**Important Derivation and theory questions of CBSE** Class 12th **Physics**

Q1. (a) Define electric dipole moment. Is it scalar or vector. Derive the expression for the electric field of dipole on the equatorial plane.

(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is Zero. Compare it with equipotential surface of two positive charges

(c) A parallel plate capacitor is charged by battery. When the battery is disconnected and a dielectric slab is then inserted in the space between the plates, Explain what changes if any occur in the value of (I) **capacitance **(ii) **potential difference **(iii) **electric field **(iv) **energy stored**. Explain how these findings will change when battery remain connected.

Q2. (a) State and prove Gauss’s theorem. Using Gauss’s law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point outside and inside the shell.

(b) Plot a graph showing variation of electric field as a function of r>R and r<R.

Q3. (a) Find electric potential due to dipole at an angle θ from axial line at distance r from centre of dipole.

(b) Derive expression for capacitance of parallel plate capacitor. When we insert dielectric slab of thickness t between its plates how capacitance will change. Support your answer with necessary derivation.

Q4. (a) Using Gauss’ law, derive an expression for the electric field intensity at any point due to an infinite long ,thin , uniformly charged straight wire of linear charge density λ C/m.

(b)A uniform electric field E = E_{x }if or x>0 and E = -E_{x }i for x>0 are given A right circular cylinder of length l and radius r has its centre at origin and axis along x axis. Find out the net outward flux then find charge within the cylinder,

Q5. (a) Derive an expression for the force and torque experienced by an electric dipole kept in a uniform electric field. Explain condition of stable and unstable equilibrium on basis of it.

(b) Find amount of work done to rotate dipole from position of stable equilibrium to unstable equilibrium in uniform electric field.

Q6. (a) Define electrostatics potential at a point. Write its SI unit. If three point charges q_{1, }q_{2 }and q_{3 } are place that three vertices of triangle having sides r_{12,} r_{13} and r_{23 } then derive expression for potential energy of system of charges.

(b) Define equipotential surfaces. Why work done to move charge on equipotential surface is always zero . Why two equipotential surface can not intersect each other ?

Q7. (a) Define electric flux. Write its S. l. units.

(b) The electric field components in Fig. are in which given by Calculate

- (i)the flux through the cube and (1.05)
- (ii) the charge within the cube. Assume that
*a*= 0.1 m

(c) Using Gauss’s law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.

(d) How is the field directed if (i) the sheet is positively charged, (ii) negatively charged?

Q8. (a) State Kirchoff’s law for electric circuits? Deduce the condition for balance in a Wheatstone Bridge Using Kirchhoff’s law.

(b) When it is considered to be most sensitive.

(c) What will happen to balance point if we interchange battery and galvanometer at balance point.

(d) Will balance point change if we increase temperature of balance wheat stone bridge having same resistance in all four branches of different material.

Q9. (a) Explain the term drift velocity of electron in a conductor. Hence obtain the expression for the current through a conductor in terms of drift velocity. Show that resistivity does not depends on dimension of conductor whereas resistance depends.

(b) Two cells of emf E_{1} and E_{2 } and internal resistance r_{1 }and r_{2} are connected as shown

Deduce expression for equivalent emf and equivalent internal resistance of the combination.

Q.10. Derive an expression for the torque acting on a loop of N turns, area A, carrying current i, when held in a uniform magnetic field with the help of circuit, Give its relation with magnetic moment.

Q11. Write an expression for the force experienced by a charged particle moving in a uniform magnetic field B. Prove that when a particle is projected in magnetic field it will follow helical path. Also find expression for its pitch.

Q12. (a) Depict the magnetic field lines due to two straight, long, parallel conductors carrying currents I_{1} and I_{2} in the same direction. Hence deduce an expression for the force acting per unit length on one conductor due to the other. Is this force attractive or repulsive then define one ampere.

(b) Figure shows a rectangular current-carrying loop placed 7.5 cm away from a long, straight, current-carrying conductor. What is the direction and magnitude of the net force acting on the loop.

Q.13. With the help of a neat and labeled diagram, explain the underlying principle and working of a moving coil galvanometer.(a)What is the function of:

- (i) uniform radial field
- (ii) soft iron core in such a device?

(b)Write two factors on which the current sensitivity of a moving coil galvanometer depend.

(c) Two moving coil meters M_{1} and M_{2} have the following particulars.

R_{1} = 10Ω N_{1} = 30 A_{1} = 3.6×10^{-3} m^{2 } B_{1} = 0.25 T

R_{2} = 14Ω N_{2} = 42 A_{2} = 1.8×10^{-3} m^{2 } B_{2} = 0.50 T

Compare current and voltage sensitivity.

