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Bosco from Navy Children School, asked a question
Subject: Physics , asked on 18/2/15

list of derivations in physics class 12 cbse chapterwise (for board exams).please hurry up!!!

Khushboo From Delhi Public School, added an answer, on 7/3/15
34 helpful votes in Physics
Ray Optics:
Derivation of mirror formula,
Derivation of lens formula
Refraction at spherical surface
Lens Makers Formula
Refraction through Prism
Optical Instruments Derivation of formula for magnification

Electromagnetic Induction & Alternating Current:

Motional Emf
Deriving a formula for induced emf in a rotating coil (AC Generator)
Conceptual questions based on Eddy currents
mutual induction between two coils and two solenoids 
Derivation of current voltage relationship for Pure R, pure L and pure C inductive and capacitative reactance calculation of impedance, current and voltage across each element
LCR Series - Phasor diagrams in all cases LR, LC circuits also can be done from LCR
Resonance 
Average power in A.C. circuits pure R(not very high chance), pure L and pure C and LCR series






Transformer

Magnetism
Not many derivations in this chapter

Magnetic Effects of current:
Field at the center of a circular coil
Field at any point on the axis of circular coil
Working of cyclotron
Derivations related to Cyclotron 
Field due to a toroid
field due to a solenoid
Torque on a current carrying coil placed in a magnetic field
Moving coil galvanometer
 
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Anshika05gmail.com From Delhi Public School, added an answer, on 8/3/15
8 helpful votes in Physics
where are the rest of derrivations 
 
