NCERT Class 12 Physics Solutions: Chapterwise PDFs, Formulas, Important Questions

The students can click the links below to access the NCERT Class 12 Physics solutions chapter-wise.

Sl. No	Name of Chapter	PDFs
1	Chapter 1 Electric Charges and Fields	Download Free PDF
2	Chapter 2 Electrostatic Potential and Capacitance
3	Chapter 3 Current Electricity	Download Free PDF
4	Chapter 4 Moving Charges and Magnetism	Download Free PDF
5	Chapter 5 Magnetism and Matter
6	Chapter 6 Electromagnetic Induction	Download Free PDF
7	Chapter 7 Alternating Current	Download Free PDF
8	Chapter 8 Electromagnetic Waves	Download Free PDF
9	Chapter 9 Ray Optics and Optical Instruments	Download Free PDF
10	Chapter 10 Wave Optics	Download Free PDF
11	Chapter 11 Dual Nature of Radiation and Matter	Download Free PDF
12	Chapter 12 Atoms	Download Free PDF
13	Chapter 13 Nuclei	Download Free PDF
14	Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits

 

 

 

Chapter 1: Electric Charges and Fields

Electric charge, a fundamental characteristic of matter, results in the interaction of matter with an electric or magnetic field. An electric field accompanies an electric charge, while the motion of an electric charge produces a magnetic field. The charges are of two types: positive and negative. Materials that allow the flow of electricity with ease are referred to as conductors.

Electric Charges and Fields: Topics Covered

Exercise	Topics Covered
1.1	Introduction
1.2	Electric Charge
1.3	Conductors and Insulators
1.4	Basic Properties of Electric Charge
1.5	Coulomb’s Law
1.6	Forces Between Multiple Charges
1.7	Electric Field
1.8	Electric Field Lines
1.9	Electric Flux
1.10	Electric Dipole
1.11	Dipole In A Uniform External Field
1.12	Continuous Charge Distribution
1.13	Gauss’s Law
1.14	Applications of Gauss’s Law

Electric Charges and Fields: Formulas

• Coulomb's Law - $F=k_e{\displaystyle \frac{|q_1{q}_2|}{r^2}}$
• Electric Field due to a point charge - $E=k_e{\displaystyle \frac{q}{r^2}}$
• Electric field due to a continuous charge distribution - $E={\displaystyle \frac{1}{4\pi {ϵ}_0}}\int {\displaystyle \frac{dq}{r^2}}$
• Electric field due to an infinite line charge - $E={\displaystyle \frac{\lambda }{2\pi {ϵ}_{0}r}}$
• Electric field due to an infinite plane sheet of charge - $E={\displaystyle \frac{\sigma }{2{ϵ}_0}}$
• Electric field between two oppositely charged parallel plates - $E={\displaystyle \frac{\sigma }{{ϵ}_0}}$
• Electric Potential Energy of a system of two point charges - $U=k_e{\displaystyle \frac{q_1{q}_2}{r}}$
• Electric potential due to a Point charge - $V=k_e{\displaystyle \frac{q}{r}}$

Chapter 2: Electrostatic Potential and Capacitance

The Electrostatic Potential and Capacitance NCERT Solutions are well-structured and follow a logical sequence. Class 12 Electrostatic Potential and Capacitance Solutions are provided by expert teachers in a step-by-step manner, which makes it easier for students to follow along. All the Chapter 2 Physics Class 12 Important Questions are covered here. The candidates can find the solutions for all the Chapter 2 Physics Class 12 numericals.

In an electrostatic field, the energy required to move a single positive charge from an infinite distance to a specific point is known as the electrostatic potential at that position. Capacitance refers to the ability of a conductor to store an electrical charge. It is defined as the ratio of the magnitude of the charge stored on a conductor to the potential difference across the conductor.

