| Science NCERT Exemplar Solutions (Class 6th to 10th) | ||||||||||||||
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| 6th | 7th | 8th | 9th | 10th | ||||||||||
| Science NCERT Exemplar Solutions (Class 11th) | ||||||||||||||
| Physics | Chemistry | Biology | ||||||||||||
| Science NCERT Exemplar Solutions (Class 12th) | ||||||||||||||
| Physics | Chemistry | Biology | ||||||||||||
Class 12th Physics NCERT Exemplar Solutions
1. Electric Charges And Fields
This chapter introduces the fundamental concept of **electric charge**, its properties like quantisation and conservation, and the force between charges described by **Coulomb's Law** ($\textsf{F} = \textsf{k} \frac{\textsf{q}_1\textsf{q}_2}{\textsf{r}^2}$). It defines the **electric field** ($\vec{\textsf{E}}$) created by charges and represents it using electric field lines. The concept of an electric dipole is discussed. **Gauss's Law** ($\oint \vec{\textsf{E}} \cdot \textsf{d}\vec{\textsf{A}} = \frac{\textsf{q}_\text{enclosed}}{\varepsilon_0}$), a powerful tool in electrostatics, is introduced and applied to find electric fields due to simple charge distributions, providing a framework for understanding electrostatic interactions.
2. Electrostatic Potential And Capacitance
Building on electric fields, this chapter introduces **electrostatic potential** ($\textsf{V}$), the potential energy per unit charge, and **potential difference**. The relationship between electric field and potential ($\textsf{E} = -\frac{\textsf{dV}}{\textsf{dr}}$) is crucial. **Equipotential surfaces** and their properties are discussed. The concept of **capacitance** ($\textsf{C} = \frac{\textsf{Q}}{\textsf{V}}$), a measure of charge storage capacity, is explained. **Capacitors**, devices for storing electrical energy, their series and parallel combinations, and the **energy stored in a capacitor** ($\textsf{U} = \frac{1}{2}\textsf{CV}^2$) are covered, along with the effect of inserting a **dielectric** material.
3. Current Electricity
This chapter deals with **electric current**, the flow of electric charge. It defines current ($\textsf{I} = \frac{\textsf{dQ}}{\textsf{dt}}$) and **drift velocity**. **Ohm's Law** ($\textsf{V = IR}$) is fundamental, relating voltage, current, and resistance ($\textsf{R} = \rho\frac{\textsf{L}}{\textsf{A}}$). Concepts like resistivity ($\rho$), conductivity ($\sigma = \frac{1}{\rho}$), and their temperature dependence are discussed. **Kirchhoff's laws** (junction rule and loop rule) are applied to analyze complex circuits. The **heating effect of electric current** ($\textsf{H} = \textsf{I}^2\textsf{Rt}$) and **electric power** ($\textsf{P} = \textsf{VI}$) are explained. Cells, their internal resistance, and combinations are also covered, essential for circuit analysis.
4. Moving Charges And Magnetism
This chapter establishes the connection between electricity and magnetism: **moving charges create magnetic fields**. It introduces the magnetic field ($\vec{\textsf{B}}$) and the force on a moving charge in magnetic and electric fields, the **Lorentz force** ($\vec{\textsf{F}} = \textsf{q}(\vec{\textsf{E}} + \vec{\textsf{v}} \times \vec{\textsf{B}})$). The magnetic fields due to current-carrying wires are calculated using the **Biot-Savart Law** and **Ampere's Circuital Law**. Force on a current-carrying conductor, torque on a current loop, and the working of a **moving coil galvanometer** are explained. Concepts like the cyclotron and velocity selector are also introduced.