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hiteshsagtani076... , added an answer, on 14/4/13
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Siddhant Jain From V S P K International School, added an answer, on 29/8/16
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Electrostatics- 1.      Derive an expression for the electric field at a point on the axial position of an electric dipole. 2.      Derive an expression for the electric field at a point on the equatorial position of an electric dipole. 3.       Electric field lines & their properties. Sketch of filed lines for q > 0, q < 0, q1 + q2 = 0, two similar charges, uniform charge cylinder & charged plane conductor. 4.      Derive an expression for the energy stored in a capacitor. Show that whenever two conductors share charges by bringing them into electrical contact, there is a loss of energy. 5.       Derive an expression for the effective capacitance when capacitors are connected in (a) series and (b) parallel 6.       Explain the principle of a capacitor and derive an expression for the capacitance of a parallel plate capacitor. 7.      State Gauss theorem and apply it to find the electric field at a point due to (a) a line of charge (b) A plane sheet of charge (c) A Charged spherical conducting shell. Also plot their sketch with distance. 8.      State Coulomb's law and express it in vector form. Derive it using Gauss theorem. 9.      Derive an expression for the torque on an electric dipole in a uniform electric field. 10.  Derive an expression for the work done in rotating an electric dipole in a uniform electric field 11.   Derive an expression for the energy stored (Potential Energy) in a dipole in a uniform electric field. 12.   Derive an expression for the electrostatic potential energy of a system of point charges 13.  Derive an expression for the capacitance of a parallel plate capacitor with (a) a dielectric slab (b) a metallic plate in between the plates of the capacitor. 14.   Define electric potential at a point. Derive an expression for the electric potential at a point due to (a) a point charge (b) a system of point charges (c) a dipole. 15.  Show that the work done in an electric field is independent of path. 16.  Potential energy due to dipole placed in uniform electric field. Position of stable equilibrium & unstable equilibrium. 17.  Electrostatic potential energy ( numerical) 18.  Properties of conductor 19.  What are dielectrics? Distinguish polar and non polar dielectrics. Define the term Polarization vector. 20.  Electric potential due to charged sphere and its sketch with distance. 21.  Relation between electric field and potential. 22.  Equipotential surfaces and its properties. Sketch of equipotential surfaces for a point charge, two equal and opposite charges, two similar charges & uniform electric field   Current Electricity- 1.      Define drift speed & relation of current & drift speed. Relation of drift speed & electric field 2.      Define current density, resistance, resistivity, conductance & conductivity & its unit 3.      Sketch graph for resistance & resistivity for metal (conductors), non-metal (insulators)  & semiconductor ( carbon, Si, Ge etc) 4.      Deduce Ohm's law from elementary ideas and hence write an expression for resistance and resistivity. 5.      Derive an expression for conductivity in terms of mobility or Vector form of ohms law. 6.       Explain the color coding of carbon resistors. 7.      Derive an expression for the current in a circuit with external resistance R when (a) n identical cells of emf E and internal resistance r are connected in series (b) m identical cells are connected in parallel 8.      State and explain Kirchhoff’s laws. 9.      State and explain the principle of Wheat Stone's principle. Deduce it using Kirchhoff’s laws. 10.  Sensitivity of Wheatstone bridge & factors on which it depends? 11.  Describe how you will determine the resistance of a given wire using Meter Bridge. 12.  Explain the principle of a potentiometer. Describe how will you determine (a) the ratio of emfs of two primary cells using potentiometer. (b) The internal resistance of a primary cell using potentiometer. 13.  Explain the variation of resistance and resistivity with temperature and hence define temperature coefficient of resistance and resistivity. 14.   Heating effect of electric current.   Magnetic Effect of Current  & Magnetism 1.      State Biot Savart law for the magnetic field due to current carrying element. Use this law to find magnetic field at a point on axis of current carrying loop. Also find its direction. Hence find magnetic field at centre of loop. 2.      State ampere circuital law. Use this law to find magnetic field due to solenoid & magnetic field due to toroid. 3.      Motion of charge particle in magnetic field at angle 0⁰, 180⁰ & at any angle θ 4.      Motion of charge particle in magnetic field at angle 90⁰; hence find its time period, velocity, frequency, K.E. 5.      Motion of charge particle in magnetic field at angle θ, hence find its time period, velocity, frequency & pitch. 6.      Cyclotron its principle, label diagram, frequency, role of electric field and magnetic field & K.E. limitations ( why only for proton not for α, electron, neutron) 7.       Expression for force on current carrying conductor, hence find maximum and minimum force. 8.      Show that two long straight current carrying wire in same direction attract each other, hence derive an expression for force per unit length and define 1 ampere. 9.      Derive an expression for torque acting on current carrying loop placed in uniform magnetic field at angle θ with magnetic field. 10.  Moving coil galvanometer its principle, construction label diagram role of radial magnetic field, soft iron core, phosphorous bronze strip & spring. 11.  Sensitivity of galvanometer ( current sensitivity NBA/k & voltage sensitivity NBA/kR ) 12.  Conversion of galvanometer into ammeter & conversion of galvanometer into voltmeter. 13.  Results of magnetic field due bar magnet at axial line & equatorial line. 14.  Torque acting on bar magnet placed in uniform magnetic field, hence find maximum and minimum torque. 15.  Potential energy of a bar magnet placed in uniform magnetic field. Discuss position of stable & unstable equilibrium. 16.  Magnetic moment and its unit 17.  Magnetic moment due to revolving electron, hence define Bohr magneton 18.  Earth’s Magnetism ( Magnetic declination, angle of dip, horizontal component of earth’s magnetic field) 19.  Define magnetizing field, intensity of magnetization, magnetic induction, magnetic intensity magnetic permeability & susceptibility) 20.  Why diamagnetic weekly repel by magnet? 21.  Why ferromagnetic material is strongly attract by magnet? 22.  