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| Science NCERT Exemplar Solutions (Class 12th) | ||||||||||||||
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Class 12th Physics NCERT Exemplar Solutions
1. Electric Charges And Fields
This chapter lays the foundation of electrostatics by introducing the fundamental entity of electric charge and its intrinsic properties like conservation and quantisation. The force between static charges is quantified by Coulomb's Law, an inverse-square law given by $F = k \frac{|q_1 q_2|}{r^2}$. The concept of an electric field ($\vec{E}$) as a region of influence around a charge is developed. A major tool, Gauss's Law ($\oint \vec{E} \cdot d\vec{A} = \frac{q_{in}}{\varepsilon_0}$), is introduced, which elegantly relates the electric flux through a closed surface to the net charge enclosed. This law is then applied to calculate the electric fields for various symmetric charge distributions, such as a line charge or a spherical shell.
2. Electrostatic Potential And Capacitance
This chapter explores the energy aspects of electrostatics through the concepts of electrostatic potential ($V$) and potential energy. It establishes the crucial relationship between the electric field and potential ($E = -dV/dr$). The chapter then introduces capacitance ($C = Q/V$) as a measure of a conductor's ability to store charge and electrical energy. It provides a detailed analysis of capacitors, particularly the parallel plate capacitor, and examines how their capacitance is affected by the introduction of a dielectric medium. The principles of combining capacitors in series and parallel are discussed, along with the calculation of the energy stored in a capacitor ($U = \frac{1}{2}CV^2$).
3. Current Electricity
This chapter shifts from static charges to charges in motion, defining electric current. The microscopic model of current is explained through the concept of electron drift velocity. The fundamental relationship governing simple circuits, Ohm's Law ($V = IR$), is introduced, along with the concepts of resistance ($R$) and resistivity ($\rho$). For analyzing complex circuits, the chapter presents Kirchhoff's laws (the junction rule and the loop rule), which are based on the conservation of charge and energy. It also covers the heating effect of current, electric power ($P = VI$), and the practical aspects of electrical cells, including their internal resistance and combinations.
4. Moving Charges And Magnetism
This chapter unveils the profound connection between electricity and magnetism, establishing that moving charges produce magnetic fields. It defines the magnetic field ($\vec{B}$) and the total force on a charge in combined electric and magnetic fields, the Lorentz force: $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$. The chapter provides tools to calculate the magnetic field produced by currents, namely the Biot-Savart Law and Ampere's Circuital Law. These laws are used to find the fields for a straight wire, a circular loop, and a solenoid. The chapter also explores the torque on a current loop in a magnetic field, which is the working principle of the moving coil galvanometer.
5. Magnetism And Matter
This chapter explores magnetism as a property of matter itself. It begins with the behavior of bar magnets and their magnetic fields, introducing the concept of a magnetic dipole. A key focus is on Earth's magnetism, detailing its various components. The chapter provides a comprehensive classification of magnetic materials into three categories based on their response to an external magnetic field: diamagnetic, paramagnetic (obeying Curie's Law), and ferromagnetic materials. The microscopic origins of these properties are explained. The chapter concludes by discussing the properties of permanent magnets and electromagnets and their practical applications.
6. Electromagnetic Induction
This chapter introduces the phenomenon of electromagnetic induction (EMI), where a changing magnetic field induces an electric current. The principles are quantified by Faraday's laws of induction ($\mathcal{E} = -d\Phi_B/dt$), which relate the induced emf to the rate of change of magnetic flux. The direction of the induced current is determined by Lenz's Law, a consequence of the conservation of energy. The chapter explains the concepts of motional emf, self-inductance ($L$), and mutual-inductance ($M$). It also discusses practical applications and consequences of EMI, such as eddy currents and the working principle of the AC generator.
7. Alternating Current
This chapter provides a detailed analysis of circuits with Alternating Current (AC). It introduces the concepts of peak and RMS (root mean square) values for AC voltage and current. The behavior of AC circuits containing resistors (R), inductors (L), and capacitors (C) is analyzed individually and in combination, particularly the series LCR circuit, using the technique of phasors. Key concepts like reactance, impedance ($Z$), and phase angle are defined. The chapter explores the phenomenon of resonance in LCR circuits and discusses power in AC circuits, including the power factor. Finally, it explains the working principle of the transformer, a vital device for voltage conversion in power transmission.
8. Electromagnetic Waves
This chapter unifies the concepts of electricity and magnetism, presenting electromagnetic (EM) waves as their synthesis. Based on the theoretical framework of Maxwell's equations, it describes EM waves as transverse waves consisting of oscillating electric and magnetic fields. The chapter details their fundamental properties, such as their propagation at the speed of light in a vacuum ($c$) and their ability to transport energy and momentum. It provides a comprehensive overview of the entire electromagnetic spectrum, from radio waves to gamma rays, highlighting the sources, detection methods, and diverse applications of each region.
