CHRIST (Deemed to University), BangaloreDEPARTMENT OF PHYSICS AND ELECTRONICSSchool of Sciences 

Syllabus for

1 Semester  2022  Batch  
Course Code 
Course 
Type 
Hours Per Week 
Credits 
Marks 
MPH131  CLASSICAL MECHANICS  Core Courses  4  4  100 
MPH132  ANALOG AND DIGITAL CIRCUITS  Core Courses  4  4  100 
MPH133  QUANTUM MECHANICS  I  Core Courses  4  4  100 
MPH134  MATHEMATICAL PHYSICS  I  Core Courses  4  4  100 
MPH151  GENERAL PHYSICS LAB  I  Core Courses  4  2  100 
MPH152  GENERAL ELECTRONICS LAB  Core Courses  4  2  100 
MPH181  RESEARCH METHODOLOGY  Core Courses  2  2  50 
2 Semester  2022  Batch  
Course Code 
Course 
Type 
Hours Per Week 
Credits 
Marks 
MPH231  STATISTICAL PHYSICS  Core Courses  4  04  100 
MPH232  ELECTRODYNAMICS  Core Courses  4  4  100 
MPH233  QUANTUM MECHANICS  II  Core Courses  4  4  100 
MPH234  MATHEMATICAL PHYSICS  II  Core Courses  4  4  100 
MPH251  GENERAL PHYSICS LAB  II  Core Courses  4  2  100 
MPH252  COMPUTATIONAL METHODS LAB USING PYTHON  Core Courses  4  2  100 
MPH281  STATISTICAL TECHNIQUES IN RESEARCH AND PROFESSIONAL ETHICS  Core Courses  2  2  50 
3 Semester  2021  Batch  
Course Code 
Course 
Type 
Hours Per Week 
Credits 
Marks 
MPH331  NUCLEAR AND PARTICLE PHYSICS  Core Courses  4  4  100 
MPH332  SOLID STATE PHYSICS  Core Courses  4  4  100 
MPH333  ATOMIC, MOLECULAR AND LASER PHYSICS  Core Courses  4  4  100 
MPH341A  FUNDAMENTALS OF MATERIALS SCIENCE  Discipline Specific Elective Courses  4  4  100 
MPH341B  ELECTRONIC INSTRUMENTATION AND CONTROL SYSTEM  Discipline Specific Elective Courses  4  4  100 
MPH341C  INTRODUCTION TO ASTRONOMY AND ASTROPHYSICS  Discipline Specific Elective Courses  4  4  100 
MPH341D  HARVESTING SOLAR ENERGY  Discipline Specific Elective Courses  4  04  100 
MPH351  GENERAL PHYSICS LAB  III  Core Courses  4  2  100 
MPH352A  MATERIAL SCIENCE LAB  I  Discipline Specific Elective Courses  4  2  100 
MPH352B  ELECTRONICS LAB  I  Discipline Specific Elective Courses  4  2  100 
MPH352C  ASTROPHYSICS LAB  I  Discipline Specific Elective Courses  4  2  100 
MPH352D  ENERGY SCIENCE LABI  Discipline Specific Elective Courses  4  2  100 
MPH381A  DISSERTATION  Discipline Specific Elective Courses  8  4  100 
MPH381B  TEACHING METHODOLOGY  Discipline Specific Elective Courses  8  4  100 
4 Semester  2021  Batch  
Course Code 
Course 
Type 
Hours Per Week 
Credits 
Marks 
MPH431  SPECTROSCOPIC TECHNIQUES  Core Courses  4  4  100 
MPH441A  ADVANCED MATERIALS AND SYNTHESIS STRATEGIES  Discipline Specific Elective Courses  4  4  100 
MPH441B  PHYSICS OF SEMICONDUCTOR DEVICES  Discipline Specific Elective Courses  4  4  100 
MPH441C  STELLAR ASTROPHYSICS  Discipline Specific Elective Courses  4  4  100 
MPH441D  HARVESTING WIND, OCEAN, BIOMASS AND GEOTHERMAL ENERGY  Discipline Specific Elective Courses  4  04  100 
MPH442A  MATERIAL CHARACTERIZATION TECHNIQUES  Discipline Specific Elective Courses  4  4  100 
MPH442B  ELECTRONIC COMMUNICATION  Discipline Specific Elective Courses  4  4  100 
MPH442C  GALACTIC ASTRONOMY AND COSMOLOGY  Discipline Specific Elective Courses  4  4  100 
MPH442D  ENERGY STORAGE AND MANAGEMENT  Discipline Specific Elective Courses  4  04  100 
MPH451A  MATERIAL SCIENCE LAB  II  Discipline Specific Elective Courses  4  2  100 
MPH451B  ELECTRONICS LAB  II  Discipline Specific Elective Courses  4  2  100 
MPH451C  ASTROPHYSICS LAB  II  Discipline Specific Elective Courses  4  2  100 
MPH451D  ENERGY SCIENCE LABII  Discipline Specific Elective Courses  4  2  100 
MPH481A  DISSERTATION  Discipline Specific Elective Courses  8  4  100 
MPH481B  TEACHING TECHNOLOGY  Discipline Specific Elective Courses  8  4  100 
MPH482  COMPREHENSIVE VIVAVOCE  Core Courses  0  2  50 
 
