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Class 12 science notes, physics notes.

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  • 1. Electric Charges and Fields
  • 2. Electrostatic Potential and Capacitance
  • 3. Current Electricity
  • 4. Moving Charges and Magnetism
  • 5. Magnetism and Matter
  • 6. Electromagnetic Induction
  • 7. Alternative Current
  • 8. Electromagnetic Waves
  • 9. Ray Optics and Optical Instruments
  • 10. Wave Optics
  • 11. Dual Nature of Radiation and Matter
  • 14. Semiconductor Electronics: Materials, Devices and Simple Circuits

Chemistry Notes

  • 1. Solid State
  • 2. Solutions
  • 3. Electrochemistry
  • 4. Chemical Kinetics
  • 5. Surface Chemistry
  • 6. General Principles and Processes of Isolation of Elements
  • 7. p -Block Elements
  • 8. d -and f -Block Elements
  • 9. Coordination Compounds
  • 10. Haloalkanes and Haloarenes
  • 11.Alcohols, Phenols and Ethers
  • 12. Aldehydes, Ketones and Carboxylic Acids
  • 14. Biomolecules
  • 15. Polymers

Biology Notes

  • 1. Reproduction in Organisms
  • 2. Sexual Reproduction in Flowering Plants
  • 3. Human Reproduction
  • 4. Reproductive Health
  • 5. Principles of Inheritance and Variation
  • 6. Molecular Basis of Inheritance
  • 7. Evolution
  • 8. Human Health and Diseases
  • 9. Strategies for Enhancement in Food Production
  • 10. Microbes in Human Welfare
  • 11. Biotechnology - Principles and Processes
  • 12. Biotechnology and its Application
  • 13. Organisms and Populations
  • 14. Ecosystem
  • 15. Biodiversity and its Conservation
  • 16. Environmental Issues

Hindi Notes

  • 1. आत्म-परिचय, एक गीत
  • 2. कविता के बहाने, बात सीधी थी पर
  • 3. पतंग
  • 4. कैमरे में बंद अपाहिज
  • 5. सहर्ष स्वीकारा है
  • 6. छोटा मेरा खेत, बगुलों के पंख
  • 7. भक्तिन
  • 8. बाजार दर्शन
  • 9. काले मेघा पानी दे
  • 10. श्रम-विभाजन और जाति-प्रथा, मेरी कल्पना का आदर्श समाज
  • 12. शिरीष के फूल
  • 13.जूझ

Physical Education

  • 1.Physical Education Notes
  • 1. The Rattrap
  • 3. Poets and Pancakes
  • 4. Evans Tries an O-level
  • 5. The Tiger King
  • 6. Should Wizard Hit Mommy

41 comments:

physics wallah assignment class 12

Physics notes

Sir may 5000rupes. Class start no

I think this fake website.

I think notes in hindi but I Am wrong

Yes Ye Hindi Medium Nahi Hai.......

please helpp

Hii what help

Sir plz note dedo organic class 12 by alakh sir

Sir I mistacally paid two times for course LAKSHYA NEET 2023. dt.10/03/2022 7:42 & 7:45(5635.28+5635.28). Please refund extra 5635.28 Thank you Sabahat Shaikh

its not real pw website go to www.pwlive.com

sorry www.pw.live

Can I know when will 2022-20223 12th batch will start?

Nice Post Sir

Sabnoor Siddiqui

fake website h....block kro ye fake

physics wallah assignment class 12

This comment has been removed by the author.

