About NCERT Solutions for Class 12 Physics
Chapter-wise solved exercises, key formulas, mark distribution, and expert study strategies — everything you need to score 95+ in your board exams.
Chapters (Part I + II)-15 Theory Marks (Board)-70
Practical Marks-30 Exam Duration-3 hrs
Your Complete Guide to NCERT Solutions for Class 12 Physics
NCERT Class 12 Physics is not just a textbook — it is the single most authoritative resource for CBSE board examinations and the primary reference for JEE Main, JEE Advanced, and NEET. The challenge most students face is not a lack of resources but an overload of low-quality answers that skip conceptual reasoning and jump straight to numerical answers.
Myclass24's NCERT Solutions for Class 12 Physics are different. Every answer walks you through the why before the how, ensuring you understand the physics behind each problem. This is the difference between a student who memorises solutions and a student who actually understands the subject — and that difference shows up in board marks, JEE ranks, and NEET scores.
Class 12 Physics is divided into two textbooks. Part I covers Electrostatics, Current Electricity, Magnetism, Electromagnetic Induction, and Alternating Currents. Part II covers Electromagnetic Waves, Optics, Dual Nature of Radiation, Atoms, Nuclei, and Semiconductor Electronics. Together, they span 15 chapters and approximately 200 in-text + exercise questions.
Smart Study Note: CBSE typically lifts 60–70% of board exam questions directly from NCERT exercises and examples. Solving every question in your NCERT textbook is not optional — it is the baseline minimum for scoring above 85%.
NCERT Solutions for Class 12 Physics – Chapter-wise List
Chapter No. | Chapter Name |
|---|---|
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | Semiconductor Electronics: Materials, Devices, and Simple Circuits |
NCERT Solutions for Class 12 Physics – Units Overview
| Unit | Key Subtopics Covered | Types of Questions in NCERT Solutions |
|---|---|---|
| 1. Electrostatics | Electric charges & fields, Coulomb’s law, Gauss’s law, electric potential, capacitors, energy stored in capacitors | Derivations (electric field, potential), numerical problems on capacitors & potential, proof-based questions |
| 2. Current Electricity | Electric current, Ohm’s law, resistivity & conductivity, combination of resistors, Kirchhoff’s rules, Wheatstone bridge, meter bridge | Numerical problems on circuits, derivations of resistance formulas, and application-based questions |
| 3. Magnetic Effects of Current & Magnetism | Biot–Savart law, Ampere’s law, motion of charged particles in magnetic fields, magnetic dipole, Earth’s magnetism, galvanometer | Derivations (field due to current), numerical problems on force & torque, diagram-based questions |
| 4. Electromagnetic Induction & Alternating Current | Faraday’s laws, Lenz’s law, self & mutual induction, AC circuit (LC, LCR), resonance, transformers | Numericals on induced emf & AC circuits, derivations of resonance condition, application problems |
| 5. Electromagnetic Waves | Displacement current, Maxwell’s equations (qualitative), characteristics of EM waves, spectrum | Conceptual & theoretical questions, spectrum-based questions |
| 6. Optics | Reflection, refraction, lens & mirror formula, total internal reflection, wave optics (interference, diffraction, polarization) | Ray diagrams, derivations (lens/mirror formula), numericals on optical instruments, wave theory proofs |
| 7. Dual Nature of Radiation & Matter | Photoelectric effect, Einstein’s photoelectric equation, de Broglie hypothesis, electron emission | Numericals on photoelectric effect, conceptual questions on de Broglie wavelength |
| 8. Atoms | Rutherford’s experiment, Bohr’s model, energy levels, hydrogen spectrum, spectral series | Derivations of energy levels, numerical problems on frequency/wavelength, and theory questions |
| 9. Nuclei | Properties of the nucleus, radioactivity, nuclear decay, half-life, nuclear reactions, and binding energy | Numericals on decay constant, half-life, binding energy, and conceptual application questions |
| 10. Semiconductor Electronics | Intrinsic & extrinsic semiconductors, p-n junction diode, Zener diode, transistor, logic gates, digital electronics | Circuit-based questions, truth tables, characteristics of devices, application-based numericals |
Table 1 — Master Formula Sheet: All Key Equations
Memorising formulas without understanding their origin is a short-term strategy. However, having a clean reference of all important equations — with their variables clearly defined — saves revision time significantly. Below is the most complete formula table you will find for Class 12 Physics NCERT.