Electrostatic Potential and Capacitance: Topics Covered

Exercise	Topics Covered
2.1	Introduction
2.2	Electrostatic Potential
2.3	Potential Due To A Point Charge
2.4	Potential Due To An Electric Dipole
2.5	Potential Due To A System Of Charges
2.6	Equipotential Surfaces
2.7	Potential Energy Of A System Of Charges
2.8	Potential Energy In An External Field
2.9	Electrostatics Of Conductors

Electrostatic Potential and Capacitance: Formulas

Topic	Formulas
ic Potential due to a point charge  Electric Potential due to a point charge	$V=k_e{\displaystyle \frac{q}{r}}$
Electric Potential due to a system of point charges	$V=k_e\underset{i}{\sum }{\displaystyle \frac{q_i}{r_i}}$
Potential Energy of a charge in an external field	$U=qV$
Capacitance of a parallel plate capacitor (without dielectric)	$C={\displaystyle \frac{{ϵ}_{0}A}{d}}$
Energy stored in a capacitor	$U={\displaystyle \frac{1}{2}}C{V}^2$
Capacitance of a parallel plate capacitor (with dielectric)	$C={\displaystyle \frac{\kappa {ϵ}_{0}A}{d}}$
Capacitance of a parallel plate capacitor (with dielectric)	$C={\displaystyle \frac{\kappa {ϵ}_{0}A}{d}}$
Work done in moving a charge in an electric field	$W=q(V_f-V_i)$

Chapter 3: Current Electricity

Current Electricity Class 12 NCERT solutions are helpful for students preparing for board exams as they provide a good foundation for the exam. Solving the Current Electricity Class 12 numericals given in the NCERT textbook also helps students to practice and improve their problem-solving skills. All the Current Electricity Class 12 questions and answers are provided here for the students to refer to. Candidates can check the exercise solutions for Physics Chapter 3, Class 12, here.

Electric current refers to the movement of electrons from one part of a circuit to another. If a wire connects two points with varying electrical potentials, the electrons will move from the first point to the second until both have the same potential, at which point the current stops flowing. Current only flows in a conductor when there is a potential difference present throughout it.

Current Electricity: Topics Covered 

Exercise	Topics Covered
3.1	Introduction To Current Electricity
3.2	Electric Current
3.3	Electric Currents In Conductors
3.4	Ohm’s law
3.5	Drift Of Electrons And The Origin Of Resistivity
3.6	Limitations Of Ohm’s Law
3.7	Resistivity Of Various Materials
3.8	Temperature Dependence Of Resistivity
3.9	Electrical Energy, Power
3.10	Cells, Emf, Internal Resistance
3.11	Cells In Series And In Parallel
3.12	Kirchhoff’s Rules
3.13	Wheatstone Bridge

Current Electricity: Important Formulas

• Ohm's Law: $V=IR$
• Resistance: $R={\displaystyle \frac{\rho L}{A}}$
• Resistance in Series: $R_{\text{eq}}=R_1+R_2+\cdots +R_n$
• Resistance in Parallel: ${\displaystyle \frac{1}{R_{\text{eq}}}}={\displaystyle \frac{1}{R_1}}+{\displaystyle \frac{1}{R_2}}+\cdots +{\displaystyle \frac{1}{R_n}}$
• Temperature Dependence of Resistivity: $\rho (T)={\rho }_0[1+\alpha (T-T_0)]$
• Conductivity: $\sigma ={\displaystyle \frac{1}{\rho }}$
• Power Dissipated in a Resistor: $P=I^{2}R=V^2/R=IV$
• Current Density: $J={\displaystyle \frac{I}{A}}$
• Kirchhoff's First Law (Junction Rule): $\sum I_{\text{in}}=\sum I_{\text{out}}$

Chapter 4: Moving Charges and Magnetism

Physics Chapter 4 Class 12 exercise solutions are prepared by subject matter experts who have a deep understanding of the concepts. Therefore, the Moving Charges and Magnetism NCERT solutions are accurate and reliable. Moving Charges and Magnetism Class 12 NCERT solutions are solved by the subject experts.

This chapter covers the concept of how the magnetic field interacts with moving charged particles such as electrons, protons, and current-carrying wires. When a conductor carries current, a magnetic field is generated around it, and the direction of this magnetic field can be determined by using Ampere's swimming rule. The region around a magnet or any current-carrying conductor where its magnetic effect can be detected is referred to as the magnetic field.