Introduction to Program:  
The postgraduate programme in physics helps to provide in depth knowledge of the subject which is supplemented with tutorials, brainstorming ideas and problemsolving efforts pertaining to each theory and practical course. The twoyear MSc programme offers 16 theory papers and 7 laboratory modules, in addition to the foundation courses and guided project spreading over four semesters. Foundation courses and seminars are introduced to help the students to achieve holistic development and to prepare themselves to face the world outside in a dignified manner. Study tour to reputed national laboratories, research institutions and industries, under the supervision of the department is part of the curriculum.  
Programme Outcome/Programme Learning Goals/Programme Learning Outcome: PO8: Design and perform experiments in basic as well as advanced areas of PhysicsPO9: Demonstrate skills in modeling and simulations of physical phenomena using industrially and academically relevant software  
Assesment Pattern  
 
Examination And Assesments  
Continuous internal assessment (CIA) forms 50% and the end semester examination forms the other 50% of the marks in both theory and practical. For the Holistic and Seminar course, there is no end semester examination and hence the mark is awarded through CIA. CIA marks are awarded based on their performance in assignments (written material to be submitted and valued), midsemester test (MST), and class assignments (Quiz, presentations, problem solving etc.). The midsemester examination and the end semester examination for each theory paper will be for three hours duration. The CIA for practical sessions is done on a day to day basis depending on their performance in the prelab, the conduct of the experiment, and presentation of lab reports. Only those students who qualify with minimum required attendance and CIA will be allowed to appear for the end semester examination.
Examination pattern for theory
EndSemester Exam [ESE]
• A student is eligible to appear for the ESE only if she/he has put in 85% of attendance and satisfactory performance in the continuous internal assessment.
• The question paper shall be set for 100 marks. These marks will then be reduced to 50% of the total marks assigned for the paper.
• There is no provision for taking improvement exams. If a student fails in an ESE paper, he can take the exam again the next time it is offered.
• The practical examination shall be conducted with an internal (batch teacher) and an external examiner.
Examination pattern for practical

MPH131  CLASSICAL MECHANICS (2022 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 
Max Marks:100 
Credits:4 
Course Objectives/Course Description 

The course enables students to understand the basic concepts of Newtonian mechanics and introduces other formulations (Lagrange, Hamilton, Poisson) to solve trivial problems. The course also includes constraints, rotating frames, central force, Kepler problems, canonical transformation and their generating functions, small oscillations and rigid body dynamics. The course lays out the platform to develop the student's skills toward a deep understanding of classical mechanics. 