| Chapter | Concept | Formula | Key Variables |
|---|---|---|---|
| Ch 1 – Electrostatics | Coulomb's Law | F = kq₁q₂/r² | k = 9×10⁹ N·m²/C²; q = charge; r = distance |
| Ch 1 – Electrostatics | Electric Field (Gauss's Law) | ∮E·dA = Qenc/ε₀ | ε₀ = 8.85×10⁻¹² C²/N·m² |
| Ch 2 – Capacitance | Energy in Capacitor | U = ½CV² = Q²/2C | C = capacitance (F); V = voltage; Q = charge |
| Ch 3 – Current Electricity | Drift Velocity | vd = eEτ/m | τ = relaxation time; e = 1.6×10⁻¹⁹ C; m = mass of electron |
| Ch 4 – Magnetism | Biot-Savart Law | dB = (μ₀/4π)(Idl×r̂)/r² | μ₀ = 4π×10⁻⁷ T·m/A; I = current; r = distance |
| Ch 4 – Magnetism | Force on Current-Carrying Wire | F = BIL sinθ | B = magnetic field; I = current; L = length; θ = angle |
| Ch 6 – EMI | Faraday's Law | ε = −dΦB/dt | ΦB = magnetic flux (Weber); ε = induced EMF |
| Ch 6 – EMI | Self Inductance | ε = −L(dI/dt) | L = self inductance (Henry); I = current |
| Ch 7 – AC | Impedance of LCR Circuit | Z = √[R² + (XL−XC)²] | XL = ωL; XC = 1/ωC; ω = angular frequency |
| Ch 7 – AC | Resonant Frequency | fr = 1/(2π√LC) | L = inductance; C = capacitance |
| Ch 9 – Ray Optics | Lens Maker's Equation | 1/f = (n−1)[1/R₁ − 1/R₂] | n = refractive index; R₁, R₂ = radii of curvature |
| Ch 10 – Wave Optics | YDSE Fringe Width | β = λD/d | λ = wavelength; D = slit-to-screen distance; d = slit separation |
| Ch 11 – Dual Nature | Einstein's Photoelectric Equation | KEmax = hν − φ | h = 6.626×10⁻³⁴ J·s; ν = frequency; φ = work function |
| Ch 11 – Dual Nature | de Broglie Wavelength | λ = h/mv = h/p | m = mass; v = velocity; p = momentum |
| Ch 12 – Atoms | Bohr's Radius (nth orbit) | rn = n²a₀/Z | a₀ = 0.529 Å (Bohr radius); Z = atomic number |
| Ch 12 – Atoms | Energy of nth Orbit | En = −13.6 Z²/n² eV | n = principal quantum number; Z = atomic number |
| Ch 13 – Nuclei | Radioactive Decay Law | N = N₀e−λt | λ = decay constant; N₀ = initial nuclei; t = time |
| Ch 13 – Nuclei | Half-Life | T½ = 0.693/λ | λ = decay constant |
| Ch 13 – Nuclei | Binding Energy per Nucleon | BE = Δm × 931.5 MeV | Δm = mass defect (in u); 1 u = 931.5 MeV/c² |
Chapter-Wise NCERT Solutions For Class 12 Physics
Chapter 1: Electrostatics
Electrostatics forms the foundation of the electricity section in Class 12 Physics. This chapter covers electric charges, Coulomb’s law, electric field and electric lines of force, Gauss’s law, electric potential, potential difference, and capacitors. Students also learn about energy stored in capacitors, parallel plate capacitors, and a combination of capacitors in series and parallel. The NCERT Solutions explain the derivation of the electric field due to a point charge, a line of charge, and a spherical shell, as well as the potential at a point due to point charges. Questions in this chapter typically include numerical problems on electric field and potential, proving properties using Gauss’s law, and application-based examples like charge distribution and potential energy calculations. Word problems often connect electrostatics to real-life scenarios such as capacitors in circuits.
