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Paper pattern
A · all 16 · 1 mark each · 12 multiple choice and 4 assertion-reason16
B · all 5 · 2 marks each · short answer, internal choice in 210
C · all 7 · 3 marks each · short answer21
D · all 2 · 4 marks each · case-based, a passage or data then sub-questions8
E · all 3 · 5 marks each · long answer, internal choice in all three15
Board paper total70
CBSE Physics (042) Class XII question paper design and sample question paper, 2026-27: 33 questions, 70 marks, 3 hours, about a third of the questions with an internal choice.

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Likely questions

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2 marks · short answer
State Gauss's theorem. A point charge q is placed at the centre of a cube of side a. What is the electric flux through one face of the cube?Unit IWhy do two electric field lines never cross each other? Draw the field lines due to two equal positive charges placed close together.Unit ITwo identical metal spheres carry charges of +7 μC and −3 μC and attract each other with a force F. They are touched together and put back at the same distance. Find the new force in terms of F, and say whether it attracts or repels.Unit IAn electric dipole is placed in a uniform electric field. Show that the net force on it is zero. At what angle between p and E is the torque on it largest?Unit IWhy is no work done in moving a charge along an equipotential surface? Draw the equipotential surfaces for a uniform electric field.Unit IICharges of +3 nC, −1 nC, +4 nC and +2 nC sit at the corners of a square whose diagonal is 20 cm. Find the electric potential at the centre of the square.Unit IIA parallel plate capacitor is charged by a battery, and the battery is then removed. A dielectric slab of constant K is now slid in to fill the gap. How do the charge, the potential difference and the stored energy change?Unit IIDistinguish between polar and non-polar molecules, with one example of each. What happens to each kind in an external electric field?Unit IIDefine mobility of free electrons in a conductor and give its SI unit. How does it depend on the relaxation time?Unit IIITwo wires of the same metal have lengths in the ratio 1 : 2 and diameters in the ratio 2 : 1. Find the ratio of their resistances.Unit IIIState two limitations of Ohm's law, giving an example of a device or material for each.Unit IIIExplain, using ρ = m/(ne²τ), why the resistivity of a semiconductor decreases as its temperature rises.Unit IIIDraw the graph of terminal voltage V against current I for a cell. How are its emf and internal resistance found from the graph?Unit IIIDefine one ampere in terms of the force between two long straight parallel current-carrying conductors.Unit IVWhy does a magnetic field not change the kinetic energy of a charged particle moving in it? An electron and a proton enter a uniform magnetic field at right angles with equal speeds: which one moves in the larger circle, and why?Unit IVA galvanometer of resistance 40 Ω gives full-scale deflection for 2 mA. What resistance is needed, and how should it be connected, to convert it into a voltmeter of range 0 to 10 V?Unit IVState the Biot-Savart law in vector form. At which points near a current element is its magnetic field zero?Unit IVDescribe Oersted's experiment. What happens to the deflection of the compass needle when the current is reversed, and when the wire is moved from above the needle to below it?Unit IVWrite two differences between magnetic field lines and the electric field lines of static charges.Unit VDefine magnetic susceptibility and relative permeability, and write the relation between them. What is the sign of the susceptibility of a diamagnetic substance?Unit VHow does the magnetisation of a paramagnetic sample change when it is (a) heated and (b) cooled in a strong magnetic field? Give the reason in each case.Unit VWhy does a current-carrying solenoid behave like a bar magnet? How can you tell which end is its north pole?Unit VA bar magnet of magnetic moment m is cut into two equal halves across its length. What is the magnetic moment of each half? Why can we never get an isolated pole this way?Unit VState Lenz's law. The north pole of a magnet is pushed towards a closed coil. Which pole appears on the face of the coil nearer the magnet? Give a reason.Unit VIDefine self inductance and give its SI unit. Find the energy stored in a 50 mH inductor carrying a current of 2 A.Unit VIA coil of 200 turns has a flux of 5 mWb through each turn. The flux falls to zero in 0.1 s. Find the average emf induced in the coil.Unit VIThe flux through each turn of a 50-turn coil of resistance 10 Ω rises steadily from 2 mWb to 8 mWb in 0.05 s. Find the induced emf and the induced current.Unit VIDefine the rms value of an alternating current. An AC voltmeter reads 220 V across the mains. What is the peak value of the voltage?Unit VIIWhy does a capacitor block DC but allow AC to pass? Find the reactance of a (100/π) μF capacitor at 50 Hz.Unit VIIWhat is wattless current? Why is a choke coil preferred to a resistor for controlling the current in an AC circuit?Unit VIIWhy is the core of a transformer laminated? Why can a transformer not be used to step up a DC voltage?Unit VIIWhat is displacement current? Why did Maxwell need to introduce it?Unit VIIIWrite two characteristics of electromagnetic waves. The peak electric field of an EM wave in vacuum is 60 V m⁻¹; find its peak magnetic field.Unit VIIIName the EM waves used (a) in radar and (b) in TV remote controls. Write the wavelength range of each.Unit VIIIHow are X-rays produced? Give one use and one harmful effect of X-rays.Unit VIIIAn object is placed 20 cm in front of a concave mirror of focal length 15 cm. Using the New Cartesian sign convention, find the position, nature and magnification of the image.Unit IXState two conditions for total internal reflection. The critical angle for a transparent medium is 30°. Find its refractive index.Unit IXTwo thin lenses of power +6 D and −2 D are kept in contact. Find the focal length of the combination. Is it converging or diverging?Unit IXA ray of light passes symmetrically through an equilateral prism of refractive index √2. Find the angle of minimum deviation and the angle of incidence.Unit IXGive two reasons why large astronomical telescopes use a concave mirror rather than a lens as the objective.Unit IXState Huygens' principle. Draw the shape of the wavefront for light from (a) a point source close by, (b) a distant star.Unit XWhy can two independent sodium lamps not be used as coherent sources? Write one way of obtaining coherent sources.Unit XIn Young's double slit experiment, how does the fringe width change if (a) the screen is moved away from the slits, (b) the whole set-up is dipped in water?Unit XHow does the width of the central maximum in single slit diffraction change if (a) the slit width is halved, (b) red light replaces violet light? Give reasons.Unit XDefine work function and threshold frequency for a metal. Write the relation between them.Unit XIDraw a graph showing how photocurrent varies with collector plate potential for two different