Q14. (a) Using Biot-Savart’s law, derive an expression for the magnetic field on the axis of circular coil hence find at the centre of a circular coil of radius R, number of turns N, carrying current *i*.

(b) Two small identical circular coils marked P and Q carry equal currents I and are placed with their geometric axes perpendicular to each other as shown in the figure. Derive an expression for the resultant magnetic field at O.

15. (a) Derive the expression for the torque on a rectangular current carrying loop suspended in a uniform magnetic field. (b) A proton and a deuteron having equal momenta enter in a region of uniform magnetic field at right angle to the direction of the field. Depict their trajectories in the field.

16(a) A small compass needle of magnetic moment ‘m’ is free to turn about an axis perpendicular to the direction of uniform magnetic field ‘B’. The moment of inertia of the needle about the axis is ‘I’. The needle is slightly disturbed from its stable position and then released. Prove that it executes simple harmonic motion. Hence deduce the expression for its time period.

(b) State Gauss’s and Curie law for magnetism and give their significance

(c) Compare properties of ferromagnetic, paramagnetic and diamagnetic substances

Q17. (a) Establish an expression of magnetic field on axis and equatorial line of bar magnet.

(b) “Increasing the current sensitivity of a galvanometer may not necessarily increase its voltage sensitivity.” Justify this statement.

(c) Outline the necessary steps to convert a galvanometer of resistance G in to voltmeter. If Galvanometer resistance is 12 ohm. Convert it to voltmeter of range 0 to 5v if full scale deflection current is 1mA. What changes are required to change it to ammeter of range 0 to 3 amp.

Q18 (a) Find magnetic field due to a long solenoid at a point inside the solenoid on its axis. Draw its magnetic lines of force and compare with electric lines of force of dipole.

(b) A straight thick long wire of uniform cross section of radius a is carrying a steady current I. Use Ampere’s circuital law to obtain a relation showing variation of the magnetic field inside (r<a) and outside(r>a) the wire from the center of its cross section. Plot a graph showing the variation of the field B with distance r.

Q.19 (a) State Faraday’s law and Lenz law by explaining Faraday’s experiment of electromagnetic induction. Figure shows a rectangular conductor *PQRS* in which the conductor *PQ* is free to move in a uniform magnetic field *B* perpendicular to the plane of the paper. The field extends from *x* = 0 to *x *= *b* and is zero for *x*>*b.* Assume that only the arm *PQ* is pulled outward from *x* = 0 to *x* = 2b and is then moved backward to *x* = 0 with constant speed *v, * obtain the expressions for the flux , induced emf , force required and power. Sketch the variations of these quantities with distance 0 <= x <-= 2b.

(b) Obtain an expression for the mutual inductance of two long coaxial solenoids S_{1 } and S_{2} wound one over other each of length L and radii r_{1} and r_{2.} And n_{1 } and n_{2} be number of turns per unit length , when a current I is set up in the outer solenoid S_{2}. What will happen to mutual inductance when we insert iron rod in it?

**Q. 20. **Explain series LCR circuit using phasor analysis. Find expression for impedance and phase angle. How impedance and phase angle changes at resonance.

(b) The above circuit diagram shows a series LCR circuit connected to a variable frequency 100 V source:

- (a) Determine the source frequency which drives the circuit in resonance.
- (b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.

(c) Determine the rms potential drops across the three elements of the circuit.

(d) How do you explain the observation that the algebraic sum of the voltages across the three elements obtained in (c) is greater than the supplied voltage?

Q21. (a)Explain principle, construction and working of transformer

(b)The primary coil of an ideal step-up transformer has 100 turns and the transformation ratio is also 100. The input voltage the power is 220 V and 1100 W respectively. Calculate:

- (i) Number of turns in the secondary.
- (ii) the current in the primary.
- (iii) voltage across the secondary.
- (iv) the current in the secondary.
- (v) power in the secondary.

Q22. Describe briefly, with the help of a labeled diagram, the basic elements of an A.C. generator. State its underlying principle. Show diagrammatically how an alternating emf is generated by a loop of wire rotating in a magnetic field. Write the expression for the instantaneous value of the emf induced in the rotating loop.

Q23.(a) The coil of an A. C. generator having N turns ,each of area A, is rotated with a constant angular velocity w. Deduce the expression for alternating e.m.f. generated in the coil. What is the source of energy generation in this device?

(b) Prove that in a AC circuit containing L only voltage is ahead of current by π/2 in phase. ‘: where as in circuit containing capacitor current is ahead of voltage by π/2.

Q24. (a)A conducting rod of length l with one end pivoted , is rotated with a uniform angular speed w in a vertical plane normal to a uniform magnetic field B. Deduce an expression for the emf induced in this rod. If resistance is R find current induced in it ?