Conceptual questions test understanding of field lines, potential, and properties of conductors and insulators. The NCERT Solutions guide students step by step, ensuring a clear understanding of the vector concepts involved in electric field calculations. Mastery of this chapter is crucial as it forms the basis for current electricity, magnetism, and electrostatic applications in modern technology. Regular practice improves problem-solving skills, derivation accuracy, and conceptual clarity, making it easier to handle both board exam and competitive exam questions.
Chapter 2: Current Electricity
Current Electricity focuses on the flow of electric charges through conductors. Subtopics include electric current, Ohm’s law, resistivity and conductivity, combination of resistors, and temperature dependence of resistance. Students also study Kirchhoff’s laws, Wheatstone bridge, meter bridge, and potentiometer, which are widely used in experiments and practical applications. NCERT Solutions cover derivations of resistance formulas, calculation of equivalent resistance in series and parallel combinations, and numerical problems on circuits. Questions are often framed around solving complex networks using Kirchhoff’s laws, finding currents, voltages, and verifying bridge balance.
Conceptual questions include explaining current flow, potential drop across resistors, and the working principle of a potentiometer. Higher-order problems combine circuit analysis with practical applications, such as determining energy consumption and internal resistance of a cell. The NCERT Solutions provide stepwise approaches, diagrams, and tips to solve problems efficiently. This chapter lays the foundation for magnetism, electromagnetic induction, and AC circuits, making it a critical part of Class 12 Physics preparation. Practising these solutions ensures students gain accuracy, speed, and confidence in solving numerical problems.
Chapter 3: Magnetic Effects of Current and Magnetism
This chapter introduces the magnetic field and its interaction with electric currents. Subtopics include Biot–Savart law, Ampere’s circuital law, magnetic field due to current-carrying conductors, force on a moving charge, torque on a current loop, and Earth’s magnetism. Students also study the magnetic dipole, solenoid, and galvanometer. NCERT Solutions explain derivations such as the magnetic field on the axis of a circular coil, torque on a rectangular current loop, and magnetic moment.
Questions include numerical problems on force, torque, and field calculations, proving vector properties, and conceptual questions on the direction of the magnetic field using the right-hand rule. Word problems often link magnetic effects to real-life applications, such as measuring current in a galvanometer or understanding electromagnetic devices. This chapter builds a bridge between current electricity and electromagnetic induction, preparing students for advanced topics in AC circuits and electronics. Regular practice of NCERT Solutions helps students master vector calculations, diagrams, and derivations, which are heavily tested in board and competitive exams.
Chapter 4: Electromagnetic Induction and Alternating Currents
Electromagnetic induction explains the production of induced emf and current in a circuit due to changing magnetic flux. Subtopics include Faraday’s law, Lenz’s law, self and mutual induction, eddy currents, and AC circuits, including LC, LCR circuits, resonance, and transformers. NCERT Solutions provide stepwise derivations for induced emf, reactance calculations, and resonance conditions.
Questions range from numerical problems on AC, voltage, impedance, and phase relationships, to conceptual questions on Lenz’s law and energy considerations in transformers. Application-based problems link electromagnetic induction to electric generators, induction coils, and power distribution systems. Students are also guided on solving complex AC circuits using phasor diagrams. Practising these solutions ensures clarity in derivation methods, formula application, and logical reasoning, which is crucial for both board exams and competitive exams like JEE, where AC circuits and resonance problems are common.
Chapter 5: Electromagnetic Waves
This chapter introduces Maxwell’s equations (qualitative) and displacement current, describing how changing electric and magnetic fields propagate as electromagnetic waves. Subtopics include characteristics of EM waves, the spectrum of EM waves, and their applications in communication. NCERT Solutions focus on conceptual clarity, explaining wave propagation, transverse nature, and speed of EM waves. Questions are mostly theoretical, testing understanding of wave properties, energy transport, and applications. Students also solve numerical problems on frequency and wavelength in various media. This chapter provides the foundation for modern technologies like radio, radar, and mobile communication, and links to optics and wave theory.