5. Magnetism And Matter
This chapter explores the magnetic properties of materials and Earth's magnetism. It discusses the magnetic field lines of a bar magnet and the concept of a magnetic dipole moment. **Earth's magnetism** and its components (magnetic declination, dip, horizontal intensity) are introduced. Different categories of **magnetic materials** – **diamagnetic**, **paramagnetic**, and **ferromagnetic** – are explained based on their behavior in external fields, relating macroscopic properties to microscopic structure and **Curie's Law**. The chapter also touches upon permanent magnets and electromagnets, highlighting how materials are chosen for specific magnetic applications.
6. Electromagnetic Induction
This chapter introduces **electromagnetic induction**, the phenomenon where a changing magnetic flux induces an electromotive force (emf) and current in a circuit. **Faraday's laws of induction** quantify the magnitude of the induced emf, while **Lenz's Law** determines its direction, stating that the induced current opposes the change that produces it. Concepts like **motional emf** (induced by movement in a magnetic field) and **self and mutual inductance** are explained. The chapter covers **eddy currents** and their applications/disadvantages, and discusses the working principle of the **AC generator**, a device that converts mechanical energy into electrical energy based on this principle.
7. Alternating Current
This chapter deals with **Alternating Current (AC)** and voltage, which vary periodically in magnitude and direction. It introduces concepts like instantaneous, peak, and RMS values of AC. Analysis of AC circuits containing resistors (R), inductors (L), and capacitors (C), individually and in series (LCR circuit), is done using phasor diagrams and impedance. Concepts like reactance, impedance, phase difference, **resonance** (in LCR circuits), Q-factor, and **power in AC circuits** are discussed. The chapter also explains the working principle of the **transformer**, a crucial device for stepping up or down AC voltages, vital for power transmission in India.
8. Electromagnetic Waves
This chapter introduces **electromagnetic waves**, non-mechanical waves that propagate through vacuum and media at the speed of light ($\textsf{c}$). They consist of oscillating electric and magnetic fields perpendicular to each other and the direction of propagation, predicted by **Maxwell's equations**. The chapter discusses their characteristics, including energy and momentum. The entire **electromagnetic spectrum**, from radio waves to gamma rays, is presented, highlighting the properties and diverse applications of different parts of the spectrum (communication, medical imaging, heating), showcasing the unified nature of electricity and magnetism in the form of radiation.
9. Ray Optics And Optical Instruments
This chapter treats light as rays propagating in straight lines, forming the basis of **ray optics** or geometric optics. It covers **reflection** from plane and spherical mirrors (laws of reflection, mirror formula $\frac{1}{\textsf{v}} + \frac{1}{\textsf{u}} = \frac{1}{\textsf{f}}$) and **refraction** as light passes between media (laws of refraction, **Snell's Law** $\textsf{n}_1 \sin \theta_1 = \textsf{n}_2 \sin \theta_2$, refraction through prism and lens). **Total internal reflection** and its applications are discussed. Image formation by lenses (lens formula $\frac{1}{\textsf{v}} - \frac{1}{\textsf{u}} = \frac{1}{\textsf{f}}$, power of a lens) and the working of optical instruments like the **human eye**, microscope, and telescope are covered.
10. Wave Optics
Moving beyond the ray model, this chapter explains optical phenomena using the **wave nature of light**. **Huygens' principle** is introduced to describe wave propagation and explain reflection/refraction. **Interference**, the superposition of waves resulting in constructive or destructive effects, is detailed, with **Young's double-slit experiment** as a classic demonstration of **wave interference** (fringe width $\beta = \frac{\lambda\textsf{D}}{\textsf{d}}$). **Diffraction**, the bending of waves around obstacles or through slits, is discussed (single slit diffraction). The chapter also introduces **polarization**, a property specific to transverse waves, and its methods and applications.
11. Dual Nature Of Radiation And Matter
This chapter explores the revolutionary concept of **wave-particle duality**, stating that both light (**radiation**) and **matter** (like electrons) exhibit properties of waves and particles. It discusses the **photoelectric effect**, which supports the particle nature of light (photons) and is explained by **Einstein's photoelectric equation** ($\textsf{h}\nu = \phi_0 + \textsf{KE}_\text{max}$). **De Broglie's hypothesis** ($\lambda = \frac{\textsf{h}}{\textsf{p}}$) proposes the wave nature of matter particles, experimentally confirmed by Davisson and Germer. This duality is a fundamental concept in quantum mechanics, changing our understanding of the universe's building blocks.