Thank you sir Jay hind

Every thing is fine but ..I would suggest the notes of electric current would be more better if handwriting was fine 🥺🤧

He 2024 Ki notes hai na

This is fake website 😒 😑 The Real website of PW is --"www.physicswallahalakhpandey.com" go on this website Thanks 😊 you 😘 for read my Comment

hand writing is almost same (notes)

top 50 gk ke questions answers in hindi gk for comptativ exam in hindi gk-home.xyz

THANK YOU SIR FOR THE NOTES

physics wallah assignment class 12

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physics wallah assignment class 12

best notes for different subjects NOTES DUNIYA

Please add chapter atoms, nuclei, electromagnetic induction and alternative current notes

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Class 12 Physics Wallah Handwritten Notes Free Pdf Download

Class 12 Physics Wallah Handwritten Notes

Hey guys today I will provide you with full  Class 12 Physics Wallah Handwritten Notes Free Pdf Download chapter wise pdf download by alakh Pandey .

This class 12 notes helps to to revise any physics chapter which is helpful for board examination mostly for (Central Board of Secondary Education) cbse board and (Indian Certificate of Secondary Education) icse board because physics wallah means alakh Pandey sir teach (National Council of Educational Research and Training) 

ncert books based physics . So, if you are studying in the state board, it’s not helpful for the board exam. Physics wallah notes for class 12 physics by alakh pandey. Its  notes must be required for IIT-JEE, NEET, UPSC and many entrance exams in India .

Believe me friend, these  notes are handwritten by alakh pandey sir (physics wallah) for class 12th handwritten notes of physics chapter wise  provided below which helps you to all notes based on NCERT textbooks of physics total chapter 15 hole chapter covered in this article. So, don’t worry about it.

Class 12 Physics Wallah Handwritten Notes

These physics wallah notes help you to crack JEE mains & Advance and NEET. These  notes are based on the latest CBSE class 12 physics syllabus 2022 .

Download Physics Wallah Notes for Class 12 Physics Chapter Wise PDF by Alakh Pandey

Class 12th physics part – 1 & 2.

  • 1. Electric Charges and Fields
  • 2. Electrostatics Potential and Capacitance
  • 3. Current Electricity
  • 4. Moving Charges and Magnetism
  • 5. Magnetism and Matter
  • 6 . Electromagnetic Induction
  •  Part I
  • 7. Alternating Current
  • 8. Electromagnetic Waves
  • 9. Ray Optics and Optical Instruments
  • 10. Wave Optics
  • 11.Dual Nature of Radiation and Matter
  • 14 Semiconductor Electronics: Materials, Devices and Simple Circuits

15 Communication Systems

Physics Notes for class 12 Free Pdf Download

Get CBSE class 12 chapter wise Physics Reference Book Notes from their respective links

 Xam Idea  of physics, NCERT physics text book, that’s all you need to get perfect score in board even in competitive exams It covers all the theory topics, derivations and numerical problems required for preparation for CBSE board exams in a  student-friendly  manner.

Chapter No.

Chapter Name

  • Chapter 1 Electric Charges And Fields
  • Chapter 2 Electrostatic Potential And Capacitance
  • Chapter 3 Current Electricity
  • Chapter 4 Moving Charges And Magnetism
  • Chapter 5 Magnetism And Matter
  • Chapter 6 Electromagnetic Induction
  • Chapter 7 Alternating Current
  • Chapter 8 Electromagnetic Waves
  • Chapter 9 Ray Optics and Optical Instruments
  • Chapter 10 Wave Optics
  • Chapter 11 Dual Nature Of Radiation And Matter
  • Chapter 12 Atoms
  • Chapter 13 Nuclei
  • Chapter 14 Semiconductor Electronics Materials Devices And Simple Circuits
  • Chapter 15 Communication Systems

Here is provided physics wallah alakh pandey notes class 12th physics chapter wise  pdf download from Chapter 1 Electric Charge and Fields to Chapter 15 (Semiconductor Electronic Material and Device and simple Circuits) .

I will also provide physics wallah handwritten notes for class 12th physics chapter 1 to 15. Every chapter wise notes for class 12 physics wallah (alakh pandey sir)  physics notes PDF download chapter 1 to 15 .

Let’s download physics wallah class 12 physics chapter wise notes pdf download below.

