
thermodynamics
Reversible and irreversible
processes
Carnot engine
MAHARASHTRA STATE BOARD
CLASS XI AND XII
CHAPTER 5
OSCILLATIONS
CONTENT
Introduction
Periodic and oscillatory
motions
Simple harmonic motion
Simple harmonic motion
and uniform circular
motion
Velocity and acceleration
in simple harmonic motion
Force law for simple
harmonic motion
Energy in simple harmonic
motion
Some systems executing
simple harmonic motion
Damped simple harmonic
motion
Forced oscillations and
resonance
MAHARASHTRA STATE BOARD
CLASS XI and XII
CHAPTER 6
SUPERPOSITION OF WAVES
CONTENT:
Introduction
Transverse and
longitudinal waves
Displacement relation in a
progressive wave
The speed of a travelling
wave
The principle of
superposition of waves
Reflection of waves
Beats
Doppler effect
MAHARASHTRA STATE BOARD
CLASS XI AND XII
PHYSICS
CHAPTER 7
WAVE OPTICS
CONTENT:
Huygen's principle.
Huygen's principles & proof of laws of reflection/refraction.
Condition for construction & destruction of coherent waves.
Young's double slit experiment.
Modified Young's double slit experiment.
Intensity of light in Y.D.S.E.
Diffraction due to single slit.
Polarisation & doppler effect.
MAHARASHTRA STATE BOARD
CLASS XI AND XII
PHYSICS
CHAPTER 8
ELECTROSTATICS
Introduction.
Coulomb's law
Calculating the value of an electric field
Superposition principle
Electric potential
Deriving electric field from potential
Capacitance
Principle of the capacitor
Dielectrics
Polarization, and electric dipole moment
Applications of capacitors.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
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This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
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Ethnobotany and Ethnopharmacology:
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Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
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Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
2. Previously we have been studied Series and parallel combination of resistors.
In series combination
𝑅1 𝑅2 𝑅3
𝐸 𝐾
𝑅 = 𝑅1 + 𝑅2 + 𝑅3
In parallel combination
𝑅1 𝑅2 𝑅3 1
𝑅
=
1
𝑅1
+
1
𝑅2
+
1
𝑅3
𝐸
𝐾
3. A circuit containing several complex connections of electrical components
cannot be easily reduced into a single loop by using the rules of series and parallel
combination of resistors.
More complex circuits can be analyzed by using Kirchhoff’s laws. Gustav
Robert Kirchhoff (1824-1887) formulated two rules for analyzing a complicated
circuit.
5. Before describing these laws we will define some terms used for electrical
circuits.
Junction
Any point in an electric circuit
where two or more conductors are joined
together is a junction.
Loop
Any closed conducting path in an
electric network is called a loop or mesh.
Branch
A branch is any part of the
network that lies between two junctions.
𝑅1 𝑅2 𝑅3
𝐸
𝐾
𝐴 𝐵 𝐶 𝐷
𝐹
𝐺
𝐻
𝐼
Here points A,B,C,D,E,F,G,H and
I are junctions
Here ABHIA, ABCGHIA,
ABCDFGHIA, BCGHB, BCDFGHB
and CDFGC are representing
loops
Here AI, BH, CG, DF are
representing some branches
6. Kirchhoff’s First Law: (Current law/ Junction law)
Statement
The algebraic sum of the
currents at a junction is zero in an
electrical network, i.e.,
𝑘=1
𝑛
𝐼𝑘 = 0
Sign Conventions
The currents arriving at the
junction are considered positive and
the currents leaving the junction are
considered negative.
Explanation
𝐼1
𝐼2
𝐼3
𝐼4
𝐼5
The currents 𝐼1, 𝐼2 are arriving at the
junction are considered positive and the
currents 𝐼3, 𝐼4 and 𝐼5 leaving the junction
are considered negative.
∴ 𝐼1 + 𝐼2 − 𝐼3 − 𝐼4 − 𝐼5 = 0
or 𝐼1 + 𝐼2 = 𝐼3 + 𝐼4 + 𝐼5
This law is simply a statement of
“conservation of charge”.