intensities of light of the same frequency. What does it show about the stopping potential?Unit XIA lamp gives out 10 W of light of wavelength 663 nm. Find the number of photons it emits per second. (h = 6.63 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s)Unit XIAn electron is accelerated from rest through a potential difference of 144 V. Find its de Broglie wavelength.Unit XIDefine impact parameter. What is the scattering angle of an alpha particle whose impact parameter is zero, and why?Unit XIIState two limitations of Rutherford's nuclear model of the atom.Unit XIIWrite Bohr's quantisation condition for the angular momentum of an electron. Find the angular momentum of an electron in the third orbit of hydrogen. (h = 6.63 × 10⁻³⁴ J s)Unit XIIState Bohr's second postulate. How did de Broglie's hypothesis explain it?Unit XIIFind the wavelength of the photon emitted when the electron in a hydrogen atom falls from n = 3 to n = 2. In which part of the spectrum does it lie? (Eₙ = −13.6/n² eV, hc = 1240 eV nm)Unit XIIShow that the density of nuclear matter is the same for all nuclei.Unit XIIIWrite any two properties of the nuclear force. Why can gravity not hold the protons of a nucleus together?Unit XIIIDefine mass defect and binding energy of a nucleus. What is the energy equivalent of 1 u in MeV?Unit XIIIDistinguish between nuclear fission and nuclear fusion, giving one example of each.Unit XIIIDistinguish between n-type and p-type semiconductors, giving one example of a dopant for each.Unit XIVWhat is a hole in a semiconductor? Why does the conductivity of an intrinsic semiconductor increase with temperature?Unit XIVHow does the width of the depletion region of a p-n junction change when it is (a) forward biased and (b) reverse biased? Give a reason for each.Unit XIVThe input frequency of a full-wave rectifier is 50 Hz. What is the frequency of the output? Give a reason.Unit XIV
3 marks · short answer
Derive an expression for the electric field at a point on the equatorial line of an electric dipole. How does it change for a short dipole?Unit IUsing Gauss's theorem, derive the electric field due to a uniformly charged infinite plane sheet. Show that it does not depend on the distance from the sheet.Unit ICharges +q, +q and −q are placed at the corners of an equilateral triangle of side a. Find the size and direction of the net force on the charge −q.Unit IDerive an expression for the electric potential at a point due to a short electric dipole. Show that it is zero on the equatorial line.Unit IIDerive the expression for the equivalent capacitance of three capacitors in series. Capacitors of 3 μF and 6 μF are joined in series, and this pair is joined in parallel with a 4 μF capacitor across 12 V. Find the charge on the 4 μF capacitor and on the 3 μF capacitor.Unit IIDerive an expression for the potential energy of an electric dipole in a uniform electric field. Find the work done in turning it from the position of stable equilibrium to that of unstable equilibrium.Unit IIDerive an expression for the drift velocity of free electrons in a conductor in terms of the relaxation time. Hence obtain the relation I = neAv_d.Unit IIITwo cells of emfs ε₁ and ε₂ and internal resistances r₁ and r₂ are joined in parallel with like terminals together. Derive expressions for the equivalent emf and internal resistance.Unit IIIShow that the power lost in cables of resistance R_c, when power P is sent at voltage V, is P²R_c/V². A 220 V, 100 W bulb is used on a 110 V supply: find its power, assuming its resistance stays the same.Unit IIIUsing the idea of drift velocity, show that the resistivity of a conductor is ρ = m/(ne²τ). Name the factors on which it depends.Unit IIIState Ampere's circuital law. Use it to obtain the magnetic field due to an infinitely long straight wire carrying a steady current, and sketch how the field varies with distance from the wire.Unit IVDerive an expression for the force per unit length between two long straight parallel conductors carrying currents I₁ and I₂. Show that the force is attractive when the currents are in the same direction.Unit IVA charged particle enters a uniform magnetic field with its velocity at right angles to the field. Show that it moves in a circle, and that its frequency of revolution does not depend on its speed.Unit IVDerive an expression for the torque on a rectangular current loop placed in a uniform magnetic field. Write it in vector form using the magnetic dipole moment, and state when the loop is in stable equilibrium.Unit IVDistinguish between diamagnetic, paramagnetic and ferromagnetic substances on the basis of susceptibility, relative permeability and behaviour in a non-uniform field. Give one example of each.Unit VWrite the expressions for the torque on, and the potential energy of, a bar magnet in a uniform magnetic field. Name the positions of stable and unstable equilibrium. How much work is needed to turn a magnet of moment 0.5 A m² from stable to unstable equilibrium in a field of 0.2 T?Unit VWrite the expressions for the magnetic field of a short bar magnet at a far point on its axial line and on its equatorial line, with their directions. Compare them with the fields of an electric dipole.Unit VDescribe Faraday's experiment with a bar magnet and a coil joined to a galvanometer. State three observations and the conclusion drawn from them.Unit VIA rod of length l slides with velocity v on two parallel rails in a uniform magnetic field B perpendicular to their plane. Derive the expression for the emf induced across the rod, using the change in flux.Unit VIState Lenz's law and show that it is in accordance with the law of conservation of energy. Draw a diagram showing the direction of the induced current when the north pole of a magnet approaches a coil.Unit VIAn AC voltage v = vₘ sin ωt is applied across a pure inductor. Show that the current lags the voltage by π/2. Define inductive reactance and draw the phasor diagram.Unit VIIState the condition for resonance in a series LCR circuit and obtain the resonant frequency. Draw graphs of current against frequency for two values of resistance, and give one use of resonance.Unit VIIDerive an expression for the average power in an AC circuit. Define power factor and state when it is zero and when it is one.Unit VIIFor a parallel plate capacitor being charged, show that the displacement current between the plates equals the conduction current in the connecting wires. Write the Ampere-Maxwell law.Unit VIIIHow are electromagnetic waves produced? Draw a labelled diagram of a plane EM wave travelling along the z-axis, and explain why it is transverse.Unit VIIIName the EM waves (a) absorbed by the ozone layer, (b) used to detect bone fractures and (c) given out by radioactive nuclei. Give one source of each and arrange them in order of increasing frequency.Unit VIIIDerive the relation n₂/v − n₁/u = (n₂ − n₁)/R for refraction at a convex spherical surface, when the object is in the rarer medium and a real image is formed. Draw the ray diagram.Unit IXExplain, with a ray diagram, why a coin at the bottom of a tank of water appears raised. If the water is 60 cm deep (n = 4/3), by how much does the coin appear