Chapter 6: Optics
Optics in Class 12 Physics focuses on the behaviour of light and its interaction with matter. This chapter is divided into ray optics and wave optics. Ray optics covers reflection and refraction of light, lens and mirror formulas, total internal reflection, refraction through prisms, and optical instruments like microscopes and telescopes. Wave optics introduces interference, diffraction, and polarisation, emphasising the wave nature of light. NCERT Solutions provide step-by-step derivations of lens/mirror formulas, magnification, and conditions for constructive and destructive interference.
Students also practice numerical problems on focal length, image formation, fringe width, and diffraction minima. Conceptual questions involve explaining optical phenomena, the behaviour of light in different media, and the resolving power of optical instruments. Application-based questions link optics to lasers, fibre optics, and modern communication devices. Diagrams are an essential part of this chapter, and the NCERT Solutions guide students in accurate diagrammatic representation for better understanding. Practising these solutions helps in mastering derivations, solving numerical problems quickly, and answering conceptual questions confidently, which are heavily tested in board exams and competitive exams.
Chapter 7: Dual Nature of Radiation and Matter
This chapter explores the particle-like and wave-like behaviour of light and matter. Subtopics include the photoelectric effect, Einstein’s photoelectric equation, matter waves, and the de Broglie hypothesis. NCERT Solutions explain derivations for the photoelectric equation, calculation of stopping potential, and de Broglie wavelength. Questions include numerical problems on the kinetic energy of photoelectrons, threshold frequency, and wavelength of particles. Conceptual questions test understanding of wave-particle duality and experimental evidence. Application-based problems link these concepts to electron microscopes and modern quantum devices. This chapter is crucial for students preparing for higher studies in physics, engineering, and technology, as it forms the foundation of quantum mechanics.
Chapter 8: Atoms
The Atoms chapter introduces atomic models and structure. Key topics include Rutherford’s nuclear model, Bohr’s theory of the hydrogen atom, energy levels, spectral series, and line spectra. NCERT Solutions provide derivations for energy levels, orbital radius, and frequencies of spectral lines. Questions range from numerical problems on energy transitions, wavelength calculations, and radius of orbits to conceptual questions on atomic structure and spectral lines. Students also solve application-based problems on identifying spectral series and emission spectra. Understanding this chapter is essential for modern physics topics like nuclear energy and quantum mechanics.
Chapter 9: Nuclei
This chapter deals with nuclear structure and radioactivity. Subtopics include properties of nuclei, nuclear forces, radioactivity, decay laws, half-life, binding energy, and nuclear reactions (fission and fusion). NCERT Solutions cover derivations for decay constant, half-life, and energy released in nuclear reactions. Numerical problems involve calculating the remaining quantity of a radioactive substance, the energy released, and the binding energy per nucleon. Conceptual questions test understanding of the stability of nuclei, nuclear forces, and applications of nuclear energy. This chapter is important for both board exams and entrance exams, especially when solving radioactive decay and nuclear reaction numericals.
Chapter 10: Semiconductor Electronics
Semiconductor Electronics introduces semiconductors and their applications in modern electronics. Subtopics include intrinsic and extrinsic semiconductors, p-n junction diode, Zener diode, transistor (CE, CB), logic gates, and digital electronics.
NCERT Solutions explain circuit diagrams, diode and transistor characteristics, and truth tables for logic gates. Questions include deriving input-output relationships, solving circuit problems, and application-based scenarios like rectifiers and amplifiers. Conceptual questions test the working principles of devices and their applications in communication and electronics. This chapter connects theoretical concepts with practical electronic devices, making it highly relevant for both exams and real-world understanding of electronics.
Perfect! Here’s the final set of Class 12 Physics chapters (11 to 14) explained in ~300 words each, covering subtopics, derivations, and types of questions:
Chapter 11: Three-Dimensional Geometry
(Note: In Physics, this chapter is part of Maths, so for Physics, we continue with the remaining units.)
Since Class 12 Physics has 14 chapters, the remaining ones are: Electromagnetic Waves (already covered), Optics (covered), Dual Nature of Matter (covered), Atoms (covered), Nuclei (covered), Semiconductor Electronics (covered).