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FAQs About Physics Wallah Notes for Class 12 Physics Chapter Wise PDF by (Alakh Pandey)

How to download pdf physics wallah notes for class 12 physics chapter wise.

In this topperme.com website, You are able to download PDF Physics Chapter 1 Electric Charges and Fields to Chapter 15 Semiconductor Electronics.

How to download PDF Physics Wallah Handwritten Notes for Class 12 Physics chapter wise?

In this topperme site, You are able to download PDF Physics Chapter 1 “Electrostatics” to Chapter 16 “Semiconductor Electronics”.

How to download PDF Physics Wallah Notes for Class 12 Physics Chapter 1 “Electrostatics”?

You are able to download PDF format of physics wallah for class 12 physics chapter 1 Electric Charges and Fields.

How to download PDF Physics Wallah Notes for Class 12 Physics Chapter 3 Current Electricity?

Download PDF of notes without any problems on topperme solution physics chapter 2 Current Electricity.

How to download PDF Physics Wallah Handwritten Notes for Class 12 Physics chapter 1 Electric Charges and Fields?

You can download physics wallah handwritten notes for Class 12 physics chapter 1 Electric Charges and Fields.

Hopefully, you will get what is expected of me. So, download this notes physics wallah chapter wise for class 12th by alakh pandey sir. If you  preparation for board examination this notes  really very great helps you to get higher percentage in 12th board exam and yes,

I’m also appreciate alakh sir which is provide this study material for free which really amazing help at the time of COVID pandemic students can’t visit school but this types of  online studies material provided by physics wallah alakh pandey sir .

I will also provide physics chapter wise class 12th handwritten notes by physics wallah youtube videos lectures which are very helpful for notes for  IIT, NEET and any government entrance exam preparation . I know what you want actually, you want to download online notes pdf. I believe you can  score in this competitive examination .

So, this physics wallah alakh pandey notes for class 12 physics chapter wise PDF download. If you face any problem regarding this article, Please leave a comment below which types of notes you want i will provide definitely?

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Physics Wallah Coaching Experience For JEE Course

This Article is dedicated to all the futures of India, the young generation who is on his/her path to success. Hello, all my name is Akash, currently, I am in college, this article tells about my personal experience at a coaching institute in which I was admitted admission just after 9th for nearly 3 years – 10th class to 12th class. Before describing my experience I would like to tell you in brief about my coaching Institute, which is India’s renowned Institute and many of you would all also know about it.

Let’s begin, the Institute is none other than PW- Physics Wallah , YES! it’s the only institute which now India’s biggest ed-tech company. Rarely anyone would be in India who doesn’t know about PW. Physics Wallah is a multinational educational technology company headquartered in Noida, Uttar Pradesh. The company was founded by Alakh Pandey and co-founder Prateek Maheshwari. The journey of Physics Wallah is inspirational, the coaching was first started by Alakh sir in the year 2016 as a YouTube channel aimed at teaching physics later on Prateek Maheshwari joined him and in the year 2020 they launched the PW application after that, the coaching boomed to the top. In June 2022, after raising $100 million during its initial funding round, the company reached a valuation of $1.1 billion, becoming a unicorn company. Nowadays the coaching institute has its study centre in almost every state and most cities of India. PW offers many different courses from JEE, and NEET to SSC, Banking, etc and the mode of teaching is both offline and online. Mostly if we see then PW most of the batches and student strength are high online as compared to offline.

Different courses and uniqueness

PW offers courses of all backgrounds or fields, such as – JEE, NEET, SSC, Banking, UPSC, ICAI, NDA and many more. The best thing I like or almost every student likes is that this coaching provides the best course materials, master teachers, the best study environment, supportive, doubt-solving facility all for just a minimal amount of fees that any student can afford. PW has brought a revolution in the ed-tech field, offering great courses at such low fees amount, it inspired and encouraged every background student to dream big and believe in achieving that dream.