raised when seen from directly above?Unit IXDerive the expression for the focal length of two thin lenses in contact. Hence write the power of the combination.Unit IXA thin equiconvex lens of glass (n = 1.5) has a focal length of 20 cm in air. Find the radius of curvature of its faces, and its focal length when it is immersed in water (n = 4/3).Unit IXDraw a ray diagram for refraction through a glass prism, and derive n = sin[(A + Dm)/2] / sin(A/2).Unit IXUsing Huygens' principle, verify the law of reflection at a plane surface. Draw a labelled diagram.Unit XTwo coherent waves, each of intensity I₀, superpose at a point with a phase difference φ. Obtain the resultant intensity and state where it is maximum and where it is zero.Unit XUsing Huygens' wavelets, explain why a minimum forms at θ = λ/a in single slit diffraction. Draw the intensity distribution.Unit XWrite Einstein's photoelectric equation. Using it, explain (a) why there is a threshold frequency, (b) why the maximum kinetic energy of photoelectrons does not depend on intensity, (c) why emission is instantaneous.Unit XIExplain why the wave nature of a moving car is not observed, while that of an electron is. Find the de Broglie wavelength of an electron moving with speed 7.28 × 10⁶ m/s.Unit XIDescribe the observations of Hallwachs and Lenard on the photoelectric effect. What did they conclude about the particles emitted?Unit XIUsing Bohr's postulates, derive an expression for the radius of the nth orbit of the hydrogen atom and show that rₙ ∝ n².Unit XIIThe ground state energy of hydrogen is −13.6 eV. Find the kinetic and potential energies of the electron in this state, and the energy needed to excite it to n = 3.Unit XIIAn alpha particle of kinetic energy 5.5 MeV moves head-on towards a gold nucleus (Z = 79). Find its distance of closest approach. How does this distance change if the kinetic energy is halved?Unit XIICalculate the binding energy per nucleon of ⁵⁶₂₆Fe. Mass of the ⁵⁶Fe nucleus = 55.9207 u, mₚ = 1.00727 u, mₙ = 1.00866 u, 1 u = 931.5 MeV.Unit XIIIDraw a graph of the potential energy of a pair of nucleons as a function of their separation. Mark the regions where the nuclear force is attractive and repulsive, and state two properties of the force.Unit XIIICalculate the energy released when two ²₁H nuclei fuse to form ⁴₂He (²₁H = 2.0141 u, ⁴₂He = 4.0026 u, 1 u = 931.5 MeV). Why does fusion need a very high temperature?Unit XIIIDraw the energy band diagrams of a conductor, a semiconductor and an insulator, and distinguish between them on the basis of the energy gap.Unit XIVExplain, with a labelled diagram, the formation of the depletion region and the barrier potential at a p-n junction.Unit XIVDraw the circuit diagram of a half-wave rectifier and explain its working with the help of input and output waveforms.Unit XIV
5 marks · long answer
(a) Define electric dipole moment and give its SI unit. (b) Derive an expression for the electric field at a point on the axial line of an electric dipole, and write it for a short dipole. (c) Charges of ±4 μC are 3 mm apart. Find the field at a point on the axis 20 cm from the centre.Unit I(a) State Gauss's theorem. (b) Use it to derive the electric field due to an infinitely long, uniformly charged straight wire, and draw the graph of E against r. (c) Find the field 2 cm from a wire with λ = 3 × 10⁻⁸ C m⁻¹.Unit I(a) Derive an expression for the capacitance of a parallel plate capacitor when a dielectric of constant K fills the space between its plates. (b) Two plates of area 2 × 10⁻² m² are 1 mm apart in air. Find the capacitance, and the new capacitance when the gap is filled with a dielectric of K = 5. (ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻²)Unit II(a) Define electric potential at a point and derive an expression for the potential due to a point charge. (b) Charges of +5 nC and −2 nC are 21 cm apart. Find the two points on the line through them where the electric potential is zero.Unit IIState Kirchhoff's rules and the conservation law behind each. One branch has an 8.0 V cell in series with 2.0 Ω, and another has a 4.0 V cell in series with 2.0 Ω. The branches are joined in parallel, positive terminals together, across a 1.0 Ω resistor. Use Kirchhoff's rules to find the current in each branch and the potential difference across the 1.0 Ω resistor.Unit III(a) Draw the circuit of a Wheatstone bridge and use Kirchhoff's rules to obtain its balance condition. (b) In a Wheatstone bridge, arm AB = 12 Ω, BC = 18 Ω, CD = 6.0 Ω and DA = 4.0 Ω. A 6.0 V cell of negligible internal resistance is joined across A and C, and a galvanometer across B and D. Show that the bridge is balanced and find the current drawn from the cell. (c) Will the bridge stay balanced if the cell and the galvanometer are interchanged? Give a reason.Unit III(a) Using the Biot-Savart law, derive the magnetic field at a point on the axis of a circular loop of radius R carrying current I. (b) Write the field at its centre. (c) Find the field at the centre of a coil of 100 turns and radius 10 cm carrying 0.50 A.Unit IV(a) Explain, with a labelled diagram, the principle and working of a moving coil galvanometer. (b) Why is a radial magnetic field used? (c) Define current sensitivity and give two ways to increase it. (d) Why can a galvanometer not be used as an ammeter without changes?Unit IV(a) Define magnetisation M and magnetic intensity H, and show that B = μ₀μrH, where μr = 1 + χ. (b) A long solenoid with 800 turns per metre carries 2.5 A, and its core has relative permeability 1000. Find H, B and M.Unit V(a) Explain the effect of temperature on the magnetic properties of diamagnetic, paramagnetic and ferromagnetic substances. (b) What happens to a ferromagnetic substance when it is heated to a high enough temperature, and is the change sudden or gradual? (c) Explain ferromagnetism using the idea of domains, with a sketch.Unit VDefine mutual inductance. Derive an expression for the mutual inductance of two long coaxial solenoids and show that M₁₂ = M₂₁. Two coils have M = 0.4 H; find the emf in one when the current in the other changes at 15 A/s.Unit VIDefine self inductance. Derive an expression for the self inductance of a long air-cored solenoid. Show that the energy stored in an inductor carrying a current I is ½LI².Unit VI(a) Using a phasor diagram, derive expressions for the impedance of a series LCR circuit and the phase angle between the current and the voltage. (b) A series LCR circuit has R = 80 Ω, X_L = 100 Ω and X_C = 40 Ω. Find its impedance and state whether the current leads or lags the voltage.Unit VIIExplain the principle and working of an AC generator with a labelled diagram, and derive the expression for the emf induced. A coil of 50 turns, each of area 0.2 m², rotates at 50 revolutions per second in a field of 0.05 T: find the peak emf.Unit VII(a) How are electromagnetic waves produced? Explain their transverse nature with a labelled diagram. (b) Write three characteristics of EM waves. (c) An EM wave of frequency 50 MHz travels in a non-magnetic medium of relative permittivity 9. Find its speed and wavelength in the medium.Unit VIIIName the seven parts of the electromagnetic spectrum