Chapter 12: Communication Systems
Communication Systems introduces students to how information is transmitted over distances using electrical and electromagnetic methods. Subtopics include basic elements of communication (transmitter, channel, receiver), bandwidth, modulation (AM, FM), and the propagation of electromagnetic waves. Students also study noise, signal-to-noise ratio, and the principles of optical fiber and satellite communication.
NCERT Solutions explain diagrams of communication systems, derivations for modulation and bandwidth requirements, and numerical problems related to wave frequencies. Conceptual questions often include explaining the working of AM/FM transmitters, the advantages of different modulation techniques, and the effects of noise. Application-based problems link theory to real-life communication technologies like mobile phones, radio, television, and internet communication. Practicing these solutions helps students understand modern communication devices and signal transmission, which are important in board exams and for foundational knowledge in electronics and telecommunications.
Table 2 — Chapter-wise Important Laws, Theorems & Principles
Beyond formulas, CBSE board exams test your understanding of fundamental laws and their statements. These are the definitions and principles that appear in 2-mark and 3-mark questions year after year.
| Chapter | Law / Theorem / Principle | What It States (in one line) | Exam Relevance |
|---|---|---|---|
| Ch 1 | Gauss's Law | Net electric flux through a closed surface equals enclosed charge divided by ε₀. | 3–5 Marks |
| Ch 2 | Superposition Principle | Net electric field or potential is the vector/scalar sum of individual contributions. | 2–3 Marks |
| Ch 3 | Kirchhoff's Current Law (KCL) | Sum of currents entering a junction equals sum of currents leaving it. | 3–5 Marks |
| Ch 3 | Kirchhoff's Voltage Law (KVL) | Sum of EMFs in a closed loop equals sum of voltage drops in that loop. | 3–5 Marks |
| Ch 4 | Ampere's Circuital Law | Line integral of magnetic field around a closed loop equals μ₀ times enclosed current. | 3 Marks |
| Ch 6 | Lenz's Law | Induced current always opposes the change in magnetic flux that causes it. | 2–3 Marks |
| Ch 6 | Faraday's Law of EMI | Induced EMF is directly proportional to the rate of change of magnetic flux. | 3–5 Marks |
| Ch 9 | Snell's Law of Refraction | n₁ sinθ₁ = n₂ sinθ₂ — ratio of sines of angles equals inverse ratio of refractive indices. | 2–3 Marks |
| Ch 10 | Huygens' Principle | Every point on a wavefront acts as a fresh source of secondary spherical wavelets. | 2–3 Marks |
| Ch 10 | Malus's Law | Intensity of polarised light after passing through analyser: I = I₀cos²θ. | 2 Marks |
| Ch 11 | Einstein's Photoelectric Law | Maximum kinetic energy of emitted electrons = photon energy minus work function. | 3–5 Marks |
| Ch 12 | Bohr's Postulates | Electrons orbit in fixed shells; energy emitted/absorbed equals difference between shell energies. | 3–5 Marks |
| Ch 13 | Radioactive Decay Law | Rate of disintegration is proportional to the number of undecayed nuclei at any instant. | 3–5 Marks |
| Ch 14 | p-n Junction Principle | Depletion layer forms at junction; forward bias reduces and reverse bias increases barrier potential. | 3 Marks |
Table 3 — CBSE Class 12 Physics Mark Distribution (Unit-wise)
CBSE publishes an official unit-wise weightage every year. Understanding how marks are distributed helps you allocate revision time intelligently — spending equal time on every chapter is one of the most common mistakes high-stakes students make.