Course Outcome 

CO1: Understand and conceptualize the forces acting on static and dynamic bodies and their resultants. CO2: Solve problems related to damped, undamped and forced vibrations acting on molecules and rigid bodies undergoing oscillations. CO3: Apply Lagrangian and Hamiltonian formalism to other branches of physics. 
Unit1 
Teaching Hours:15 

Constraints and Lagrangian formulation


Mechanics of a particle, mechanics of a system of particles, constraints and their classification, principle of virtual work, D’Alembert’s principle, Generalized coordinates, Lagrange’s equations of motion, applications of Lagrangian formulation (simple pendulum, Atwood’s machine, bead sliding in a wire), cyclic coordinates, concept of symmetry, homogeneity and isotropy, invariance under Galilean transformations.  
Unit2 
Teaching Hours:15 

Rotating Frames of Reference and Central Force


Rotating frames, inertial forces in the rotating frame, effects of Coriolis force, Foucault’s pendulum, Central force: definition and examples, Twobody central force problem, classification of orbits, stability of circular orbits, condition for closure of orbits, Kepler’s laws, Virial theorem, applications.  
Unit3 
Teaching Hours:15 

Canonical Transformation, Poisson Bracket and Hamilton's Equations of motion


Canonical transformations, generating functions, conditions of canonical transformation, examples, Legendre’s dual transformation, Hamilton’s function, Hamilton’s equation of motion, properties of Hamiltonian and Hamilton’s equations of motion, Poisson Brackets, properties of Poisson bracket, elementary PB’s, Poisson’s theorem, JacobiPoisson theorem on PBs, Invariance of PB under canonical transformations, PBs involving angular momentum, principle of Least action, Hamilton’s principle, derivation of Hamilton’s equations of motion from Hamilton’s principle, HamiltonJacobi equation. Solution of simple harmonic oscillator by HamiltonJacobi method.  
Unit4 
Teaching Hours:15 

Small Oscillations and Rigid Body Dynamics


Types of equilibrium and the potential at equilibrium, Lagrange’s equations for small oscillations using generalized coordinates, normal modes, vibrations of carbon dioxide molecule, forced and damped oscillations, resonance, degrees of freedom of a free rigid body, angular momentum, Euler’s equation of motion for rigid body, time variation of rotational kinetic energy, Rotation of a free rigid body, Eulerian angles, Motion of a heavy symmetric top rotating about a fixed point in the body under the action of gravity.  
Text Books And Reference Books: [1] Srinivasa Rao, K. N. (2002). Classical mechanics: University Press. [2] Goldstein, H. (2001). Classical mechanics (3rd ed.): Addison Wesley. [3] Rana, N. C., & Joag, P. S. (1994). Classical mechanics. New Delhi: Tata McGraw Hill.
 
Essential Reading / Recommended Reading [1] Greiner, W. (2004). Classical mechanics: System of particles and Hamiltonian dynamics. New York: SpringerVerlag. [2] Barger, V., & Olsson, M. (1995). Classical mechanics  A modern perspective (2nd ed.): Tata McGraw Hill. [3] Gupta, K. C. (1988). Classical mechanics of particles and rigid bodies: Wiley Eastern Ltd. [4] Takwale, R. G., & Puranik, P. S. (1983). Introduction to classical mechanics. New Delhi: Tata McGraw Hill.  
Evaluation Pattern
 
MPH132  ANALOG AND DIGITAL CIRCUITS (2022 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 

This module introduces the students to the applications of analog and digital integrated circuits. First part of the module deals with the operational amplifier, linear applications of opamp., active filters, oscillators, nonlinear applications of opamp, timer and voltage regulators. The second part deals with digital circuits which exposes to the logic gates, encoders and decoders, flipflops registers and counters. 

Course Outcome 

CO1: ● Understand the basics of analog and digital circuit. CO2: ● Understand the applications of linear circuits with opamp and various digital devices like flipflop, registers and counters. CO3: ● Design various operational amplifier based linear and nonlinear circuits. 
Unit1 
Teaching Hours:15 

Linear applications of opamp


The ideal opamp  characteristics of an opamp., the ideal opamp., Equivalent circuit of an opamp., Voltage series feedback amplifier  voltage gain, input resistance and output resistance, Voltage follower. Voltage shunt feedback amplifier  virtual ground, voltage gain, input resistance and output resistance, Current to voltage converter. Differential amplifier with one opamp. voltage gain, input resistance. Linear applications: AC amplifier, AC amplifier with single supply voltage, Summing amplifier, Inverting and noninverting amplifier, Differential summing amplifier, Instrumentation amplifier using transducer bridge, The integrator, The differentiator.  
Unit2 
Teaching Hours:15 

Nonlinear applications of opamp.