7. Kirchhoff’s Second Law: (Voltage law/ Loop law)
Statement
The algebraic sum of the potential
differences and the electromotive forces
in a closed loop is zero.
𝐸 + 𝐼𝑅 = 0
Sign Conventions
Choose the loop to apply
Kirchhoff’s law. Assume any direction.
3) Emf is positive if assumed direction
leaving positive terminal of battery.
4) Potential difference is negative if the
conventional current in the assumed
direction.
Explanation
For a loop ABFGA,
∴ 𝐸1 = 𝐼1𝑅1 + 𝐼3𝑅5 + 𝐼1𝑅3
∴ −𝐼3𝑅5 −𝐼2 𝑅4 + 𝐸2 − 𝐼2𝑅2 = 0
9. Wheatstone’s bridge is generally
used to measure resistances in the range
from tens of ohm to hundreds of ohms.
The Wheatstone Bridge was
originally developed by Charles
Wheatstone (1802- 1875) to measure the
values of unknown resistances. It is also
used for calibrating measuring
instruments, voltmeters, ammeters, etc.
Wheatstone bridge is an
arrangement of four resistances which can
be used to measure one of them in terms
of rest. Here arms 𝐴𝐵 and 𝐵𝐶 are called
ratio arms and arms 𝐴𝐶 and 𝐵𝐷 are called
conjugate arms.
10. Balanced bridge :
The bridge is said to be balanced
when current in galvanometer is zero i.e.
no current flows through the
galvanometer or in other words
𝑉𝐵 = 𝑉𝐷.
In the balanced condition,
𝑃
𝑄
=
𝑆
𝑅
On mutually changing the position
of Resistance Box and galvanometer this
condition will not change.
11. Balancing condition for Wheatstone bridge/network
Figure shows Wheatstone bridge.
Using Kirchhoff’s loop law for a loop 𝐴𝐵𝐷𝐴 we
get,
−𝐼1𝑃 − 𝐼𝑔𝐺 + 𝐼2𝑆 = 0 …(1)
Using Current law at junction A, we get
𝐼 = 𝐼1 + 𝐼2
Using Kirchhoff’s loop law for a loop 𝐵𝐶𝐷𝐵 we
get,
−(𝐼1 − 𝐼𝑔)𝑄 + (𝐼2 + 𝐼𝑔)𝑅 + 𝐼𝑔𝐺 = 0 …(2)
12. Balancing condition for Wheatstone bridge/network
Balancing condition for Wheatstone bridge is
Thus equation (1) and (2) becomes
−𝐼1𝑃 + 𝐼2𝑆 = 0
∴ 𝐼1𝑃 = 𝐼2𝑆 …(3)
𝐼𝑔 = 0
And
−(𝐼1 − 𝐼𝑔)𝑄 + (𝐼2 + 𝐼𝑔)𝑅 + 0 = 0
∴ 𝐼1𝑄 = 𝐼2𝑅 …(4)
Thus, dividing equation (3) by (4), we get
𝑃
𝑄
=
𝑆
𝑅
This is the balancing condition
for Wheatstone bridge.
14. Meter bridge
Construction
𝑋 𝑅
𝐿𝑒𝑓𝑡 𝐺𝑎𝑝 𝑅𝑖𝑔ℎ𝑡 𝐺𝑎𝑝
𝐶
𝐽
𝐺
𝐸 𝐾
A meter bridge consists of a wire of length 1 𝑚 and of uniform cross-sectional area stretched out and clamped between two thick
metallic strips bent at right angles with two gaps across which resistors are to be connected.
Usually, an unknown resistance X is connected in the left gap and a resistance box is connected in the other gap, as
shown in figure.
One end of a galvanometer (𝐺) is connected to the metallic strip midway between the two gaps. The other end of the
galvanometer is connected to a jockey which moves along the wire to make electrical connection.