in order of increasing frequency. For radio waves, microwaves and infrared waves, give the wavelength range, how they are produced and one use of each.Unit VIII(a) Draw a labelled ray diagram of a compound microscope forming the final image at the least distance of distinct vision, and derive its magnifying power. (b) A compound microscope has an objective of focal length 1.0 cm, an eyepiece of focal length 5.0 cm and a tube length of 16 cm. Find its magnifying power in normal adjustment.Unit IX(a) Draw a labelled ray diagram of an astronomical refracting telescope in normal adjustment, and derive its magnifying power. (b) A telescope has an objective of focal length 120 cm and an eyepiece of focal length 4 cm. Find its magnifying power and tube length in normal adjustment. (c) Give one advantage of a reflecting telescope.Unit IX(a) Derive the lens maker's formula for a thin double convex lens, and hence obtain the thin lens formula. (b) A double convex lens of glass (n = 1.5) has radii of curvature of 30 cm and 60 cm. Find its focal length in air.Unit IX(a) Using Huygens' principle, deduce Snell's law of refraction with a labelled diagram. (b) Light of wavelength 600 nm in air enters glass of refractive index 1.5. Find its speed, wavelength and frequency in glass.Unit X(a) Describe Young's double slit experiment with a labelled diagram and write the expression for fringe width. (b) In such an experiment, d = 0.4 mm, D = 1.2 m and λ = 500 nm. Find the distance between the third bright fringe and the second dark fringe on the same side of the centre.Unit X(a) Describe an experiment to study the photoelectric effect with a labelled diagram. (b) Draw graphs to show how photocurrent varies with collector potential for (i) different intensities at the same frequency, (ii) different frequencies at the same intensity, and state what each graph shows.Unit XI(a) Write Einstein's photoelectric equation and draw the graph of stopping potential against frequency. Explain how Planck's constant and the work function can be found from it. (b) Light of frequency 1.0 × 10¹⁵ Hz falls on a metal of threshold frequency 6 × 10¹⁴ Hz. Find the stopping potential. (h = 6.63 × 10⁻³⁴ J s, e = 1.6 × 10⁻¹⁹ C)Unit XIDescribe the Geiger-Marsden alpha-particle scattering experiment with a labelled diagram. Give its observations and the conclusions about the structure of the atom. Draw the graph of the number of scattered alpha particles against scattering angle.Unit XII(a) State Bohr's postulates for the hydrogen atom. (b) Derive the expressions for the speed and the total energy of the electron in the nth orbit. (c) Show that the speed of the electron in the first orbit is about 1/137 of the speed of light.Unit XII(a) Draw the curve of binding energy per nucleon against mass number. (b) Use it to explain the release of energy in nuclear fission and fusion. (c) Why is the binding energy per nucleon nearly constant for 30 < A < 170?Unit XIII(a) What is nuclear fission? Write a balanced equation for the fission of ²³⁵U by a slow neutron. (b) Calculate the energy released by the fission of 1 kg of ²³⁵U if each fission releases 200 MeV. (c) In what form does the energy released in fission first appear?Unit XIII(a) Draw the circuit diagrams used to study the forward and reverse bias characteristics of a p-n junction diode. (b) Draw the I-V characteristics and explain their shape. (c) What is meant by breakdown voltage?Unit XIV(a) With a labelled circuit diagram, explain the working of a full-wave rectifier. (b) Draw its input and output waveforms. (c) How can the output be made smoother?Unit XIV
4 marks · case-based
In a classic experiment, tiny charged oil drops are sprayed between two horizontal metal plates. The electric field between the plates is adjusted until a drop hangs at rest. One drop of mass 4.8 × 10⁻¹⁵ kg hangs still when the field is 1.0 × 10⁵ N C⁻¹. The drop carries extra electrons. Take g = 10 m s⁻² and e = 1.6 × 10⁻¹⁹ C. (i) Write the condition for the drop to stay at rest. (1 mark) (ii) Should the field point upward or downward? Give a reason. (1 mark) (iii) Find the charge on the drop and the number of extra electrons. What does this show about electric charge? (2 marks)Unit IA small charge of 8.85 nC is placed at the centre of a closed plastic cube of side 20 cm. A student wants to find the electric flux through the box. Take ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻². (i) Find the total flux through the cube. (1 mark) (ii) What happens to the total flux if the cube is replaced by a sphere of radius 50 cm with the same charge at its centre? (1 mark) (iii) A second charge of −8.85 nC is now placed inside the cube, and a third charge of +5 nC just outside it. Find the new total flux, and say whether the field at points on the surface changes. (2 marks)Unit IEach key of some computer keyboards works as a small parallel plate capacitor. A metal plate fixed under the key sits above another fixed plate, with air between them. Pressing the key brings the plates closer, and the change in capacitance tells the computer which key was pressed. For one key, the plate area is 50 mm² and the gap is 0.6 mm; pressing the key reduces the gap to 0.15 mm. Take ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻². (i) Write the formula for the capacitance of a parallel plate capacitor. (1 mark) (ii) Does the capacitance increase or decrease when the key is pressed? Why? (1 mark) (iii) Find the capacitance before and after the key is pressed. (2 marks)Unit IIA camera flash unit uses a 100 μF capacitor. A small circuit charges it to 300 V from the battery. When a photo is taken, the capacitor empties through the flash tube in about 1 ms, giving a bright flash. (i) Find the charge stored on the capacitor. (1 mark) (ii) Find the energy stored. (1 mark) (iii) Find the average power delivered during the flash. If two such capacitors were joined in series and charged to the same 300 V, what energy would they store together? (2 marks)Unit IIA student studies an old torch cell. She joins it to a rheostat and an ammeter, with a voltmeter across its terminals. Her readings are: I = 0.20 A, V = 1.40 V; I = 0.40 A, V = 1.30 V; I = 0.60 A, V = 1.20 V. A graph of V against I is a straight line. (i) What is the emf of the cell? (1 mark) (ii) Find its internal resistance. (1 mark) (iii) The cell is now joined across a 2.5 Ω resistor. Find the current and the terminal voltage. (2 marks)Unit IIIA laboratory uses a Wheatstone bridge as a temperature sensor. Arms AB, AD and DC each have a fixed 100 Ω resistor. Arm BC is a metal wire whose resistance is 100 Ω at 0 °C, with α = 4.0 × 10⁻³ °C⁻¹. A 6.0 V cell of negligible internal resistance is joined across A and C. A voltmeter that draws almost no current is joined across B and D. (i) What does the voltmeter read when the wire is at 0 °C, and why? (1 mark) (ii) Find the resistance of the wire in boiling water at 100 °C. (1 mark) (iii) Find the voltmeter reading at 100 °C. (2 marks)Unit IIIIn the physics lab, Meera has a galvanometer with 30 divisions on each side of zero. Using the half-deflection method, she finds its resistance to be 100 Ω and its figure of merit to be 1 × 10⁻⁴ A per