Active filters and oscillators: First order low pass filter, Second order low pass filter, First order high pass filter, Second order high pass filter, Phase shift Oscillator, Wienbridge oscillator, Square wave generator. Nonlinear circuits: Comparator, Schmitt trigger, Digital to analog converter with weighted resistors and R2R resistors, Positive and negative clippers, Small signal half wave rectifier, Positive and negative clampers.  
Unit3 
Teaching Hours:15 

Combinational digital circuits


Logic gates  basic gates  OR, AND, NOT, NOR gates, NAND gates, Boolean laws and theorems (Review only). Karnaugh map, Simplification of SOP equations, Simplification of POS equations, Exclusive OR gates. Combinational circuits: Multiplexer, Demultiplexer, 116 decoder, BCD to decimal decoder, Seven segment decoder, Encoder, Half adder, Full adder  
Unit4 
Teaching Hours:15 

Sequential digital circuits


Flip flops: RS flipflop, Clocked RS flipflop, Edge triggered RS flipflop, D flipflop, JK flipflop, JK masterslave flipflop. Registers: Serial input serial output shift register, Serial input parallel output shift register, Parallel input serial output shift register, Parallel input parallel output shift register, Ring counter. Counters: Ripple counter, Decoding gates, Synchronous counter, Decade counter, Shift counter  Johnson counter.  
Text Books And Reference Books: [1]. Gayakwad, R. A. (2002). Opamps. and linear integrated circuits. New Delhi: Prentice Hall of India. [2]. Leach, D. P., & Malvino, A. P. (2002). Digital principles and applications. New York: Tata McGraw Hill.  
Essential Reading / Recommended Reading [1]. Anand Kumar, A. (2018). Fundamental of digital circuits. New Delhi, PrenticeHall of India. [2]. Morris Mano, M. (2018). Digital logic and computer design: Pearson India. [3]. Jain, R. P. (1997). Modern digital electronics. New York: Tata McGraw Hill.  
Evaluation Pattern
 
MPH133  QUANTUM MECHANICS  I (2022 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 

This course being an essential component in understanding the behaviour of fundamental constituents of matter is divided into two modules spreading over the first and second semesters. The first module is intended to familiarize the students with the basics of quantum mechanics, exactly solvable eigenvalue problems, timeindependent perturbation theory and timedependent perturbation theory. 

Course Outcome 

CO1: By the end of the course the learner will be able to ● Design concepts in quantum mechanics such that the behaviour of the physical universe can be understood from a fundamental point of view. CO2: ● Acquire basic knowledge of Quantum Mechanics. Skills and techniques to use Quantum mechanical principles in simple and complicated systems. CO3: ● Learn to differentiate between bound and unbound states of a system. Develop the skills and techniques to solve eigenvalue problems such as particle in a box, potential step, potential barrier, rigid rotator, hydrogen atom, etc. CO4: ● Understand the first and second order perturbation theories, adiabatic and sudden approximation methods and scattering theory. 
Unit1 
Teaching Hours:15 

Basics of Quantum mechanics


Review  origin of quantum mechanics (particle aspects, wave aspects and waveparticle duality), uncertainty principle, Schrodinger equation, time evolution of a wave packet, probability density, probability current density, continuity equation, orthogonality and normalization of the wave function, box normalization, admissibility conditions on the wave function, Operators, Hermitian operators, Poisson brackets and commutators, Eigen values, Eigen functions, postulates of quantum mechanics, expectation values, Ehrenfest theorems.
 
Unit2 
Teaching Hours:20 

Exactly solvable eigenvalue problems


Bound and unbound systems. Application of timeindependent Schrodinger wave equation  Potential step, rectangular potential barriers  reflection and transmission coefficient, barrier penetration; particle in a onedimensional box and in a cubical box, the density of states; onedimensional linear harmonic oscillator  evaluation of expectation values of x^{2} and p_{x}^{2}; Orbital angular momentum operators  expressions in cartesian and polar coordinates, eigenvalue and eigenfunctions, spherical harmonics, Rigid rotator, Hydrogen atom  solution of the radial equation.  
Unit3 
Teaching Hours:15 

Approximation methods


Time independent perturbation theory First and secondorder perturbation theory applied to nondegenerate case; firstorder perturbation theory for degenerate case, application to normal Zeeman effect and Stark effect in hydrogen atom. Timedependent perturbation theory  Firstorder perturbation, Harmonic perturbation, Fermi’s golden rule, Adiabatic approximation method, Sudden approximation method.  
Unit4 
Teaching Hours:10 