Hysteresis (difference between soft iron & permanent magnet   Electromagnetic Induction (EMI)- 1.      State Faraday Law of electromagnetic induction. 2.      State Lenz Law. Show it follows law of conservation of energy. 3.      Define motional emf. Obtain an formula for motional emf, induce current, force necessary to pull & power delivered by external source from Faraday law & Lorentz law 4.      Eddy currents and its applications (a) Electromagnetic Brakes (b) Induction Furnace 5.      Self-induction, its unit and dimensions. 6.      Self induction for long solenoid, factors on which it depends. 7.      Mutual induction, its unit and dimensions 8.      Mutual induction for two long co-axial solenoid, coplanar square & coplanar circle. 9.      What are the factors affecting mutual inductance of a pair of coils? Define coefficient of coupling. 10.  Describe the various methods of producing induced emf. Derive an expression for the instantaneous emf induced in a coil rotated in a magnetic field. . 11.  Induce emf in rectangular coil in uniform magnetic field 12.  Induce emf in rod rotating in circular path fixed at one end 13.  A.C generator,Transformer And their losses   Alternative Current- 1. Describe the principle construction and working of an AC generator. Draw neat labeled diagram 2. Define mean value of AC(over a half cycle) and derive an expression for it. 3. Define RMS value of AC and derive an expression for it. () 4. Show that the average value of AC over a complete cycle is zero. 5. Show that the current and voltage are in phase in an ac circuit containing resistance only. 6. Deduce the phase relationship between current and voltage in an ac circuit containing inductor only. 7. Deduce the phase relationship between current and voltage in an ac circuit containing capacitor only. 8. Draw the phasor diagram showing voltage and current in LCR series circuit and derive an expression for the impedance 9. What do you mean by resonance in Series LCR circuit? Derive an expression for the frequency of resonance in LCR circuit. 10. Distinguish between resistance, reactance and impedance. 11. Define quality factor (Q factor) of resonance and derive an expression for it. 12. Describe the mechanism of electromagnetic oscillations in LC circuit and write expression for the frequency of oscillations produced. 13. Derive an expression for the average power in an ac circuit. 14. Define power factor. Deduce expression for it and explain wattless current? 15. Describe the principle construction theory and working of a transformer. 16. Describe the various losses in a transformer and explain how the losses can be minimized.   Electromagnetic Waves- 1. Why did Maxwell introduce the concept of displacement current? How does the concept of displacement current lead to the production electromagnetic waves? 2. Show that conduction current is equal to displacement current 3. Prove that electromagnetic waves are transverse in nature. 4. Show that in EMW average energy density of the electric field is equals to the average energy density of magnetic field.   5. Find the intensity of EMW 6. Show that average density of EMW is constant. 7. Establish the transverse nature of electromagnetic waves. 8. Compare the properties of electromagnetic waves and mechanical waves 9. Electromagnetic Spectrum (their wavelength or frequency in some order with application and production)   NCERT II Ray-Optics- 1. Derive mirror formula for a concave mirror and convex mirror. 2. Derive an expression for lateral shift and normal shift. On what factors these depend. 3. Define TIR and write the conditions for TIR. Derive a relation between critical angle and the refractive index of the medium. Also explain the working of isosceles prism and optical fiber. 4. Derive the refraction formula for a real image formed by a convex refracting surface when the object is placed in rarer medium. Also write the assumptions and sign convention used. 5. Derive the refraction formula for a virtual image formed by a convex refracting surface when the object is placed in rarer medium. Also write the assumptions and sign convention used. 6. Derive the refraction formula for a real image formed by a convex refracting surface when the object is placed in denser medium. Also write the assumptions and sign convention used. 7. Derive the refraction formula for a virtual image formed by a convex refracting surface when the object is placed in denser medium. Also write the assumptions and sign convention used. 8. Derive the refraction formula for a image formed by a concave refracting surface when the object is placed in rarer medium. Also write the assumptions and sign convention used. 9. Derive the refraction formula for a image formed by a concave refracting surface when the object is placed in denser medium. Also write the assumptions and sign convention used. 10. Derive the lens maker’s formula. Also write the assumptions and sign convention used. 11. Derive the lens formula for convex lend and concave lens. 12. Derive the relation for equivalent focal length or power when two thin lenses are placed in contact to each other. In which condition the lens combination will act as a plane glass sheet. 13. Derive the refraction formula for prism and also find refractive index of glass prism. . 14. Draw a ray diagram to show the image formation in refracting type astronomical telescope in the near point adjustment (when image is formed at LDDV i.e. D=25cm). Derive an expression for its magnifying power. Why the diameter of objective of telescope should be large? 15. Draw a ray diagram to show the image formation in refracting type astronomical telescope in the normal adjustment (when image is formed at infinity). Derive an expression for its magnifying power. How does the magnifying power get affected on increasing the aperture of the objective lens and why? 16. Draw a ray diagram to show the image formation a compound microscope. Explain briefly the working. Derive an expression for its magnifying power. Why the diameter of objective of microscope should be small. 17. Draw a labeled diagram of a reflecting type telescope. State two advantages of this telescope over refracting type telescope. 18. Define resolving power of compound microscope. How does the resolving power of a compound microscope change when-(a) Refractive index of medium between the object and objective lens increases (b) Wavelength of the light used is increased (c) decreasing the diameter of objective (iv) increasing the focal length of its objective. 19. Define the resolving power of astronomical telescope. Write the expression for it and state, on what factors it depends.   Wave-Optics- 1. Define wave front. State Huygens principle and verify Snell’s law. 2. State Huygens principle and prove the laws of reflection on the basis of wave theory. 