9. Ray Optics And Optical Instruments
This chapter, also known as geometric optics, treats light as rays travelling in straight lines. It covers the phenomena of reflection and refraction. Reflection from plane and spherical mirrors is analyzed using the mirror formula ($1/v + 1/u = 1/f$). Refraction is governed by Snell's Law ($n_1 \sin i = n_2 \sin r$). The chapter discusses the phenomenon of Total Internal Reflection (TIR) and its applications. It then details image formation by lenses, using the lens maker's formula and the thin lens formula. Finally, it explains the working principles of important optical instruments, including the human eye, microscopes, and telescopes, by combining these principles.
10. Wave Optics
This chapter explores phenomena that can only be explained by considering the wave nature of light. It introduces Huygens' principle as a method for analyzing wavefront propagation, which is used to derive the laws of reflection and refraction. The core of the chapter is the principle of superposition, which explains interference and diffraction. Young's double-slit experiment is presented as definitive proof of interference, with the derivation of the fringe width ($\beta = \lambda D/d$). The chapter also discusses diffraction at a single slit and introduces polarization as a phenomenon exclusive to transverse waves, confirming the transverse nature of light.
11. Dual Nature Of Radiation And Matter
This chapter introduces a cornerstone of modern physics: the wave-particle duality. It discusses experimental evidence that challenges the classical wave theory of light, primarily the photoelectric effect. This effect is explained by Einstein's theory, which postulates that light consists of energy packets called photons, leading to the photoelectric equation ($K_{max} = h\nu - \phi_0$). The chapter then presents de Broglie's hypothesis, which proposes that matter particles also exhibit wave-like properties, with a wavelength given by $\lambda = h/p$. This revolutionary idea, later confirmed experimentally, fundamentally changed our understanding of both matter and radiation.
12. Atoms
This chapter focuses on the structure of the atom, tracing the development of atomic models from early ideas to the quantum model. It discusses Rutherford's nuclear model and its shortcomings. The main focus is on the Bohr model for the hydrogen atom, which successfully introduced the concepts of quantized energy levels and stable electron orbits. Using Bohr's postulates, the chapter derives expressions for the radii and energy of these orbits. The model provides a compelling explanation for the origin of the discrete line spectra of hydrogen, detailing the various spectral series (Lyman, Balmer, etc.) as resulting from electron transitions between these quantized energy levels.
13. Nuclei
This chapter delves into the heart of the atom: the nucleus. It describes the composition of the nucleus (protons and neutrons) and its properties like size and density. The concepts of mass defect and binding energy are introduced, using Einstein's mass-energy relation ($E = \Delta m c^2$) to explain nuclear stability. The phenomenon of radioactivity (the spontaneous decay of unstable nuclei via $\alpha$, $\beta$, and $\gamma$ emission) is discussed, along with the law of radioactive decay ($N = N_0 e^{-\lambda t}$) and the concept of half-life. The chapter concludes by exploring the immense energy released in the nuclear processes of fission and fusion.
14. Semiconductor Electronics: Materials, Devices And Simple Circuits
This chapter provides an introduction to the materials that power modern technology: semiconductors. It explains the concept of energy bands in solids to differentiate between conductors, insulators, and semiconductors. The chapter details how the conductivity of intrinsic semiconductors can be dramatically increased by doping to create p-type and n-type extrinsic semiconductors. The formation and characteristics of a p-n junction are central, explaining its behavior under forward and reverse bias. This leads to an understanding of key semiconductor devices like the p-n junction diode (used as a rectifier) and an introduction to transistors and fundamental logic gates (AND, OR, NOT), the building blocks of digital electronics.
15. Communication Systems
This chapter explains the basic principles behind transmitting information over distances. It breaks down a communication system into its three essential components: a transmitter, a channel, and a receiver. The chapter discusses the need for modulation—the process of superimposing a low-frequency information signal onto a high-frequency carrier wave for efficient transmission. It describes the basics of different modulation schemes, primarily Amplitude Modulation (AM). The chapter also provides an overview of the different modes of propagation of electromagnetic waves (ground wave, sky wave, and space wave) used for broadcasting and communication.
Sample Paper I
This is the first comprehensive Sample Paper meticulously designed for Class 12 Physics. It serves as an invaluable tool for self-assessment, featuring a diverse collection of questions that span the entire syllabus from electrostatics to communication systems. By attempting this paper, students can simulate the examination environment, practice effective time management, and identify specific topics that require further revision. It is a critical resource for gauging one's preparation level and building the confidence needed to excel in the board examination.
Sample Paper II
This is the second Sample Paper in the series, offering another excellent opportunity for rigorous practice and comprehensive revision of the Class 12 Physics curriculum. It presents a fresh set of questions with varying difficulty levels, designed to test a deep understanding of concepts and problem-solving skills. Working through this additional paper helps students to reinforce their knowledge, improve their speed and accuracy, and become proficient in tackling any type of question. Engaging with both sample papers ensures a robust and well-rounded preparation for the final examination.