The end points (𝐴 and 𝐵) where the wire is clamped are connected to a cell (𝐸) through a key (𝐾).
15. Meter bridge
Working
A suitable resistance R is selected from resistance box. By tapping jockey on wire
AB, point D is obtained where the galvanometer shows zero deflection.
Let 𝐴𝐷 = 𝑙𝑋 and 𝐵𝐷 = 𝑙𝑅.
𝑋 𝑅
𝐿𝑒𝑓𝑡 𝐺𝑎𝑝 𝑅𝑖𝑔ℎ𝑡 𝐺𝑎𝑝
𝐶
𝐽
𝐺
𝐸 𝐾
𝐴 𝐵
𝐷
𝑙𝑋 𝑙𝑅
16. Meter bridge
Working
where 𝑅𝐴𝐷 and 𝑅𝐵𝐷 are resistance of the parts AD and DB of the wire resistance
of the wire.
Let, 𝜌− specific resistance, 𝐴− cross-sectional area of the wire.
𝐷
𝑋 𝑅
𝐿𝑒𝑓𝑡 𝐺𝑎𝑝 𝑅𝑖𝑔ℎ𝑡 𝐺𝑎𝑝
𝐶
𝐽
𝐺
𝐸 𝐾
𝐴 𝐵
𝑙𝑋 𝑙𝑅
Then,
𝑅𝐴𝐷=𝜌𝑙𝑋/𝐴 and 𝑅𝐵𝐷=𝜌𝑙𝑅/𝐴
Then balancing condition is,
X
R
=
𝑅𝐴𝐷
𝑅𝐷𝐵
17. Meter bridge
Working
𝑋
𝑅
=
𝜌𝑙𝑋/𝐴
𝜌𝑙𝑅/𝐴
=
𝑙𝑋
𝑙𝑅
𝑋 𝑅
𝐿𝑒𝑓𝑡 𝐺𝑎𝑝 𝑅𝑖𝑔ℎ𝑡 𝐺𝑎𝑝
𝐶
𝐽
𝐺
𝐸 𝐾
𝐴 𝐵
𝑙𝑋 𝑙𝑅
Thus, balancing condition is,
∴ 𝑋 = 𝑅
𝑙𝑋
𝑙𝑅
Since, 𝑙𝑋 + 𝑙𝑅 = 100 𝑐𝑚
∴ 𝑋 = 𝑅
100−𝑙𝑅
𝑙𝑅
Thus, by knowing 𝑅, 𝑙𝑋 and 𝑙𝑅, we
can determine unknown resistance 𝑋.
18. Source of errors
1. The cross section of the wire may not be uniform.
2. The ends of the wire are soldered to the metallic strip where contact resistance is
developed, which is not taken into account.
3. The measurements of 𝑙𝑋 and 𝑙𝑅 may not be accurate.
1. The value of R is so adjusted that the null point is obtained to middle one third of
the wire (between 34 cm and 66 cm) so that percentage error in the measurement
of 𝑙𝑋 and 𝑙𝑅 are minimum and nearly the same.
2. The experiment is repeated by interchanging the positions of unknown resistance X
and known resistance box R.
3. The jockey should be tapped on the wire and not slided. We use jockey to detect
whether there is a current through the central branch. This is possible only by
tapping the jokey.
To minimize the errors
20. Potentiometer
Potentiometer is a device used
1. to compare the emfs of two cells,
2. find the emf of a cell,
3. to find the internal resistance of a cell and
4. to measure potential difference.
A potentiometer consists of uniform
wire of length 4 to 10 𝑚 arranged between A
and B as 4 to 10 𝑚 wires each of length 1m on
a wooden board. The wire has specific
resistance and low temperature coefficient of
resistance.
21. Principle of Potentiometer
The potential difference between
two points on the wire is directly
proportional to the length of the wire
between them provided the wire is of
uniform cross section, the current through
the wire is the same and temperature of
the wire remains constant.
Explanation
Consider a potentiometer
consisting a long wire AB of length L and
resistance R having uniform cross
sectional area A.