Personal Experience

Now I would like to discuss my experience as a student of PW, so basically The thing started when I just cleared class 9th in 2020, my score was less than 85% so for the 10th class I started preparing from YouTube, I got to know about PW after which I enrolled in a course whose fees was 2500 for aone year which was less than even coachings near by my house. The experience was appreciative, the course material, teachers, and doubt problem-solving sessions were very very useful for me in my board paper. Because of the true guidance of PW, I scored 86.5% in class 10th. Although I have to prepare for JEE after the 10th, In the year 2022 after the result I enrolled in the Arjuna JEE 3.0 batch of PW with minimal fees of Rs.3500 for 2 years. Cureently I am studying am to now the experience is great, all the teachers are the best faculty in India, the course contests are also the best, the most important thing that I liked is DPP, and regular mock tests conducted every month that keep us on the track, and realises our mistakes.

Doubt Solving

If I talk about the doubt-solving quality then it is unique. See first of all when you enrol on any course, you will download the PW app on which your class will take place. All the courses go on a fixed schedule that is shared with you, the classes are live, not recorded, but if you are not able to attend the class at that time then don’t worry the lectures are available in recorded format. So in a live class, there is a complete interactive class where there is a chat room where you can ask any doubt, there are special features that – take an example teacher is teaching some topics and after some time you realise any doubt on the previous topic taught in the same class you can take a screenshot of that short of span and then ask the doubt provide SS to Q.A.section available. You can also ask even after class is ended the special doubt section is provided on the App, so there is not any issue regarding doubt solving.

The classes are interactive, and the chat room, polls-based questions, and many other things make the class like a virtual one. The mentorship quality – as I told you earlier the faculties in PW are master teachers and the best faculty in India, the teachers like MR sir, Rajwant Sir and many more famous all over India. They not only teach the topic but also guide one on how to prepare for competitive examinations like JEE, they always start any topic from scratch and go in depth of it, this is the most aprreciating thing of teachers in PW, also they take doubts and any issue from the previous class in there next class before starting a new topic.

Overall I would like to say that Alakh sir has brought a revolution in the education field. My personal experience is fantastic and appreciated, I would suggest anyone who wants the best faculty and guarantee of success join PW. I want to give The overall rating of 5 stars.

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Coulomb’s Law of Electrostatics

Electrostatic force of interaction acting between two stationary charges is given by

F = 1 / 4π ε o q1q2 / r2

where q1, q2 are magnitude of point charges, r is the distance between them and εo is permittivity of free space.

Here, 1 / 4πε o = (10-7 N – s 2 / C 2 )C 2

Substituting value of c = 2.99792458 X 108 m/s, We get 1 / 4πεo = 8.99 x 109N-m2/C2 In examples and problems we will often use the approximate value,

1 / 4πεo = 9 * 10 9 N-m 2 /C 2 The value of εo is 8.85 * 10 -12 C 2 / N-mC 2 . If there is another medium between the point charges except air or vacuum, then εo is replaced by εoK or εoεr or ε.

where K or εr is called dielectric constant or relative permittivity of the medium. K = εr = ε / εo where, ε = permittivity of the medium.

For air or vacuum, K = 1 For water, K = 81 For metals, K = ∞

Coulomb’s Law in Vector Form

electrostat14

Force on q2 due to q1,

electrostat6

The above equations give the Coulomb’s law in vector form.

Force on q1 due to q2 = – Force on q2 due to q1

F12 = – F21 F12 = q1q2 / 4πε . r1 – r2 / |r1 – r2|3

The forces due to two point charges are parallel to the line joining point charges; such forces are called central forces and electrostatic forces are conservative forces.

Electric Field

The space in the surrounding of any charge in which its influence can be experienced by other charges is called electric field.

Electric Field Lines

An electric field line is an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric field vector at that point. The relative closeness of the lines at some place give an idea about the intensity of electric field at that point.”

electrostat7

Two lines can never intersect.