Scattering Theory


Scattering crosssection, Differential and total crosssection, Born approximation for the scattering amplitude, scattering by spherically symmetric potentials, screened Coulomb potential, Partial wave analysis for scattering amplitude, expansion of a plane wave into partial waves, phase shift, crosssection expansion, swave scattering by a square well, optical theorem.  
Text Books And Reference Books:
[1]. Zettli, N. (2017). Quantum mechanics. New Delhi: Wiley India Pvt Ltd. [2]. Aruldhas, G. (2010). Quantum mechanics. New Delhi: PrenticeHall of India. [3]. Ghatak, A. K. & Lokanathan, S. (1997). Quantum mechanics: McMillan India Ltd.  
Essential Reading / Recommended Reading
[1]. Schiff, L. I. (2017). Quantum mechanics (4^{th} ed.).New York: McGraw Hill Education Pvt Ltd. [2]. Miller, D. A. B. (2008). Quantum mechanics for scientists and engineers:Cambridge University Press. [3]. Shankar, R. (2008). Principles of quantum mechanics (2^{nd} ed.). New York: Springer. [4]. Tamvakis, K. (2005). Problems and solutions in quantum mechanics: Cambridge University Press. [5]. Sakurai, J. J. (2002). Modern quantum mechanics: Pearson Education Asia. [6]. Crasemann, B., & Powell, J. H. (1998). Quantum mechanics: Narosa Publishing House. [7]. Mathews, P. M., & Venkatesan, A. (1995). Quantum mechanics. New Delhi: Tata McGraw Hill. [8]. Griffiths, D. J. (1995). Introduction to quantum mechanics: Prentice Hall Inc. [9]. Gasiorowicz, S. (1974). Quantum physics: John Wiley & Sons. [10].Landau, L. D., & Lifshitz, E. M. (1965). Quantum mechanics: Pergamon Press.  
Evaluation Pattern
 
MPH134  MATHEMATICAL PHYSICS  I (2022 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:4 

Course Objectives/Course Description 

A sound mathematical background is essential to understand and appreciate the principles of physics. This module is intended to make the students familiar with the applications of tensors and matrices, special functions, partial differential equations and integral transformations, Green’s functions and integral equations. 

Course Outcome 

CO1: Develop problem solving skills in mathematics CO2: Develop critical questioning and creative thinking capability to formulate ideas mathematically 
Unit1 
Teaching Hours:15 

Vector analysis and Tensors


Vectors and matrices: Review (vector algebra and vector calculus, gradient, divergence & curl), transformation of vectors, rotation of the coordinate axes, invariance of the scalar and vector products under rotations, Vector integration, Line, surface and volume integrals  Stoke’s, Gauss’s and Green’s theorems (Problems), Vector analysis in curved coordinate, special coordinate system  circular, cylindrical and spherical polar coordinates, linear algebra matrices, CayleyHamilton theorem, eigenvalues and eigenvectors. Tensors: Definition of tensors, Kronecker delta, contravariant and covariant tensors, direct product, contraction, inner product, quotient rule, symmetric and antisymmetric tensors, metric tensor, Levi Cevita symbol, simple applications of tensors in nonrelativistic physics.
 
Unit2 
Teaching Hours:15 

Special Functions


Beta and Gamma functions, different forms of beta and gamma functions. Dirac delta function. Kronecker delta, Power series method for ordinary differential equations, Series solution for Legendre equation, Legendre polynomials and their properties, Series solution for Bessel equation, Bessel and Neumann functions and their properties, Series solution for Laguerre equation, it's solutions and properties (generating function, recurrence relations and orthogonality properties for all functions).  
Unit3 
Teaching Hours:15 

Partial Differential Equations and Integral Transforms


Method of separation of variables, the wave equation, Laplace equation in cartesian, cylindrical and spherical polar coordinates, heat conduction equations and their solutions in one, two and three dimensions. Review of Fourier series, Fourier integrals, Fourier transform, Properties of Fourier sine and cosine transforms, applications. Laplace transformations, properties, convolution theorem, inverse Laplace transform, Evaluation of Laplace transforms and applications.  
Unit4 
Teaching Hours:15 