12. Atoms
This chapter delves into the structure of the atom, focusing on the **Bohr model** for the hydrogen atom. It discusses Rutherford's alpha scattering experiment leading to the nuclear model and its limitations. **Bohr's postulates** regarding quantized energy levels and angular momentum are explained. The chapter uses Bohr's theory to calculate the energy levels, radii, and velocities of electrons in hydrogen. The origin of atomic spectra, specifically the different **spectral series** (Lyman, Balmer, Paschen, Brackett, Pfund) of hydrogen, is explained based on electron transitions between energy levels, demonstrating the quantized nature of atomic energy.
13. Nuclei
This chapter focuses on the **atomic nucleus**, its composition (protons and neutrons), size, and mass. Concepts like **mass defect** ($\Delta \textsf{m}$) and **binding energy** ($\textsf{E}_\text{b} = \Delta \textsf{mc}^2$) are introduced to explain nuclear stability. **Radioactivity** – the spontaneous decay of unstable nuclei ($\alpha$, $\beta$, $\gamma$ emissions) – is discussed, along with the laws of radioactive decay ($N = N_0 e^{-\lambda t}$) and the concept of **half-life** ($T_{1/2}$). **Nuclear energy** released through **fission** (splitting heavy nuclei, used in nuclear reactors) and **fusion** (combining light nuclei, powering the sun) is explained, highlighting their immense energy potential and applications.
14. Semiconductor Electronics: Materials, Devices And Simple Circuits
This chapter introduces **semiconductors**, materials with electrical conductivity between conductors and insulators, forming the basis of modern electronics. It discusses energy bands in solids and classifies materials based on conductivity. **Intrinsic and extrinsic semiconductors** (p-type and n-type), formed by doping, are explained. The **p-n junction** and its behaviour under forward and reverse bias are detailed. Basic **semiconductor devices** like the **p-n junction diode** (as a rectifier) and the **transistor** (as an amplifier or switch) are covered. The chapter also introduces **logic gates** (AND, OR, NOT) as fundamental building blocks of digital circuits, crucial for the digital revolution impacting India and the world.
15. Communication Systems
This chapter provides an introduction to **communication systems**, which involve the transmission of information from a source to a destination. It describes the basic elements of a communication system: transmitter, channel, and receiver. Concepts like signals (analog and digital), modulation (the process of superimposing a low-frequency message signal onto a high-frequency carrier wave), and demodulation are explained. Different types of **modulation** (Amplitude Modulation - AM, Frequency Modulation - FM, Phase Modulation - PM) and the propagation of electromagnetic waves (ground, sky, space waves) are discussed, highlighting the principles behind modern communication technologies connecting people globally, including across India.
Sample Paper I
This entry provides **Sample Paper I**, a dedicated practice resource for students preparing for their Class 12th Physics examinations using the NCERT Exemplar Solutions. It offers a comprehensive collection of questions covering concepts, numerical problems, and theoretical aspects from all chapters (1-15). Attempting this sample paper under simulated exam conditions is highly beneficial for self-assessment, identifying weaker areas, improving problem-solving speed and accuracy, and building confidence for the actual board examination. It serves as a crucial step in the revision process.
Sample Paper II
This entry presents **Sample Paper II**, offering another valuable opportunity for students to practice and consolidate their understanding of the entire Class 12th Physics syllabus covered in the NCERT Exemplar Solutions (Chapters 1-15). This paper provides a fresh set of varied questions, allowing students to encounter different question types and difficulty levels. Engaging with both sample papers enables thorough revision, solidifying conceptual understanding, refining problem-solving strategies, and enhancing overall preparedness for achieving success in the Physics board examination.