A cell of emf 𝐸 having internal
resistance 𝑟 is connected across AB as
shown in the figure. When the circuit is
switched on, current 𝐼 passes through the
wire.
22. Explanation
Current through AB is
𝐼 = 𝐸/(𝑅 + 𝑟).
Potential Difference across AB is
𝑉𝐴𝐵 = 𝐼𝑅
∴ 𝑉𝐴𝐵 =
𝐸𝑅
(𝑅+𝑟)
Therefore, the potential difference
per unit length of the wire is,
∴
𝑉𝐴𝐵
𝐿
=
𝐸𝑅
𝑅+𝑟 𝐿
As long as E remains constant
𝑉𝐴𝐵
𝐿
i.e. potential gradient (k) along wire 𝐴𝐵
also remains constant.
Consider a point C on the wire at
distance 𝑙 from the point A, as shown in
the figure. The potential difference
between A and C is 𝑉𝐴𝐶.
Therefore, 𝑉𝐴𝐶 =𝑘𝑙 i.e. 𝑉𝐴𝐶 ∝𝑙.
24. A) To Compare emf of Cells
There are two methods to compare emf of cells.
I] Direct Method/Individual Cell Method And
II] Sum and Difference Method
25. I) Individual Cell Method
𝐾
𝐸
𝑅ℎ
𝐴
𝐵
𝐸1
𝐸2
𝐾1
𝐾2
𝑃
𝑄
Key 𝐾 is closed and then, key 𝐾1 is closed and key
𝐾2 is kept open.
The null point for cell 𝐸1 is obtained, by touching
jockey on wire AB, say at 𝑃. Let 𝐴𝑃 = 𝑙1
∴ 𝐸1 = 𝑘𝑙1
Let 𝑘 be the potential
gradient
∴ 𝐸2 = 𝑘𝑙2
∴ 𝐸1/𝐸2 = 𝑘𝑙1/𝑘𝑙2
∴ 𝐸1/𝐸2 = 𝑙1/𝑙2
Thus, we can compare the emfs of
the two cells. If any one of the emfs is
known, the other can be determined.
26. I) Sum and Difference Method
𝐾
𝐸
𝑅ℎ
𝐴
𝐵
𝐸1
𝑃
𝑄
𝐸2
1 2
3
4
In this case, cell 𝐸1 and 𝐸2 will assist
each other. (i.e. 𝐸1 + 𝐸2)
∴ 𝐸1 + 𝐸2 = 𝑘𝑙1
∴ 𝐸1 + 𝐸2/𝐸1 − 𝐸2 = 𝑘𝑙1/𝑘𝑙2
By componendo and
dividendo method, we get,
∴
𝐸1
𝐸2
=
𝑙1 + 𝑙2
𝑙1 − 𝑙2
Thus, emf of two cells can be compared.
27. A) To find internal resistance of Cell
𝐾
𝐸
𝑅ℎ
𝐴
𝐵
𝐸1
𝑟
𝑅
𝐾1
𝑆
𝑃 𝑄
𝑅
Let 𝑘 be the potential gradient of potentiometer wire.
Initially, the key 𝐾 is closed and 𝐾1
is open.
The null point is
then obtained. Let 𝑙1 be
length of the potentiometer
wire between the null
point (say P) and the point
𝐴. This length corresponds
to emf 𝐸1 .
𝑃
∴ 𝐸1 = 𝑘𝑙1
28. A) To find internal resistance of Cell
Now, the key 𝐾 and 𝐾1 are closed
The null point is then
obtained. Let 𝑙2 be length of
the potentiometer wire
between the null point (say
Q) and the point 𝐴. This
length corresponds to
terminal potential difference
of cell 𝐸1 (say 𝑉).