division. She wants to use it to check the voltage of a 3 V battery pack. (i) What current gives full-scale deflection? (1 mark) (ii) What must she join to the galvanometer, and how, to make a voltmeter? (1 mark) (iii) Find the value of this component for a range of 0 to 3 V, and the total resistance of her voltmeter. (2 marks)Unit IVScientists study charged particles by sending them through magnetic fields. In one set-up, a narrow beam of protons moving at 2.0 × 10⁶ m/s enters a uniform magnetic field of 0.10 T at right angles to the field. The beam bends into a circular arc. (Take the proton mass as 1.67 × 10⁻²⁷ kg and e = 1.6 × 10⁻¹⁹ C.) (i) Why does the speed of the protons stay the same inside the field? (1 mark) (ii) What would the path be if the protons entered at 30° to the field? (1 mark) (iii) Find the radius of the circular path. How would the radius change for alpha particles entering with the same speed? (2 marks)Unit IVRiya tests three small rods, X, Y and Z, with a strong magnet in her school lab. Rod X is weakly pushed away, rod Y is weakly pulled in, and rod Z jumps to the magnet. When hung freely between the poles, X sets across the field while Y and Z set along it. Her teacher then heats rod Z strongly, and it is hardly attracted any more. (i) Classify X, Y and Z as dia-, para- or ferromagnetic. (1 mark) (ii) Which rod has a negative susceptibility? (1 mark) (iii) Why did strong heating change the behaviour of Z, and what kind of substance does Z behave like while it is very hot? (2 marks)Unit VA short bar magnet of magnetic moment 0.40 A m² lies on a table, away from other magnets (ignore the Earth's field). A student places a tiny field sensor first on its axis and then on its equatorial line, each time 10 cm from its centre. Later the magnet is placed in a uniform field of 0.25 T. (Take μ₀/4π = 10⁻⁷ T m A⁻¹.) (i) Find the field on the axis. (1 mark) (ii) Find the field on the equatorial line, and give its direction relative to m. (1 mark) (iii) Find the torque on the magnet when m makes 30° with the uniform field, and the work needed to turn it from 0° to 90°. (2 marks)Unit VA metal rod 50 cm long slides at a steady 2 m/s on two parallel rails joined by a 0.5 Ω resistor. A uniform field of 0.5 T acts perpendicular to the plane of the rails. The resistance of the rod and rails is negligible. (i) Find the emf induced across the rod. (1 mark) (ii) Find the current in the circuit. (1 mark) (iii) The speed of the rod is doubled. Find the new current, and use Lenz's law to explain why a steady push is still needed to keep the rod moving. (2 marks)Unit VIA coil of 100 turns and area 0.02 m² is held with its plane perpendicular to a uniform magnetic field. The field rises steadily from 0.1 T to 0.5 T in 0.2 s. The coil has a resistance of 2 Ω and its ends are joined. (i) Name the law that gives the magnitude of the induced emf. (1 mark) (ii) Find the induced emf. (1 mark) (iii) Find the induced current and the charge that flows through the coil. (2 marks)Unit VIA village gets electricity from an 11,000 V line. A distribution transformer near the village steps it down to 220 V for homes. Its primary coil has 5000 turns. Together the homes draw 22 kW. Assume the transformer is ideal. (i) Is this a step-up or a step-down transformer? Give a reason. (1 mark) (ii) Find the number of turns in the secondary coil. (1 mark) (iii) Find the current in the secondary coil and in the primary coil. (2 marks)Unit VIIIn a laboratory, a series LCR circuit has R = 60 Ω, X_L = 120 Ω and X_C = 40 Ω at the supply frequency of 50 Hz. It is connected to a 200 V (rms) supply. An AC ammeter in the circuit reads the rms current. The students want to know how much power the circuit really uses. (i) Find the impedance of the circuit. (1 mark) (ii) Find the rms current and state whether it leads or lags the voltage. (1 mark) (iii) Find the power factor and the average power consumed. (2 marks)Unit VIIA microwave oven in a home kitchen works at a frequency of about 2.45 GHz (a typical real-world value; your textbook gives no figure). The boundaries between regions of the spectrum are not sharp. The waves are made by a magnetron and are reflected by the metal walls inside the oven. Food containing water heats up quickly, while a dry glass plate stays fairly cool. (i) To which region of the EM spectrum do these waves belong? (1 mark) (ii) Find their wavelength, taking c = 3 × 10⁸ m s⁻¹. (1 mark) (iii) Explain why food containing water heats up, and give one other use of this region of the spectrum. (2 marks)Unit VIIIIndia's internet travels through optical fibre cables as pulses of light. Each fibre has a thin glass core surrounded by a cladding of slightly lower refractive index. Light inside the core meets the core-cladding boundary at angles larger than the critical angle. So it is reflected again and again, and reaches the far end with very little loss, even around bends. (i) Name the phenomenon that keeps the light inside the fibre. (1 mark) (ii) Why must the cladding have a lower refractive index than the core? (1 mark) (iii) The core has n = 1.50 and the cladding n = 1.44. Find the sine of the critical angle at the boundary, and the speed of light in the core (c = 3 × 10⁸ m s⁻¹). (2 marks)Unit IXAt a dental check-up, Meena sees the dentist hold a small concave mirror of focal length 4 cm close to her tooth. On the way home, she notices the convex rear-view mirror of her scooter, which shows a wide view of the road. Both mirrors obey the same mirror equation when the New Cartesian sign convention is used. (i) Which of the two mirrors always forms a virtual, erect and diminished image? (1 mark) (ii) Write the sign of the focal length of each mirror. (1 mark) (iii) The dentist holds the mirror 3 cm from the tooth. Find the position of the image and its magnification. (2 marks)Unit IXPriya sets up Young's double slit experiment in her school laboratory. Light of wavelength 600 nm from a laser falls on two slits 0.3 mm apart, and fringes form on a screen 1.5 m away. She notices that the central fringe is bright and that all fringes are equally spaced. She then repeats the experiment with the whole set-up inside a tank of water of refractive index 4/3. (i) Why do the two slits act as coherent sources? (1 mark) (ii) Find the fringe width in air. (1 mark) (iii) Find the fringe width in water and the distance of the fourth bright fringe from the centre in water. (2 marks)Unit XA teacher shines light of wavelength 600 nm on a slit whose width can be adjusted. The diffraction pattern falls on a wall 2 m away. With the slit 0.4 mm wide, the class sees a broad bright band at the centre with fainter bands on both sides. (i) What is diffraction? (1 mark) (ii) Find the width of the central bright band. (1 mark) (iii) The teacher narrows the slit to 0.2 mm and switches to blue light of wavelength 450 nm. Find the new width of the central band and say whether it is wider or narrower. (2 marks)Unit XA student shines light of three frequencies on the same metal surface in a photocell and measures the stopping potential each time. Her readings are: 6 × 10¹⁴ Hz, 0.6 V; 7 × 10¹⁴ Hz, 1.0 V; 8 × 10¹⁴ Hz, 1.4 V. She plots V₀ against