(b) Define the term Self Inductance. Obtain expression for the Self Inductance of long solenoid.

Q25. (a) Explain origin of displacement current. How Maxwell modify Ampere’s law to explain consistency of electric circuits.

(b) Give applications of electromagnetic waves by explaining electromagnetic spectrum.

Q. 26. (a)With the help of a ray diagram, show the formation of image of a point object by refraction of light at a spherical surface separating two media of refractive indices n_{1 }and n_{2} (n_{2} > n_{1}) respectively. Using this diagram, derive the relation. Write the sign conventions used. What happens to the focal length of convex lens when it is immersed in water?

(b) Derive lens maker’s formula hence derive lens formula from it.

27.(a) Using Huygens’ principle, draw a diagram to show propagation of a wave-front originating from a monochromatic point source and line source. Explain behavior of wave front when it undergo refraction through prism and convex lens.

(b) Describe diffraction of light due to a single slit. Explain formation of a pattern of fringes obtained on the screen and plot showing variation of intensity with angle in single slit diffraction. Write one feature which distinguishes the observed pattern from the double slit interference pattern.

How would the diffraction pattern of a single slit be affected when:

(i) the width of the slit is decreased?

(ii) the monochromatic source of light is replaced by a source of white light

Q. 28.What is interference of light? Write two essential conditions for sustained interference pattern to be produced on the screen. Draw a graph showing the variation of intensity versus the position on the screen in Young’s experiment when (a) both the slits areopened and (b) one of the slits is closed.

What is the effect on the interference pattern in Young’s double slit experiment when:

- (i) screen is moved closer to the plane of slits?
- (ii) separation between two slits is increased. Explain your answer in each case.

Q. 29.(a) What are coherent sources ? Why are coherent sources required to produce interference of light ? Prove that if two coherent sources y_{1} = a coswt and y_{2} =a cos (wt +φ) super impose then resultant intensity will be I =4I_{0} cos^{2} φ/2.

(b) Give an example of interference of light in everyday life. In Young’s double slit experiment, the two slits are 0.03 cm apart and the screen is placed at a distance of 1.5 m away from the slits. The distance between the central bright fringe and fourth bright fringe is 1 cm. Calculate the wavelength of light used.

Q30 Give condition for diffraction of light due to single slit. Compare intensity pattern of interference and diffraction then derive an expression for the width of the central maximum due to diffraction of light at a single slit. A slit of width ‘a’ is illuminated by a monochromatic light of wavelength 700 nm at normal incidence. Calculate the value of ‘a’ for position of

- 1. first minimum at an angle of diffraction of 30°.
- 2. first maximum at an angle of diffraction of 30°.

Q31(a) For a ray of light traveling from a denser medium of refractive index n_{1} to a rarer medium of refractive index n_{2}, prove that n_{2}/n_{1}=Sin i_{c}, where *i*_{c} is the critical angle of incidence for the media.

(b) Explain with the help of a diagram, how the above the principle is used for transmission of video signals using optical fibers.

Q32Draw a ray diagram to show the working of a compound microscope. Deduce an expression for the total magnification when the final image is formed at the near point. In a compound microscope, an object is placed at a distance of 1.5 cm from the objective of focal length 1.25 cm. If the eye piece has a focal length of 5 cm and the final image is formed at the near point, estimate the magnifying power of the microscope.

Q33. State the importance of coherent sources in the phenomenon of interference. In Young’s double slit experiment to produce interference pattern, obtain the conditions for constructive and destructive interference. Hence deduce the expression for the fringe width. What will be change in fringe width if apparatus of Young is immersed in water?

(b) Show that the angular width of the first diffraction fringe is half of that of the central fringe.

(c) If a monochromatic source of light is replaced by white light ,what change would you observe in the diffraction pattern?

Q34.(a)Define magnifying power of a telescope. Draw a labeled diagram derive its expression.

(b) A small telescope has an objective lens of focal length 150 cm and an eye piece of focal length 5 cm. If this telescope is used to view a 100 m high tower 3 km away, find the height of the final image when it is formed 25 cm away from the eye piece.

(c)How is the working of a telescope different from that of a microscope? The focal lengths of the objective and eyepiece of a microscope are 1.25 cm and5 cm respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of 30 in normal adjustment.

Q35. (a) Draw a ray diagram showing the image formation by a compound microscope. Hence obtain expression for total magnification when the image is formed at infinity.

(b) State Huygen’s principle. Using this principle draw a diagram to show how a plane wave front incident at the interface of the two media gets refracted when it propagates from a rarer to a denser medium. Hence verify Snell’s law of refraction.