Moving Charges and Magnetism: Topics Covered

Exercise	Topics Covered
4.1	Introduction To Moving Charges And Magnetism
4.2	Magnetic Force
4.3	Motion In A Magnetic Field
4.4	Magnetic Field Due To A Current Element, Biot–Savart Law
4.5	Magnetic Field On The Axis Of A Circular Current Loop
4.6	Ampere’s Circuital Law
4.7	The Solenoid
4.8	Force Between Two Parallel Currents, The Ampere
4.9	Torque On Current Loop, Magnetic Dipole
4.10	The Moving Coil Galvanometer

Moving Charges and Magnetism: Formulas

• Magnetic field at the centre of a circular loop: $B={\displaystyle \frac{{\mu }_{0}I}{2R}}$
• Radius of the path of a charged particle in a magnetic field: $r={\displaystyle \frac{mv}{qB}}$
• Torque on a magnetic dipole in a uniform magnetic field: $\tau =\mathbf{m}\times \mathbf{B}$
• Potential energy of a magnetic dipole in a uniform magnetic field: $U=-\mathbf{m}\cdot \mathbf{B}$
• Cyclotron frequency: $f={\displaystyle \frac{qB}{2\pi m}}$
• Force between two parallel current-carrying conductors: $F={\displaystyle \frac{{\mu }_0{I}_1{I}_{2}L}{2\pi d}}$

Chapter 5: Magnetism and Matter

Class 12 Physics Chapter 5 NCERT solutions are an excellent resource for students who want to score well in their exams and have a strong foundation in the subject. NCERT Solutions are created to give students the correct answers that are entirely based on the most recent curriculum guidelines set forth by the CBSE board.

Magnetism refers to the occurrence of attractive or repulsive forces between two magnetic objects. All substances have some level of magnetic characteristics. When these substances are placed in a magnetic field, these substances are impacted by the magnetic field, and their behaviour determines whether they are classified as paramagnetic (attracted) or diamagnetic (repelled).

Magnetism and Matter: Topics Covered

Exercise	Topics Covered
5.1	Introduction To Magnetism And Matter
5.2	The Bar Magnet
5.3	Magnetism And Gauss’s Law
5.4	Magnetisation And Magnetic Intensity
5.5	Magnetic Properties Of Materials

Magnetism and Matter: Formulas

1. Magnetic Dipole Moment of a Current Loop: $\mathbf{m}=I\mathbf{A}$
2. Magnetic Susceptibility: ${\chi }_m={\displaystyle \frac{M}{H}}$
3. Magnetic Field due to a Magnetic Dipole (at Axial Point): $B_{\text{axial}}={\displaystyle \frac{{\mu }_0}{4\pi }}{\displaystyle \frac{2m}{r^3}}$
4. Magnetization: $M={\chi }_{m}H$
5. Torque on a Magnetic Dipole in a Uniform Magnetic Field: $\tau =\mathbf{m}\times \mathbf{B}$

Chapter 6: Electromagnetic Induction

For Students in Class 12, the Electromagnetic Induction Class 12 NCERT Solutions are essential for exam preparation. Students can use Chapter 6 Physics Class 12 Important Questions with answers to learn for the board exam and competitive exams like NEET and JEE. Students should routinely practise these solutions in order to fully understand the topics in the Chapter Electromagnetic Induction.

Electromagnetic induction is a phenomenon where a voltage or EMF (Electromotive Force) is generated across an electrical conductor when it is placed in a specific position with respect to a varying magnetic field or when a stationary magnetic field is applied to a moving conductor. The Law of Induction, which describes this process, was discovered by Michael Faraday in 1830.

Electromagnetic Induction: Topics Covered

Exercise	Topics Covered
6.1	Introduction To Electromagnetic Induction
6.2	The Experiments Of Faraday And Henry
6.3	Magnetic Flux
6.4	Faraday’s Law Of Induction
6.5	Lenz’s Law And Conservation Of Energy
6.6	Motional Electromotive Force
6.7	Inductance
6.8	AC Generator

Electromagnetic Induction: Formulas

• Faraday's Law of Electromagnetic Induction: $\mathcal{E}=-{\displaystyle \frac{d{\mathrm{\Phi }}_B}{dt}}$
• Lenz's Law: $\mathcal{E}=-{\displaystyle \frac{d{\mathrm{\Phi }}_B}{dt}}$
• Energy stored in an inductor: $U={\displaystyle \frac{1}{2}}L{I}^2$
• Magnetic flux:  ${\mathrm{\Phi }}_B=\mathbf{B}\cdot \mathbf{A}=BA\cos \theta$

Chapter 7: Alternating Current

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The movement of electric charge is what defines electric current. While direct current involves charge flowing in a single direction, alternating current periodically changes the direction of flow.