ν and gets a straight line. (i) What is meant by stopping potential? (1 mark) (ii) Find the threshold frequency of the metal. (1 mark) (iii) Use the slope to estimate Planck's constant, and find the work function of the metal in eV. Take e = 1.6 × 10⁻¹⁹ C. (2 marks)Unit XIIn an electron microscope, electrons start from rest and are accelerated through a potential difference V. Their very short de Broglie wavelength lets the microscope show details far smaller than visible light can. A technician sets V = 10,000 V. (i) Write the de Broglie relation. (1 mark) (ii) Find the de Broglie wavelength of the electrons. (1 mark) (iii) If protons were accelerated through the same potential difference, would their wavelength be longer or shorter? Find λₑ/λₚ, taking mₚ = 1836 mₑ. (2 marks)Unit XIA teacher passes an electric discharge through hydrogen gas at low pressure. Through a spectroscope, students see four sharp coloured lines: red at 656 nm, blue-green at 486 nm, and two violet lines at 434 nm and 410 nm. The energy of level n is Eₙ = −13.6/n² eV, and hc = 1240 eV nm. (i) Is this an emission spectrum or an absorption spectrum? Give a reason. (1 mark) (ii) Why does the gas give only a few sharp lines and not a continuous band of colours? (1 mark) (iii) Show that the red line comes from the transition n = 3 to n = 2. (2 marks)Unit XIIIn Bohr's model, the electron in hydrogen moves only in certain circular orbits. Its energy in the nth orbit is Eₙ = −13.6/n² eV and the radius is rₙ = n² × 0.53 Å. A hydrogen atom in its ground state absorbs a photon, and its electron moves to n = 2. (i) What is the radius of the new orbit? (1 mark) (ii) What energy did the photon carry? (1 mark) (iii) Find the kinetic and potential energies of the electron in the n = 2 orbit. (2 marks)Unit XIIScattering experiments show that the radius of a nucleus of mass number A is R = R₀ ∛A, with R₀ = 1.2 fm. Chlorine occurs as two kinds of atoms, ³⁵Cl and ³⁷Cl, while ³H and ³He have the same mass number but different atomic numbers. (i) What are ³H and ³He called? (1 mark) (ii) Find the radius of a ²⁷Al nucleus. (1 mark) (iii) Show that all nuclei have nearly the same density. (2 marks)Unit XIIIIn a nuclear power station, ²³⁵U nuclei absorb slow neutrons and split. A typical reaction is ¹₀n + ²³⁵₉₂U → ¹⁴⁴₅₆Ba + ⁸⁹₃₆Kr + 3¹₀n. The binding energy per nucleon is about 7.6 MeV for uranium and about 8.5 MeV for the two products. (i) Show that the reaction is balanced. (1 mark) (ii) In what form does most of the released energy first appear? (1 mark) (iii) Estimate the energy released per fission from the binding energy values. (2 marks)Unit XIIIPure silicon has very few free carriers at room temperature: about 1.5 × 10¹⁶ m⁻³, compared with about 5 × 10²⁸ atoms m⁻³. Engineers add a tiny amount of impurity to change this. One sample is doped with phosphorus and another with boron. (i) Which sample is n-type? (1 mark) (ii) Name the majority carriers in the boron-doped sample. (1 mark) (iii) In the phosphorus-doped sample, nₑ = 5 × 10²² m⁻³. Find nₕ. (2 marks)Unit XIVA student studies a silicon diode. In forward bias she records: 0.5 V, 0 mA; 0.6 V, 1 mA; 0.7 V, 10 mA; 0.8 V, 30 mA. In reverse bias the current stays at about 1 μA from 1 V to 20 V. (i) What is the threshold voltage of the diode? (1 mark) (ii) Why is the reverse current almost constant? (1 mark) (iii) Find the dynamic resistance of the diode between 0.7 V and 0.8 V. (2 marks)Unit XIV

Answer frames

How to lay out a long answer, with a write-up check. 105 frames so far.

3-MARK ANSWER FRAME · UNIT IState the three basic properties of electric charge. Explain quantisation of charge and show that a body cannot carry a charge of 2.4 × 10⁻¹⁹ C.3-MARK ANSWER FRAME · UNIT IState Coulomb's law. Write it in vector form and show that the forces two charges exert on each other are equal and opposite.3-MARK ANSWER FRAME · UNIT IState the superposition principle. Three charges of +2 μC each sit at the corners of an equilateral triangle of side 10 cm. Find the net force on any one charge.3-MARK ANSWER FRAME · UNIT IDefine electric field at a point. Derive an expression for the electric field due to a point charge q at a distance r from it. Draw the graph of E against r.3-MARK ANSWER FRAME · UNIT IState four properties of electric field lines. Draw the field lines for (a) an electric dipole and (b) two equal positive charges.5-MARK ANSWER FRAME · UNIT IDerive expressions for the electric field of an electric dipole at a point on (a) its axial line and (b) its equatorial line. Compare the two for a short dipole.3-MARK ANSWER FRAME · UNIT IDerive an expression for the torque on an electric dipole placed in a uniform electric field. When is the dipole in stable equilibrium?3-MARK ANSWER FRAME · UNIT IDefine electric flux and give its SI unit. State Gauss's theorem. A charge q is placed at the centre of a cube: find the flux through the cube and through each face.5-MARK ANSWER FRAME · UNIT IState Gauss's theorem. Use it to find the electric field due to a uniformly charged thin spherical shell at a point (a) outside and (b) inside the shell. Draw the graph of E against r.3-MARK ANSWER FRAME · UNIT IIDefine electric potential at a point. Derive an expression for the potential due to a point charge q at a distance r. Draw the graph of V against r.3-MARK ANSWER FRAME · UNIT IIDerive an expression for the electric potential at a point due to a short electric dipole. Hence find the potential on its axial and equatorial lines.3-MARK ANSWER FRAME · UNIT IIWhat is an equipotential surface? State its properties. Draw equipotential surfaces for a point charge and for a uniform field, and show that E is normal to an equipotential surface.5-MARK ANSWER FRAME · UNIT II(a) Derive an expression for the potential energy of a system of two point charges. (b) Derive the potential energy of an electric dipole in a uniform electric field, and state its positions of stable and unstable equilibrium.3-MARK ANSWER FRAME · UNIT IIState the electrostatic properties of a conductor, giving a reason for each. What is electrostatic shielding?3-MARK ANSWER FRAME · UNIT IIWhat is a dielectric? Distinguish between polar and non-polar molecules. Explain, with a labelled diagram, how a dielectric slab reduces the electric field inside it.5-MARK ANSWER FRAME · UNIT IIDerive the expressions for the equivalent capacitance of three capacitors connected (a) in series and (b) in parallel. Find the equivalent capacitance of 2 μF, 3 μF and 6 μF in series.5-MARK ANSWER FRAME · UNIT IIDerive an expression for the capacitance of a parallel plate capacitor. How does the capacitance change when a dielectric of constant K completely fills the space between the plates? Derive the new value.3-MARK ANSWER FRAME · UNIT IIWrite the expressions for the energy stored in a capacitor. A capacitor C, charged to V, is joined to an identical uncharged capacitor. Find the common potential and the energy lost.5-MARK ANSWER FRAME · UNIT IIIDefine drift velocity and relaxation time. Derive an expression for the drift velocity of free electrons in a conductor, and hence obtain I = neAv_d.3-MARK ANSWER FRAME · UNIT IIIUsing the concept of drift velocity, show