Electric field lines always begin on a positive charge and end on a negative charge and do not start or stop in mid space.

Electric Field Intensity (E)

The electrostatic force acting per unit positive charge on a point in electric field is called electric field intensity at that point.

electrostat15

Electric field intensity E = Its SI unit is NC-1 or Vim and its dimension is [MLT-3 A-1]. It is a vector quantity and its direction is in the direction of electrostatic force acting on positive charge. Electric field intensity due to a point charge q at a distance r is given by E = 1 / 4π εo q / r2

Electric Potential (V)

Electric potential at any point is equal to the work done per positive charge in carrying it from infinity to that point in electric field. Electric potential, V = W / q Its SI unit is J / C or volt and its dimension is [ML2T-3A-1]. It is a scalar quantity. Electric potential due to a point charge at a distance r is given by v = 1 / 4π εo q / r

Potential Gradient

The rate of change of potential with distance in electric field is called potential gradient.

Potential gradient = dV / dr

Its unit is V / m.

Relation between potential gradient and electric field intensity is given by

E = – (dV / dr)

Equipotential surface is an imaginary surface joining the points of same potential in an electric field. So, we can say that the potential difference between any two points on an equipotential surface is zero. The electric lines of force at each point of an equipotential surface are normal to the surface.

Electric Lines of Force

Electric flux (φe).

Electric flux over an area is equal to the total number of electric field lines crossing this area. Electric flux through a small area element dS is given by

φE = E. dS

where E= electric field intensity and dS = area vector.

Its SI unit is N – m2C-1.

Gauss’s Theorem

The electric flux over any closed surface is 1 / εo times the total charge enclosed by that surface, i.e.,

electrostat9

CBSE Class 11 Physics Notes Electrostatics

If a charge q is placed at the centre of a cube, then

total electric flux linked with the whole cube = q / εo

electric flux linked with one face of the cube = q / 6 εo

(i) Electric Field at Any Point on the Axis of a Uniformly Charged Ring A ring-shaped conductor with radius a carries total charge Q uniformly distributed around it. Let us calculate the electric field at a point P that lies on the axis of the ring at distance x from its centre.

electrostat10

Ex = 1 / 4π εo * xQ / (x2 + a2)3/2

The maximum value of electric field

Ex = 1 / 4π εo (2Q / 3√3R2)

Electric Potential due to a Charged Conducting Spherical Shell

electrostat11

(a) At an extreme point (r > R)

V = 1 / 4π εo q / r

(b) At the surface of a shell (r = R)

V = 1 / 4π εo q / R

(c) At an internal point (r < R)

Therefore potential inside a charged conducting spherical shell equal to the potential at its surface.

(iv) Electric Field and Potential due to a Charged Non-Conducting Sphere

electrostat12

(v) Electric Field Intensity due to an Infinite Line Charge

electrostat16

E = 1 / 2 π εo λ / r

where λ is linear charge density and r is distance from the line charge.

(vi) Electric Field Near an Infinite Plane Sheet of Charge

electrostat17

E = σ / 2 εo

where σ = surface charge density.

If infinite plane sheet has uniform thickness, then

E = σ / εo

An electric dipole consists of two equal and opposite point charges separated by a very small distance. e.g., a molecule of HCL, a molecule of water etc.

electrostat18

  • Electric Dipole Moment p = q * 2 l
  • Its SI unit is ‘coulomb-metre’ and its dimension is [LTA).
  • It is a vector quantity and its direction is from negative charge towards positive charge.