Alternating Current: Topics Covered

Exercise	Topics Covered
7.1	Introduction To Alternating Current
7.2	AC Voltage Applied To A Resistor
7.3	Representation Of AC Current And Voltage By Rotating Vectors — Phasors
7.4	AC Voltage Applied To An Inductor
7.5	AC Voltage Applied To A Capacitor
7.6	AC Voltage Applied To A Series LCR Circuit
7.7	Power In AC Circuit: The Power Factor
7.8	Transformers

Alternating Current: Formulas

• Phase Angle in an RLC Circuit: $\tan \varphi ={\displaystyle \frac{X_L-X_C}{R}}$
• Alternating Current (AC) Voltage: $v(t)=V_0\sin (\omega t+\varphi )$
• Root Mean Square (RMS) Value of AC Voltage: $V_{\text{rms}}={\displaystyle \frac{V_0}{\sqrt{2}}}$
• Root Mean Square (RMS) Value of AC Current: $I_{\text{rms}}={\displaystyle \frac{I_0}{\sqrt{2}}}$
• Impedance in an RLC Circuit: $Z=\sqrt{R^2+(X_L-X_C{)}^2}$

Chapter 8: Electromagnetic Waves

Electromagnetic Waves Class 12 NCERT Solutions cover all the topics and concepts included in the Chapter. NCERT Solutions for Physics Chapter 8 Electromagnetic Waves are designed by subject matter experts and provide a comprehensive understanding of each topic. Electromagnetic Waves Class 12 Question and Answers are an excellent resource for students preparing for their Class 12 board exams.

Energy transfer occurs through electromagnetic waves, which result from a magnetic field that changes, inducing an electric field that also changes. These waves comprise oscillating electric and magnetic fields that are perpendicular to one another. Unlike mechanical waves, electromagnetic waves can travel without requiring a medium to transmit. This characteristic allows them to propagate through a vacuum. Electromagnetic waves span a wide range of frequencies and include radio waves, microwaves, infrared waves, visible light, ultraviolet light, X-rays, and gamma rays.

Electromagnetic Waves: Topics Covered

Exercise	Topics Covered
8.1	Introduction To Electromagnetic Waves
8.2	Displacement Current
8.3	Electromagnetic Waves
8.4	Electromagnetic Spectrum

Electromagnetic Waves: Important Formulas

• Energy Density of an Electromagnetic Wave: $u={\displaystyle \frac{1}{2}}{ϵ}_0{E}^2+{\displaystyle \frac{1}{2}}{\displaystyle \frac{B^2}{{\mu }_0}}$
• Speed of Electromagnetic Waves: $c={\displaystyle \frac{1}{\sqrt{{\mu }_0{ϵ}_0}}}$

Chapter 9: Ray Optics and Optical Instruments

Physics can be a challenging subject for some students, and the Class 12 Ray Optics and Optical Instruments NCERT solutions given on this page provide step-by-step explanations to help students understand the concepts in a better way. By solving the Ray Optics and Optical Instruments Class 12 Important Questions, students can gain a better understanding of the type of questions that may appear in the exams, and they can prepare accordingly. The Ray Optics and Optical Instruments Class 12 PDF is also available here for download.

The study of how light behaves as it travels in rays or straight lines is known as ray optics. Optical instruments are objects that control and measure light using the concepts of ray optics. They include prisms, mirrors, lenses, and other instruments that allow light to be focused, dispersed, or redirected. Telescopes, microscopes, cameras, binoculars, and spectrometers are a few examples of optical equipment that are frequently used. Understanding the behaviour of light in optical instruments requires knowledge of ray optics.