that the resistivity of a conductor is ρ = m/(ne²τ). On what factors does it depend?3-MARK ANSWER FRAME · UNIT IIIDistinguish between ohmic and non-ohmic conductors. State three limitations of Ohm's law, with a sketch of the V-I graph for each.3-MARK ANSWER FRAME · UNIT IIIUsing ρ = m/(ne²τ), explain how the resistivity of (i) a metal and (ii) a semiconductor changes with temperature. Draw the graph of ρ against T for each.5-MARK ANSWER FRAME · UNIT IIIDerive an expression for the power dissipated in a resistor carrying a current. Show why electric power is transmitted over long distances at high voltage.3-MARK ANSWER FRAME · UNIT IIIDefine emf and internal resistance of a cell. Obtain the relation V = ε − Ir for its terminal voltage, and draw the graph of V against I.3-MARK ANSWER FRAME · UNIT IIITwo cells of emfs ε₁ and ε₂ and internal resistances r₁ and r₂ are connected in parallel. Derive expressions for the equivalent emf and equivalent internal resistance of the combination.5-MARK ANSWER FRAME · UNIT IIIState Kirchhoff's rules. Use them to find the current in each branch of a two-loop circuit containing two cells.5-MARK ANSWER FRAME · UNIT IIIDraw the circuit of a Wheatstone bridge and use Kirchhoff's rules to obtain its balance condition. How can the bridge be used to find an unknown resistance?3-MARK ANSWER FRAME · UNIT IVDescribe Oersted's experiment. What does it show, and how is the direction of the magnetic field round a straight wire found?5-MARK ANSWER FRAME · UNIT IVUsing the Biot-Savart law, derive an expression for the magnetic field at a point on the axis of a circular current-carrying loop. Hence write the field at its centre.3-MARK ANSWER FRAME · UNIT IVState Ampere's circuital law. Use it to find the magnetic field due to an infinitely long straight current-carrying wire, and show how the field varies with distance.3-MARK ANSWER FRAME · UNIT IVShow that a charged particle moving at right angles to a uniform magnetic field moves in a circle. Derive expressions for the radius and the frequency, and explain why the frequency does not depend on the speed.3-MARK ANSWER FRAME · UNIT IVDerive an expression for the force per unit length between two long straight parallel conductors carrying currents. Hence define one ampere.5-MARK ANSWER FRAME · UNIT IVDerive an expression for the torque on a rectangular current-carrying coil in a uniform magnetic field. Show that the coil behaves like a magnetic dipole.5-MARK ANSWER FRAME · UNIT IVWith a labelled diagram, explain the principle and working of a moving coil galvanometer. Obtain the expression for its current sensitivity.5-MARK ANSWER FRAME · UNIT IVHow can a moving coil galvanometer be converted into (a) an ammeter of range 0 to I and (b) a voltmeter of range 0 to V? Derive the resistance needed in each case, with circuit diagrams.3-MARK ANSWER FRAME · UNIT VWhat is the magnetic dipole moment of a bar magnet? What happens when a bar magnet is cut into two, and what does this show about magnetic poles?3-MARK ANSWER FRAME · UNIT VState the properties of magnetic field lines. Draw the field lines of a bar magnet, and give two differences from electric field lines.3-MARK ANSWER FRAME · UNIT VExplain, giving reasons, why a current-carrying solenoid behaves like a bar magnet. Draw the field lines of both.3-MARK ANSWER FRAME · UNIT VWrite the expressions for the magnetic field of a short bar magnet at a far point on (a) its axial line and (b) its equatorial line. Show the directions on a diagram, and compare them with an electric dipole.3-MARK ANSWER FRAME · UNIT VA bar magnet is placed in a uniform magnetic field. Write expressions for the torque on it and its potential energy. Explain the positions of stable and unstable equilibrium.3-MARK ANSWER FRAME · UNIT VDefine magnetisation, magnetic intensity and magnetic susceptibility. Obtain the relation between relative permeability and susceptibility.5-MARK ANSWER FRAME · UNIT VDistinguish between diamagnetic, paramagnetic and ferromagnetic substances, with one example of each. Explain ferromagnetism using domains.3-MARK ANSWER FRAME · UNIT VExplain the effect of temperature on the magnetic properties of diamagnetic, paramagnetic and ferromagnetic substances.3-MARK ANSWER FRAME · UNIT VIDescribe the experiments of Faraday and Henry with a magnet and with two coils. What do they show about electromagnetic induction?3-MARK ANSWER FRAME · UNIT VIDefine magnetic flux and state its SI unit. State Faraday's laws of electromagnetic induction and write the induced emf in a coil of N turns.3-MARK ANSWER FRAME · UNIT VIDistinguish between induced emf and induced current. The flux through each turn of a 100-turn coil of resistance 5 Ω changes steadily by 2 mWb in 0.02 s. Find the induced emf, the current and the charge that flows.3-MARK ANSWER FRAME · UNIT VIState Lenz's law. Use it to find the direction of the induced current when a magnet approaches a coil, and show that it follows from the law of conservation of energy.5-MARK ANSWER FRAME · UNIT VIDerive an expression for the motional emf in a rod sliding on rails in a uniform magnetic field, first from the change in flux and then from the Lorentz force. Explain why a force is needed to keep the rod moving at constant speed.5-MARK ANSWER FRAME · UNIT VIDefine self inductance and give its SI unit. Derive an expression for the self inductance of a long air-cored solenoid, and write the energy stored in an inductor.5-MARK ANSWER FRAME · UNIT VIDefine mutual inductance and give its SI unit. Derive an expression for the mutual inductance of two long coaxial solenoids, and show that M₁₂ = M₂₁.3-MARK ANSWER FRAME · UNIT VIIDefine the rms value of an alternating current. Show that it is 0.707 times the peak value.3-MARK ANSWER FRAME · UNIT VIIAn alternating voltage v = vₘ sin ωt is applied across a pure inductor. Show that the current lags the voltage by π/2, find the inductive reactance and draw the phasor diagram.5-MARK ANSWER FRAME · UNIT VIIA series LCR circuit is connected to an AC source v = vₘ sin ωt. Using a phasor diagram, derive the expression for its impedance and the phase angle. When is the current in phase with the voltage?3-MARK ANSWER FRAME · UNIT VIIWhat is resonance in a series LCR circuit? Derive the resonant frequency, draw the variation of current with frequency and give one application.3-MARK ANSWER FRAME · UNIT VIIDerive an expression for the average power consumed in an AC circuit. Define power factor and wattless current, and state the power factor for a pure resistor and a pure inductor.5-MARK ANSWER FRAME · UNIT VIIExplain the principle and working of an AC generator with a labelled diagram. Derive the expression for the instantaneous emf induced.5-MARK ANSWER FRAME · UNIT VIIState the principle of a transformer. With a labelled diagram, explain its working, derive the ratio of voltages and currents, and list the main energy losses.3-MARK ANSWER FRAME · UNIT VIIIWhat is displacement current? Using a charging capacitor, explain why it is needed and show that it equals the conduction current. Write the Ampere-Maxwell law.3-MARK ANSWER FRAME · UNIT VIIIWhat are electromagnetic waves? How are they produced? Write four of their characteristics