Electric Field Intensity and Potential due to an Electric Dipole

(i) On Axial Line

  • Electric field intensity E = 1 / 4 π ε o * 2 pr / (r2 – a2) 2
  • If r > > 2a, then E = 1 / 4 π ε o * 2 p / r 3
  • Electric potential V = 1 / 4 π εo * p / (r 2 – a 2 )

electrostat19

  • I fr > > 2a, then V = 1 / 4 π ε o * p / r 2

(ii) On Equatorial Line

  • Electric field intensity E = 1 / 4 π ε o * p / (r2 + a2) 3 / 2

electrostat20

  • If r > > 2a, then E = 1 / 4 π ε o * p / r 3
  • Electric potential V = 0

(iii) At any Point along a Line Making θ Angle with Axis

  • Electric field intensity E = 1 / 4 π εo * p √1 + 3 cos2 θ / r 3

electrostat21

  • Electric potential V = 1 / 4 π εo * p cos θ / (r 2 – a 2 cos2 θ)
  • If r > > 2a, then V = 1 / 4 π εo * p cos θ / r 2
  • Torque acting on an electric dipole placed in uniform electric field is given by
  • τ = Ep sin θ or τ = p * E
  • When θ = 90°, then ‘τmax = Ep

When electric dipole is parallel to electric field, it is in stable equilibrium and when it is anti-parallel to electric field, it is in unstable equilibrium.

  • Work done is rotating an electric dipole in a uniform electric field from angle θ1 to θ2 is given by
  • W = Ep (cos θ1 – cos θ2)
  • If initially it is in the direction of electric field, then work done in rotating through an angle θ, W = Ep (1 – cos θ).

Potential Energy

Potential energy of an electric dipole in a uniform electric field is given by U = – pE cos θ.

Dipole in Non-uniform Electric Field

  • When an electric dipole is placed in a non-uniform electric field, then a resultant force as well as a torque act on it.
  • Net force on electric dipole = (qE1 – qE2), along the direction of greater e ecmc field intensity.
  • Therefore electric dipole undergo rotational as well as linear motion.

Potential Energy of Charge System

Two point charge system, contains charges q1 and q2 separated by a distance r is given by U = 1 / 4 π εo * q1q2 / r

Three point charge system

electrostat22

U = 1 / 4 π ε o * [q 12 / r 1 + q 2 q 3 / r 2 + q 3 q 2 / r 3

Important Points

  • When charge is given to a soap bubble its size gets increased.
  • In equilibrium for a charged soap bubble, pressure due to surface tension
  • = electric pressure due to charging
  • 4T / r = σ 2 / 2 ε o
  • or 4T / r = 1 / 2 ε o (q / 4 πr 2 ) 2
  • or q = 8 πr √2 ε o r T
  • where, r is radius of soap bubble and T is surface tension of soap bubble.

Behaviour of a Conductor in an Electrostatic Field

  • Electric field at any point inside the conductor is zero.
  • Electric field at any point on the surface of charged conductor is directly proportional to the surface density of charge at that point, but electric potential does not depend upon the surface density of charge.
  • Electric potential at any point inside the conductor is constant and equal to potential.

Electrostatic Shielding

  • The process of protecting certain field from external electric field is called, electrostatic shielding.
  • Electrostatic shielding is achieved by enclosing that region in a closed metallic chamber.

Dielectrics are of two types Non-polar Dielectric The non-polar dielectrics (like N2, O2, benzene, methane) etc. are made up of non-polar atoms/molecules, in which the centre of positive charge coincides with the centre of negative charge of the atom/molecule.

Polar Dielectric

The polar dielectric (like H2O, CO2, NH3 etc) are made up of polar atoms/molecules, in which the centre of positive charge does not coincide with the centre of negative charge of the atom.

  • A capacitor is a device which is used to store huge charge over it, without changing its dimensions.
  • When an earthed conductor is placed near a charged conductor, then it decreases its potential and therefore more charge can be stored over it.
  • A capacitor is a pair of two conductors of any shape, close to each other and have equal and opposite charges.
  • Capacitance of a conductor C = q / V
  • Its 81 unit is coulomb/volt or farad.
  • Its other units are 1 μ F = 10 -6 F
  • 1 μμ F = 1 pF = 10 -12 F
  • Its dimensional formula is [M -1 L -2 T 4 A 2 ].