Ray Optics and Optical Instruments: Topics Covered

Exercise	Topics Covered
9.1	Introduction To Ray Optics And Optical Instruments
9.2	Reflection Of Light By Spherical Mirrors
9.3	Refraction
9.4	Total Internal Reflection
9.5	Refraction At Spherical Surfaces And By Lenses
9.6	Refraction Through A Prism
9.7	Optical Instruments

Ray Optics and Optical Instruments: Important Formulas

• Lens Formula: ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}-{\displaystyle \frac{1}{u}}$
• Mirror Equation: ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{v}}+{\displaystyle \frac{1}{u}}$
• Snell's Law: $n_1\sin {\theta }_1=n_2\sin {\theta }_2$
• Lens Maker's Formula: ${\displaystyle \frac{1}{f}}=(n-1)({\displaystyle \frac{1}{R_1}}-{\displaystyle \frac{1}{R_2}})$
• Magnification for Mirrors and Lenses: $m={\displaystyle \frac{h^{\prime }}{h}}={\displaystyle \frac{v}{u}}$
• Power of a Lens: $P={\displaystyle \frac{1}{f}}$
• Critical Angle: $\sin {\theta }_c={\displaystyle \frac{1}{n}}$

Chapter 10: Wave Optics

The branch of optics known as wave optics deals with the study of the behaviour of light as a wave. In wave optics, phenomena such as propagation, diffraction, interference, and polarisation of light beams are analysed. Wave optics is based on the understanding that light is an electromagnetic wave that travels through space.

Wave Optics: Topics Covered

Exercise	Topics Covered
10.1	Introduction To Wave Optics
10.2	Huygens Principle
10.3	Refraction And Reflection Of Plane Waves Using Huygens' Principle
10.4	Coherent And Incoherent Addition Of Waves
10.5	Interference Of Light Waves And Young’s Experiment
10.6	Diffraction
10.7	Polarisation

Wave Optics: Formulas

• Fringe Width: $\beta ={\displaystyle \frac{\lambda D}{d}}$
• Condition for Minima: $a\sin \theta =n\lambda$
• Path Difference: $\mathrm{\Delta }x=d\sin \theta$
• Intensity of Interference Fringes: $I=I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi$
• Condition for Constructive Interference (Bright Fringes): $\mathrm{\Delta }x=n\lambda$
• Condition for Destructive Interference (Dark Fringes): $\mathrm{\Delta }x=(n+{\displaystyle \frac{1}{2}})\lambda$

Chapter 11: Dual Nature of Radiation and Matter

Physics can have some complex topics, and the Physics Chapter 11 Class 12 exercise solutions can provide clarity on these topics by breaking them down into simpler steps. By referring to the Dual Nature of Radiation and Matter Class 12 numerical solutions and solving the exercise solutions, students can develop their analytical skills and learn to think critically about problems and their solutions. The Dual Nature of Radiation and Matter Class 12 NCERT pdf is also available here.

The dual nature of radiation and matter is the concept that describes the behaviour of both particles and waves at the atomic and subatomic level. In the early 20th century, experiments showed that both light and matter exhibit both particle-like and wave-like behaviour, leading to the development of the theory of quantum mechanics.

Dual Nature of Radiation and Matter: Topics Covered

Exercise	Topics Covered
11.1	Introduction to Dual Nature Of Radiation And Matter
11.2	Electron Emission
11.3	Photoelectric Effect
11.4	Experimental Study Of Photoelectric Effect
11.5	Photoelectric Effect And Wave Theory Of Light
11.6	Einstein’s Photoelectric Equation: Energy Quantum Of Radiation
11.7	Particle Nature Of Light: The Photon
11.8	Wave Nature Of Matter

Dual Nature of Radiation and Matter: Formulas

• De Broglie Wavelength: $\lambda ={\displaystyle \frac{h}{p}}={\displaystyle \frac{h}{mv}}$
• Einstein's Photoelectric Equation: $E=h\nu$
• Threshold Frequency: ${\nu }_0={\displaystyle \frac{\varphi }{h}}$
• Momentum of a Photon: $p={\displaystyle \frac{E}{c}}={\displaystyle \frac{h\nu }{c}}={\displaystyle \frac{h}{\lambda }}$
• Photoelectric Equation: $K_{\text{max}}=h\nu -\varphi$

Chapter 12: Atoms

Atoms Physics Class 12 NCERT Solutions offer a variety of problems that cover different aspects of the subject, providing students with a comprehensive understanding of the concepts. By solving the Atoms Class 12 Solutions, students can develop their analytical skills and learn to think critically about problems and their solutions. Class 12 Physics Atoms PDF is also available for download here.