𝐾
𝐸
𝑅ℎ
𝐴
𝐵
𝐸1
𝑟
𝑅
𝐾1
𝑆
𝑃 𝑄
𝑅
𝑃
∴ 𝑉 = 𝑘𝑙2
∴
𝐸1
𝑉
=
𝑙1
𝑙2
29. A) To find internal resistance of Cell
By Ohm’s law, we get, 𝑉 = 𝐼𝑅
And 𝐸1 = 𝐼(𝑅 + 𝑟)
𝐾
𝐸
𝑅ℎ
𝐴
𝐵
𝐸1
𝑟
𝑅
𝐾1
𝑆
𝑃 𝑄
𝑅
𝑃
∴
𝐼(𝑅 + 𝑟)
𝐼𝑅
=
𝑙1
𝑙2
∴
𝑅 + 𝑟
𝑅
=
𝑙1
𝑙2
∴ 1 +
𝑟
𝑅
=
𝑙1
𝑙2
∴ 𝑟 = 𝑅
𝑙1
𝑙2
− 1
This equation gives the internal resistance of the cell.
30. As shown in the figure, potential 𝑉 is set up between
points 𝐴 and 𝐵 of a potentiometer wire. One end of a device is
connected to positive point A and the other end is connected to a
slider that can move along wire 𝐴𝐵. The voltage 𝑉 divides in
proportion of lengths 𝑙1 and 𝑙2 as shown in the figure.
C] Applications of Potentiometer
Voltage Divider
31. Audio Control
Sliding potentiometers, are commonly used in
modern low-power audio systems as audio control
devices. Both sliding (faders) and rotary
potentiometers (knobs) are regularly used for
frequency attenuation, loudness control and for
controlling different characteristics of audio signals.
Potentiometer as a sensor
If the slider of a potentiometer is connected to
the moving part of a machine, it can work as a motion
sensor. A small displacement of the moving part
causes changes in potential which is further amplified
using an amplifier circuit. The potential difference is
calibrated in terms of the displacement of the moving
part.
32. Advantages of a Potentiometer over a Voltmeter
Merits
i) Potentiometer is more sensitive than a voltmeter.
ii) A potentiometer can be used to measure a potential difference as well as an
emf of a cell. A voltmeter always measures terminal potential difference, and as it
draws some current, it cannot be used to measure an emf of a cell.
iii) Measurement of potential difference or emf is very accurate in the case of a
potentiometer. A very small potential difference of the order 10–6 volt can be measured
with it. Least count of a potentiometer is much better compared to that of a voltmeter.
Demerits
Potentiometer is not portable and direct measurement of potential difference or
emf is not possible.
34. Galvanometer is an electro mechanical instrument which is used for the
detection of electric currents through electric circuits.
The primary purpose of galvanometer is the detection of electric current not
the measurement of current.
MOVING COIL GALVANOMENTER
It can only measure small amount of currents.
35. MOVING COIL GALVANOMENTER
A moving coil galvanometer is an instrument used for detection and
measurement of small electric currents.
36. Moving coil galvanometers are used in all kinds of different equipment
from aeroplane cockpit to sound level (VU) meters in recording studios
Cockpit of an
aeroplane
Moving coil galvanometers are used in the cockpit of an areoplane
37. Principle of Galvanometer
It works on the principle that when a current loop is placed in an external
magnetic field, it experiences torque, and the value of torque can be changed by
changing the current in the loop
38. Galvanometer
Moving coil galvanometer consists of
permanent horse-shoe magnets, coil, soft
iron core, pivoted spring, non-metallic
frame, scale and pointer.
When an electric current passes
through the coil, it deflects.
The deflection is proportional to the
current passing through the coil. The
deflection of the coil can be read with the
help of a pointer attached to it.
Position of the pointer on the scale
provided indicates the current passing
through the galvanometer or the potential
difference across it.
Thus, a galvanometer can be used
as an ammeter or voltmeter with suitable
modification.
The galvanometer coil has a
moderate resistance (about 100 ohms)
and the galvanometer itself has a small
current carrying capacity (about 1 mA).
40. A galvanometer can be converted to an ammeter by connecting a low resistance,
called SHUNT (S) in parallel to the galvanometer (G).