Green's functions and Integral equations


Dirac delta function, properties of Dirac delta function, three dimensional delta functions, boundary value problems, SturmLiouville differential operator, Green’s function of one dimensional problems, discontinuity in the derivative of Green’s functions, properties of Green’s functions, Construction of Green’s functions in special cases and solutions of inhomogeneous differential equations, Green’s function symmetry of Green’s function, eigenfunction expansion of Green’s functions, Green’s function for Poisson equation. Linear integral equations of first and second kind, Relationship between integral and differential equations, Solution of Fredholm and Volterra equations by Neumann series method.  
Text Books And Reference Books: Essential Reading: [1]. S. Prakash: Mathematical Physics, S. Chand and Sons, 2004. [2]. H. K. Dass: Mathematical Physics, S. Chand and Sons, 2008. [3].G. B. Arfken, H. J. Weber and F. E. Harris: Mathematical methods for physicists, 7th Edn., Academic press, 2013.  
Essential Reading / Recommended Reading Recommended Reading: [1]. Murray R. Spiegel, Theory and problems of vector analysis, (Schaum’s outline series) [2]. M. L. Boas: Mathematical Methods in the Physical Sciences, 2nd Edn, Wiley 1983. [3]. K.F. Riley, M.P Hobson, S. J. Bence, Mathematical methods for Physics and Engineering, Cambridge University Press (Chapter 24) [4]. P. K. Chattopadhyaya: Mathematical Physics, Wiley Eastern, 1990. [5]. E. Kryszig: Advanced Engineering Mathematics, John Wiley, 2005. [6]. Sadri Hassani: Mathematical Methods for students of Physics and related fields, Springer 2000. [7]. J. Mathews and R. Walker: Mathematical Physics, Benjamin, Pearson Education, 2006. [8]. A W. Joshi: Tensor analysis, New Age, 1995. [9]. L. A. Piper: Applied Mathematics for Engineers and Physicists, McGrawHill 1958.  
Evaluation Pattern Continuous Internal Assessment (CIA) forms 50% and the End Semester Examination forms the other 50% of the marks with total of 100%. CIA marks are awarded based on their performance in assignments, MidSemester Test (MST), and Class assignments (Quiz, presentations, problem solving, MCQ test etc.). The midsemester examination and the end semester examination for each theory paper will be for two and threehours duration respectively. CIA 1: Assignment /quiz/ group task / presentations before MST  10 marks. CIA 2: MidSem Test (Centralized), 2 hours  50 marks to be converted to 25 marks. CIA 3: Assignment /quiz/ group task / presentations after MST  10 marks. CIA 4: Attendance (7679 = 1, 8084 = 2, 8589 = 3, 9094 = 4, 95100 = 5)  maximum of 5 marks.
 
MPH151  GENERAL PHYSICS LAB  I (2022 Batch)  
Total Teaching Hours for Semester:60 
No of Lecture Hours/Week:4 

Max Marks:100 
Credits:2 

Course Objectives/Course Description 

Experiments are selected to improve the understanding of students about mechanical, magnetic, optical and basic electronic properties of materials. 

Course Outcome 

CO1: ● Gain practical knowledge about the mechanical, magnetic properties (BH loop and Curie temperature), optical properties (interference) and electronics properties (band gap and IV characteristics) of materials. CO2: ● Gain the basic skills needed to start entrepreneurship pertaining to local and regional needs. 
Unit1 
Teaching Hours:30 
Cycle1


1. Elastic constants of glass plate by Cornu's interference method. (Online/Offline) 2. Study of thermoemf and verification of thermoelectric laws (Onlilne/Offline) 3. Wavelength of iron arc spectral lines using constant deviation spectrometer. (Offline) 4. Energy gap of the semiconducting material used in a PN junction. (Offline) 5. Characteristics of a solar cell. (Online/Offline) 6. Stefan’s constant of radiation. (Offline) 7. Study of hydrogen spectra and determination of Rydberg constant (Offline)  
Unit2 
Teaching Hours:30 
Cycle2


1. Relaxation time constant of a serial bulb. (Offline) 2. e/m by Millikan’s oil drop method. (Online) 