Atoms are the basic building blocks of matter, consisting of a central nucleus made up of protons and neutrons, with electrons orbiting around it in shells or energy levels. Atoms are incredibly small, with diameters on the order of a few tenths of a nanometer.

Atoms: Topics Covered

Exercise	Topics Covered
12.1	Introduction To Atoms
12.2	Alpha-Particle Scattering And Rutherford’s Nuclear Model Of Atom
12.3	Atomic Spectra
12.4	Bohr Model Of The Hydrogen Atom
12.5	The Line Spectra Of The Hydrogen Atom
12.6	De Broglie’s Explanation Of Bohr’s Second Postulate Of Quantisation

Atoms: Important Formulas

• Frequency of Radiation Emitted or Absorbed (Bohr's Frequency Condition): $h\nu =E_i-E_f$

• Wavelength of Emitted or Absorbed Light (Rydberg Formula): ${\displaystyle \frac{1}{\lambda }}=R({\displaystyle \frac{1}{n_1^2}}-{\displaystyle \frac{1}{n_2^2}})$

Chapter 13: Nuclei

Class 12 Physics Chapter Nuclei NCERT Solutions can be a great way for students to learn and master the subject, and prepare themselves for exams and future studies. The Nuclei Class 12 NCERT solutions provide additional practice for students, and they can use them to practise and reinforce their understanding of the concepts. Class 12 Nuclei Solutions are provided in PDF format on this page.

A nucleus is the centre core of an atom in physics, and it is made up of protons and neutrons. The neutrons are electrically inert, whereas the protons have a positive charge. The mass number of the nucleus is determined by adding the protons and neutrons together, whereas the number of protons in the nucleus determines the atomic number of the element. The strong nuclear force, one of the four basic forces of nature, holds nuclei together.

Nuclei: Topics Covered

Exercise	Topics Covered
13.1	Introduction To Nuclei
13.2	Atomic Masses And Composition Of Nucleus
13.3	Size Of The Nucleus
13.4	Mass-Energy And Nuclear Binding Energy
13.5	Nuclear Force
13.6	Radioactivity
13.7	Nuclear Energy

Nuclei: Important Formulas

• Mass Defect: $\mathrm{\Delta }m=(Z{m}_p+N{m}_n)-m_{\text{nucleus}}$

• Binding Energy per Nucleon: $E_{\text{bn}}={\displaystyle \frac{E_b}{A}}$
• Mass-Energy Equivalence: $E=m{c}^2$

• Radioactive Decay Law: $N(t)=N_0{e}^{-\lambda t}$

• Activity (Rate of Decay): $A=\lambda N$

Chapter 14: Semiconductor Electronics: Materials, Devices and Simple Circuits

Find below the topics covered in this chapter:

Semiconductor Electronics: Materials, Devices and Simple Circuits: Topics Covered

Exercise	Topics Covered
14.1	Introduction To Semiconductor Electronics
14.2	Classification Of Metals, Conductors And Semiconductors
14.3	Intrinsic Semiconductor
14.4	Extrinsic Semiconductor
14.5	P-N Junction
14.6	Semiconductor Diode
14.7	Application Of Junction Diode As A Rectifier

Semiconductor Electronics: Materials, Devices and Simple Circuits - Important Formulas

• Ohm's Law for Semiconductor: $V=IR$

• Resistance of a Semiconductor: $R={\displaystyle \frac{\rho L}{A}}$
• Conductivity: $\sigma ={\displaystyle \frac{1}{\rho }}=nq\mu$
• Total Current in a Semiconductor: $I=I_n+I_p=nq{\mu }_{n}E+pq{\mu }_{p}E$

• Intrinsic Carrier Concentration: $n_i=\sqrt{N_c{N}_v}{e}^{-{\displaystyle \frac{E_g}{2kT}}}$