3. What do you mean by interference of light? Explain in brief the Young’s double slit experiment. 4. What are the coherent sources? Write the conditions for the sustained interference pattern. Also draw the intensity v/s path difference curve. 5. Find the conditions for constructive and destructive interference. How does the intensity depend on the width of slit? 6. Find the expression for the fringe width. What is the effect on the fringe width if the whole apparatus (YDSE) is completely immersed in a liquid of refractive index μ? 7. What do you mean by diffraction of light and state the condition for the diffraction? Obtain the conditions for secondary maxima and minima. Also draw the intensity distribution curve. 8. Prove that the width of central maxima is twice the width of the secondary maxima. How does the width of central maxima depend on the width of the slit? 9. State Brewster’s law and prove that the reflected and refracted rays are mutually perpendicular at the angle of polarization. 10. State law of Malus and draw an intensity V/s angle between the plane of transmission of polarizer and analyzer. 11. What is a Polaroid? How are they constructed? Mention their important applications. 12. Explain Polarization of light. Give any one method to produce plane polarized light. Dual Nature of Radiation- 1. Describe the experiment to study photoelectric effect and explain the laws of photoelectric effect and the significance of each. 2. Describe Hertz and Lenard’s experiment to demonstrate photoelectric effect. 3. Explain Einstein's photoelectric equation and explain the laws of photoelectric effect using it. 4. State and explain de Broglie relation for matter waves. 5. Describe Davisson- Germer experiment which provided experimental evidence for wave nature of matter. 6. Write the characteristics of Photon.   Semiconductor Devices- 1. Distinguish between conductors, insulators and semiconductors on the basis of energy bands. 2. What are extrinsic semiconductors? Mention its types and explain the mechanism of conduction in each. 3. Explain the conduction in N Type and P Type semiconductor on the basis of band theory. 4. Explain the formation of depletion layer and potential barrier in a PN junction diode. 5. Draw the circuit diagram used to determine the VI characteristics of a diode and draw the forward and reverse bias characteristics of a diode. Explain the conclusions drawn from the graph. 6. With the help of a labeled circuit diagram explain the working of half wave rectifier and draw the input and output waveforms. 7. With the help of a labeled circuit diagram explain the working of full wave rectifier and draw the input and output waveforms. 8. Write notes on LED, photodiode and solar cell. 9. What is a Zener diode? Draw the VI characteristics of zener diode. Explain Zener breakdown and describe the use of a zener diode as a voltage regulator. 10. Explain the action of a PNP transistor and an NPN transistor.(Explain how conduction takes place in NPN and PNP transistor.) 11. Draw the circuit diagram for determining transistor characteristics and describe the input and output characteristics of transistor in CE configuration with relevant graphs. 12. Draw the circuit diagram for determining transistor characteristics and describe the input and output characteristics of transistor in CB configuration with relevant graphs. 13. Explain the working of Transistor amplifier in CE configuration with necessary circuit diagram. Also show that it is out of phase. 14. Draw the symbol, truth table and Boolean expression for Or, AND and NOT gate. 15. Draw the symbol and truth table of NOR gate and NAND gate. 16. Explain, how the fundamental logic gates can be realized using NOR gates alone. 17. Explain how the fundamental logic gates can be realized using NAND gates alone.   Principles of Communication- 1. Derive an expression for the range of transmission via space wave from a transmitting antenna of height h. 2. Describe radio wave propagation via (a) Ground Wave (b) Space Wave and (c) Sky Wave. 3. What is the need for satellite communication? Elaborate. 4. Explain the need for modulation for long distance transmission. 5. Define amplitude modulation and illustrate it using diagrams (graphs) 6. Define modulation index and write its expression. Give it important feature. 7. What are the advantages and disadvantages of FM over AM? 8. Explain the role of repeater in communication 9. Describe the mechanism of demodulation (detection) of AM Wave using block diagram, circuit diagram and graphical representation 10. What is LOS communication? 11. What are the basic elements of a communication system? Explain the function of each. 12. Draw the block diagram of a communication system. 13. Brief of Mobile telephony GPS and FAX  
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Siddhant Jain From V S P K International School, added an answer, on 29/8/16
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TOTAL 164 DERIVATION ARE THERE 
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Ayushi From St. Paul School, added an answer, on 24/2/16
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Some Imp derivations that u should know :  1. Work done (dipole electric field) *  2. Energy in capacitor **  3. Wheatstone bridge (meter bridge)***  4. Potentiometer****  5. Bio savarts law ( for infinite wire, finite wire, loops etc)****  6. Ampere law***  7 solenoid***  8. Cyclotron *****  9. Magnetic force on charge particle**  10. Moving coil galvanometer*****  11. Energy stored in inductor**  12. LC oscillator***  13. AC generator*  14. OPTICS lens maker formula***  15. Prism min. Angle of deviation***  16. Ydse experiment ***  17. Npn transistor (amplifier , switch etc)*****  18. Bohr model ( radius*** , velocity** , energy**** , time period *and Bohr magneton***)
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Ushausha Manglik From Blue Birds International School, added an answer, on 4/3/16
1 helpful votes in Physics
And also definitions
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hiteshsagtani076... , added an answer, on 14/4/13
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 ljlkn

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Jhon Shing , added an answer, on 25/7/13

 read ncert

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Sathyam From Jawahar Navodaya Vidyalaya, added an answer, on 19/9/16
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siddhant jain gave best answer
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Krish Ramesh From Maharishi Vidya Mandir, added an answer, on 2/3/16
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lens makers formula
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