| Unit No. | Unit Name | Chapters Covered | Marks (Theory) | Priority |
|---|---|---|---|---|
| Unit I | Electrostatics | Ch 1, Ch 2 | 16 Marks | 🔴 Very High |
| Unit II | Current Electricity | Ch 3 | 7 Marks | 🔴 Very High |
| Unit III | Magnetic Effects of Current & Magnetism | Ch 4, Ch 5 | 8 Marks | 🟡 High |
| Unit IV | Electromagnetic Induction & Alternating Currents | Ch 6, Ch 7 | 10 Marks | 🔴 Very High |
| Unit V | Electromagnetic Waves | Ch 8 | 3 Marks | 🟢 Moderate |
| Unit VI | Optics | Ch 9, Ch 10 | 14 Marks | 🔴 Very High |
| Unit VII | Dual Nature of Radiation & Matter | Ch 11 | 4 Marks | 🟡 High |
| Unit VIII | Atoms and Nuclei | Ch 12, Ch 13 | 6 Marks | 🟡 High |
| Unit IX | Electronic Devices & Communication | Ch 14, Ch 15 | 2 Marks | 🟢 Low effort, Easy Marks |
| Total Theory Marks | 70 Marks | |||
CBSE Class 12 Physics Board Exam Complete Exam Info
Internal choice is provided in Section B (2 out of 7), Section C (2 out of 5), and Section E (all 3 long-answer questions). Candidates must attempt all 18 MCQs in Section A — no internal choice there.
How to Actually Use NCERT Solutions to Score Above 90%
Having NCERT Solutions is only 20% of the job. How you use them is the remaining 80%. Most students open NCERT solutions only when they are stuck — but that is reactive learning. The students who consistently score 90+ use NCERT solutions proactively, as a learning framework rather than an answer key.
Step 1: Concept First, Solution Second
Before reading any solved example or exercise answer, attempt the problem yourself. Even a rough, incorrect attempt forces your brain to engage with the question structure. When you then read the solution, you will immediately understand exactly where your reasoning diverged — and that is where the learning happens.
Step 2: Identify the Formula's Derivation
In Class 12 Physics, CBSE frequently asks you to derive formulas — not just apply them. Derivations for Gauss's Law (cylindrical and spherical), Biot-Savart Law applied to a circular loop, mirror/lens formulas, and the expression for energy in a magnetic field are all standard board-exam questions. NCERT textbook derivations are concise and board-aligned. Do not substitute them with longer derivations from coaching institutes.
Step 3: Solve All In-Text Examples Before Exercises
Many students skip the worked examples in NCERT and jump straight to the exercise problems at the end of each chapter. This is a mistake. The in-text examples are carefully chosen to demonstrate each major concept and solve a representative problem type. They are also directly quoted in board exams as "value-based" or "application-based" questions. Treat them as mandatory, not optional.
Step 4: Practise Numericals Chapter-Wise with Time Limits
Chapters 1, 3, 4, 7, 9, 12, and 13 are numerically intensive. For these chapters, time your solution attempts. A standard 5-mark numerical should take no more than 8–10 minutes in an exam. If you are consistently taking 15+ minutes, you need to practise more, not just revise theory.
- Make a separate notebook only for formulas and definitions — rewrite it after every chapter.
- Draw diagrams for every optics and magnetism problem, even simple ones. CBSE awards 1 mark for diagrams in 5-mark questions.
- For semiconductor electronics (Ch 14), make your own truth tables and practice drawing p-n junction I-V characteristic curves from memory.
- Do not ignore Alternating Current (Ch 7). LCR circuit numericals are a near-certain 5-mark question in board exams.
- Revise NCERT solutions 10 days before the exam — not the textbook, but your solved notebook.
- For Electromagnetic Waves (Ch 8), focus on the properties table and the EM spectrum; the chapter carries 3 marks and is theory-only.
- In Optics, practice both ray optics diagrams (mirrors, lenses, prism) and wave optics derivations (YDSE).
NCERT Solutions vs Coaching Notes: What Students Get Wrong
One of the most damaging misconceptions among Class 12 students is that NCERT Physics is "too basic" and must be supplemented with extensive coaching institute notes from the very beginning. This backwards approach leads to conceptual confusion because coaching notes assume NCERT-level understanding. The smarter sequence is: master NCERT first, then supplement selectively.
For students targeting board exam excellence (90%+), NCERT Solutions form 100% of the required content. For students also targeting JEE Mains Top 50k or NEET cutoffs, NCERT is still 70–75% of the work — advanced resources only bridge the remaining gap. The students who study NCERT solutions deeply and consistently outperform those who skim NCERT and rely on coaching notes for their primary understanding.