(c) When monochromatic light travels from a rarer to a denser medium, explain the following, giving reasons:

- (i) Is the frequency of reflected and refracted light same as the frequency of incident light?
- (ii) Does the decrease in speed imply a reduction in the energy carried by light wave?

Q36. (a)Explain refraction through prism .derive relation in angle of deviation and refractive index

(b) Explain rotation of image through 90 and 180 degree through right angle Prism.

(c) Calculate the refractive index of the material of an equilateral prism for which the angle of Minimum deviation is 60^{0}.

Q37 (a) Define the term threshold frequency and stopping potential. Explain Lenard experiment to analysis Photo-electric effect. Draw graph between photoelectric current and potential and photoelectric current and frequency on basis of these graph explain laws of photoelectric effect.

(b) Why we cant explain Photoelectric effect on basis of wave theory of light.

(c) In study of photoelectric effect, using Einstein photoelectric equation we can determine planck’s constant as well. When we draw graph between stopping potential we will find a straight line as shown in above diagram. Using the graph answer following questions

- Which metal possess more threshold frequency
- Which metal posses more threshold wavelength
- Which metal posses more work function
- Slope of above graph represent

Q38. Using the postulates of Bohr’s model of hydrogen atom, obtain an expression for the frequency of radiation emitted when atom make a transition from the higher energy state with quantum number *n*_{i} to the lower energy state with quantum number *n _{f}* (

*n*<

_{f}*n*). When electron in hydrogen atom jumps from energy state n

_{i}_{i}= 4 to n

_{f}= 3, 2,1 identify the spectral series to which the emission lines belong.

Q39 Draw the graph showing the variation of binding energy per nucleon. Which element show maximum stability. Also explain nuclear fusion and fission region. Use this graph to show release of energy in both the processes of nuclear fusion and fission. Write the basic nuclear process of neutron undergoing beta decay. Why is the detection of neutrinos found very difficult ?

Q40. (a) Draw a graph showing the variation of potential energy between a pair of nucleons as a function of their separation. Indicate the region in which the nuclear force is attractive and repulsive

(b) Write two important conclusion which you can draw regarding the nature of the nuclear forces

Q41 (a) Explain the formation of energy bands in semiconductor. How they get modified with doping for P type and N type semiconductor

(b) Explain briefly with the help of a circuit diagram how V-I characteristics of a p-n junction diode are obtained in (i) forward bias, and (ii) reverse bias.

(c) Explain energy band diagram of conductor, semiconductor and insulator

Q. 42. (a) Name two important process involved in formation of PN junction.

(b) State the principle of working of p-n diode as a rectifier. Explain, with the help of a circuit diagram, the use of p n -junction as a full wave rectifier. Draw a sketch of the input and output waveforms. If Input frequency is 50 Hz find out put frequency in full wave and half wave rectifier.

Q43.(a) Explain combination of cells. If MxN cells each of internal resistance r connected in series with external resistance R find current through R.

(b) Two cells of emf 10v and 2V and internal resistance 10 ohm and 5 ohm respectively, are connected in parallel with external resistance R . Find effective voltage across R.

Q44 (a) Explain the difference in EMF and voltage. Then find expression for internal resistance of cell.

(b) Explain temperature dependence of resistance. then draw suitable graph in temperature and resistance for conductor and semiconductor.

Q45. (a) Derive an expression for force experienced by current carrying conductor placed in magnetic field.

(b) If magnet of magnetic moment M placed in magnetic field B, prove that torque experienced by will be MXB. Then find conditions of stable and unstable equilibrium.

(c) A metal rod PQ of length l, resting on the smooth horizontal rails AB positioned between the poles of a permanent magnet. The rails, rod and the magnetic field are in three perpendicular directions. A galvanometer G connects the rail through a key K. Assume the magnetic field to be uniform and resistance of rod is R.

- (a) Suppose K is open and the rod is moved with a speed v in the direction as shown. Find the polarity and magnitude of Induced emf
- (b) With K open and rod moving uniformly explain why net force on rod is zero?
- (c) What will be induced emf if rod is parallel to the magnetic field ?

Q46. (a) What do you mean by quality factor of series LCR circuit. On what factors it depends?

(b) Draw graphical variation of R , X_{L} and X_{c} with frequency.

(c) A device X is connected to an ac source V= V_{0}sinwt. The variation of voltage , current and power in one complete cycle is shown in the figure

- Identify the device X
- Which of the curve A, B and C represent the voltage, current and power consumed in the circuit
- How does its impedance vary frequency ? Show graphically.
- Obtain an expression for current in the circuit.
- What is average power consumption over a cycle ?

(d) What do you understand by sharpness of resonance? How it it related with quality factor?