Conversion of a galvanometer to ammeter
What is a shunt?
A low resistance connecting
parallel to the galvanometer to
protect it from large current is
known as shunt.
Ammeter is used for measuring the current
in an electric circuit.
What is an ammeter?
41. A galvanometer can be converted to an ammeter by connecting a low
resistance, called SHUNT (S) in parallel to the galvanometer (G).
Conversion of a galvanometer to ammeter
The shunt resistance is calculated
as follows. In the arrangement shown in
the figure, 𝐼𝑔 is the current through the
galvanometer.
Therefore, the current through 𝑆 is
𝐼 − 𝐼𝑔 = 𝐼𝑠.
Since 𝑆 and 𝐺 are parallel,
𝐺𝐼𝑔 = 𝑆𝐼𝑠.
𝐺𝐼𝑔 = 𝑆 𝐼 − 𝐼𝑔 .
𝐺 = 𝑆
𝐼−𝐼𝑔
𝐼𝑠
.
42. (i) If the current 𝐼 is 𝑛 times
current 𝐼𝑔 , then 𝐼 = 𝑛𝐼𝑔. Using this in the
above expression we get
Conversion of a galvanometer to ammeter
𝐺 = 𝑆
𝐼−𝐼𝑔
𝐼𝑔
.
𝐺 = 𝑆
𝑛𝐼𝑔−𝐼𝑔
𝐼𝑔
. = 𝑆(𝑛 − 1)
𝑆 =
𝐺
𝑛−1
This is the required shunt to
increase the range n times.
43. (ii) Also if 𝐼𝑠 is the current
through the shunt resistance, then the
remaining current 𝐼 − 𝐼𝑠 will flow
through galvanometer. Hence
Conversion of a galvanometer to ammeter
𝐺 = 𝑆
𝐼−𝐼𝑔
𝐼𝑔
.
𝐺(𝐼 − 𝐼𝑠) = 𝑆𝐼𝑠.
∴ 𝐺𝐼 − 𝐺𝐼𝑠 = 𝑆𝐼𝑠.
∴ 𝐺𝐼 = 𝑆𝐼𝑠 + 𝐺𝐼𝑠 = (𝑆 + 𝐺)𝐼𝑠.
∴
𝐼𝑠
𝐼
=
𝐺
𝑆+𝐺
This equation gives the fraction of
the total current through the shunt
resistance.
44. Use of Shunt
a. It is used to divert a large part of total current by providing an alternate
path and thus it protects the instrument from damage.
b. It increases the range of an ammeter.
c. It decreases the resistance between the points to which it is connected.
46. A galvanometer can be converted to an voltmeter by connecting a high
resistance, in series to the galvanometer (G).
Conversion of a galvanometer to ammeter
The value of the resistance 𝑋 can
be calculated as follows. If 𝑉 is the voltage
to be measured, then
𝑉 = 𝑉
𝑥 + 𝑉
𝑔.
𝑉 = 𝐼𝑔𝑋 + 𝐼𝑔𝐺.
𝐼𝑔𝑋 = 𝑉 − 𝐼𝑔𝐺.
𝑋 =
𝑉−𝐼𝑔𝐺
𝐼𝑔
.
where 𝐼𝑔 is the current flowing
through the galvanometer.
47. Conversion of a galvanometer to ammeter
𝑋 =
𝑉−𝐼𝑔𝐺
𝐼𝑔
.
If 𝑛𝑣 =
𝑉
𝑉𝑔
=
𝑉
𝐼𝑔𝐺
i.e. the factor by which the voltage
range is increased
It can be shown that
𝑋 = 𝐺(𝑛𝑣 − 1).
48. Use of High Resistance
A voltmeter is connected across the points where potential difference is to be
measured. If a galvanometer is used to measure voltage, it draws some current (due
to its low resistance), therefore, actual potential difference to be measured
decreases. To avoid this, a voltmeter should have very high resistance. Ideally, it
should have infinite resistance.