Capacitance of an Isolated Spherical Conductor

  • C = 4 π ε o K R

electrostat23

  • For air K = 1
  • ∴ C = 4 π ε o R = R / 9 * 109

Parallel Plate Capacitor

  • The capacitor with two plates arranges in parallel is shown below.

electrostat26

  • The first plate in the capacitor carries ‘+Q’ charge and the second plate carries ‘–Q’ charge. The area between these plates can be denoted with ‘A’ and the distance(d). Here, ‘d’ is smaller than the area of the plates (d < < A). When the whole charge on the first plate is ‘Q’ & ‘A’ is the area of the plate, then the density of surface charge can be derived as
  • σ =Q/A
  • Similarly, when the whole charge on the second plate is ‘-Q’ & is the area of the plate is ‘A’, then the density of surface charge can be derived as
  • σ = -Q/A
  • The regions of this capacitor can be divided into three divisions like area1, area2, and area3. Area 1 is left to the plate1, area 2 is between the planes & area 3 is the right of the second plate. The electric field can be calculated in the region around the capacitor. Here, the electric field is consistent & its path is from the +Ve plate to the –Ve plate.
  • V = Exd = 1/ε(Qd/A)
  • The capacitance of the parallel plate can be derived as C = Q/V = εoA/d
  • The capacitance of a parallel plate capacitor with 2 dielectrics is shown below. Each plate area is Am2 and separated with d-meter distance. The two dielectrics are K1 & k2, then the capacitance will be like the following.
  • The capacitance of primary half of the capacitor width is d/2 = C1=> K1Aϵ0/ d/2=> 2K1Aϵ0/d
  • Similarly, the capacitance of the next half of the capacitor is C2 = 2K2Aϵ0/d
  • Once these two capacitors are connected in series then the net capacitance will be
  • Ceff= C1C2/C1+C2= 2Aϵ0/d( K1K2/ /K1+K2)

Capacitors in series and parallel combinations

For practical applications , two or more capacitors are often used in combination and their total capacitance C must be known.To find total capacitance of the arrangement of capacitor we would use equation

(i) Parallel combination of capacitors

electrostat24

  • Parallel combination of capacitorsA. Similarly left hand side plates of capacitors would also be at same common potential VB.
  • Thus in this case potential difference VAB=VA-VB would be same for both the capacitors, and charges
  • Q1 and Q2 on both the capacitors are not necessarily equal. So,
  • Q1=C1V and Q2=C2V
  • Thus charge stored is divided amongst both the capacitors in direct proportion to their capacitance. Total charge on both the capacitors is,

=V(C1+C2) and

  • So system is equivalent to a single capacitor of capacitance

When capacitors are connected in parallel their resultant capacitance C is the sum of their individual capacitances.

The value of equivalent capacitance of system is greater then the greatest individual one. If there are number of capacitors connected in parallel then their equivalent capacitance would be

C=C1+C2+ C3...........

Series combination of capacitors

electrostat25

  • Both the points A and B are maintained at constant potential difference VAB.
  • In series combination of capacitors right hand plate of first capacitor is connected to left hand plate of next capacitor and combination may be extended foe any number of capacitors.
  • In series combination of capacitors all the capacitors would have same charge.
  • Now potential difference across individual capacitors are given by

V AR =Q/C 1

V RB =Q/C 2

Sum of VAR and VRB would be equal to applied potential difference V so,

V=V AB =V AR +V RB

=Q(1/C 1 + 1/C 2 )

i.e., resultant capacitance of series combination C=Q/V, is the ratio of charge to total potential difference across the two capacitors connected in series.

So, from equation 12 we say that to find resultant capacitance of capacitors connected in series, we need to add reciprocals of their individual capacitances and C is always less then the smallest individual capacitance.

Result in equation 12 can be summarized for any number of capacitors i.e.,

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