and draw a labelled diagram showing their transverse nature.3-MARK ANSWER FRAME · UNIT VIIIName the parts of the electromagnetic spectrum from radio waves to visible light. Give the wavelength range, the source and one use of each.3-MARK ANSWER FRAME · UNIT VIIIName the EM waves at the short-wavelength end of the spectrum. For ultraviolet, X-rays and gamma rays, give the source, one use and one danger.3-MARK ANSWER FRAME · UNIT IXUsing a ray diagram, derive the mirror equation for a concave mirror. Also write the expression for its linear magnification.3-MARK ANSWER FRAME · UNIT IXExplain why a coin at the bottom of a bucket of water appears raised. Derive the relation between real depth, apparent depth and refractive index.5-MARK ANSWER FRAME · UNIT IXWhat is total internal reflection? State its conditions and obtain the relation between the critical angle and refractive index. Explain how an optical fibre works, with a labelled diagram.3-MARK ANSWER FRAME · UNIT IXDerive the relation between object distance, image distance, refractive indices and radius of curvature for refraction at a convex spherical surface.5-MARK ANSWER FRAME · UNIT IXDerive the lens maker's formula for a thin double convex lens, and hence obtain the thin lens formula.3-MARK ANSWER FRAME · UNIT IXTwo thin lenses of focal lengths f₁ and f₂ are kept in contact. Derive the focal length of the combination and write its power.5-MARK ANSWER FRAME · UNIT IXDraw a labelled ray diagram for refraction through a prism. Derive the relation between the refractive index, the angle of the prism and the angle of minimum deviation. Draw the i-δ graph.5-MARK ANSWER FRAME · UNIT IXDraw a labelled ray diagram of a compound microscope with the final image at the near point. Derive its magnifying power. How can the magnifying power be increased?5-MARK ANSWER FRAME · UNIT IXDraw a labelled ray diagram of an astronomical refracting telescope in normal adjustment and derive its magnifying power. Give two reasons why large telescopes use mirrors.3-MARK ANSWER FRAME · UNIT XState Huygens' principle. Using it, show with a diagram how a plane wavefront moves forward in a uniform medium.3-MARK ANSWER FRAME · UNIT XUsing Huygens' principle, prove the law of reflection. Draw a labelled diagram.5-MARK ANSWER FRAME · UNIT XUsing Huygens' principle, deduce Snell's law of refraction for a plane wavefront. Show that the frequency of light does not change but its wavelength does. Draw a labelled diagram.3-MARK ANSWER FRAME · UNIT XWhat is interference of light? Two coherent waves of equal amplitude meet with a phase difference φ. Find the resultant intensity and give the conditions for maximum and minimum intensity.3-MARK ANSWER FRAME · UNIT XWhat are coherent sources? Why are they needed for sustained interference? Write the conditions for sustained interference of light.5-MARK ANSWER FRAME · UNIT XDescribe Young's double slit experiment with a labelled diagram. Write the expression for fringe width and state how it depends on the wavelength, the screen distance and the slit separation.5-MARK ANSWER FRAME · UNIT XExplain the diffraction of light at a single slit. Show how the central maximum and the first minimum arise, and draw the intensity distribution.3-MARK ANSWER FRAME · UNIT XWrite the expression for the width of the central maximum in single slit diffraction. State how it depends on slit width and wavelength, and give two differences between interference and diffraction patterns.3-MARK ANSWER FRAME · UNIT XIWhat is meant by the dual nature of radiation? Define work function and describe the ways in which electrons can be emitted from a metal surface.3-MARK ANSWER FRAME · UNIT XIWhat is the photoelectric effect? Describe the observations of Hertz, Hallwachs and Lenard.5-MARK ANSWER FRAME · UNIT XIDescribe the experimental study of the photoelectric effect with a labelled diagram. Draw graphs to show the effect of intensity and of frequency on the photocurrent, and state the conclusions.5-MARK ANSWER FRAME · UNIT XIWrite Einstein's photoelectric equation. Use it to explain the laws of photoelectric emission, and show how Planck's constant and the work function can be found from a graph.3-MARK ANSWER FRAME · UNIT XIState the main features of the photon picture of electromagnetic radiation. Find the energy of a photon of wavelength 663 nm.3-MARK ANSWER FRAME · UNIT XIWhat are matter waves? Write the de Broglie relation and explain why the wave nature of a moving cricket ball is not observed, while that of an electron is.3-MARK ANSWER FRAME · UNIT XIObtain the expression for the de Broglie wavelength of an electron accelerated from rest through a potential difference V. Find its value for V = 100 V.5-MARK ANSWER FRAME · UNIT XIIDescribe the Geiger-Marsden alpha-particle scattering experiment. Write its main observations, the conclusions drawn from them, and draw the graph of the number of scattered particles against scattering angle.5-MARK ANSWER FRAME · UNIT XIIDescribe Rutherford's nuclear model of the atom. Show that the total energy of the electron in a hydrogen atom is −e²/(8πε₀r), and state two limitations of the model.3-MARK ANSWER FRAME · UNIT XIIState the three postulates of Bohr's model of the hydrogen atom.5-MARK ANSWER FRAME · UNIT XIIUsing Bohr's postulates, derive an expression for the radius of the nth orbit of the hydrogen atom and show that rₙ ∝ n². Find the radius of the third orbit if a₀ = 0.53 Å.5-MARK ANSWER FRAME · UNIT XIIUsing Bohr's postulates, derive the expression for the total energy of the electron in the nth orbit of the hydrogen atom. Draw the energy level diagram for n = 1 to 4.3-MARK ANSWER FRAME · UNIT XIIUsing Bohr's model, explain how hydrogen gives an emission line spectrum and an absorption line spectrum. Draw an energy level diagram showing a few transitions.3-MARK ANSWER FRAME · UNIT XIIIWhat are the constituents of a nucleus? Define atomic number and mass number, and explain isotopes, isobars and isotones with one example each.3-MARK ANSWER FRAME · UNIT XIIIShow that the density of nuclear matter is independent of the mass number, and estimate its value. (R₀ = 1.2 fm, mass of a nucleon ≈ 1.66 × 10⁻²⁷ kg)3-MARK ANSWER FRAME · UNIT XIIIState the properties of the nuclear force. Draw a graph showing how the potential energy of a pair of nucleons varies with their separation, and explain it.3-MARK ANSWER FRAME · UNIT XIIIWhat are mass defect and binding energy of a nucleus? Calculate the binding energy per nucleon of ⁴₂He. (Nuclear mass 4.00151 u, mₚ = 1.00727 u, mₙ = 1.00866 u, 1 u = 931.5 MeV)5-MARK ANSWER FRAME · UNIT XIIIDraw a plot of binding energy per nucleon against mass number. Use it to explain the release of energy in nuclear fission and fusion. Why is Ebn nearly constant for medium nuclei?3-MARK ANSWER FRAME · UNIT XIIIWhat is nuclear fission? Write a balanced equation for the fission of ²³⁵U, and explain with the binding energy curve why energy is released.5-MARK ANSWER FRAME · UNIT XIIIWhat is nuclear fusion? Why does it need a very high temperature? Write the overall reaction by which the Sun produces energy, and give two differences between fission and fusion.3-MARK ANSWER FRAME · UNIT XIVOn the basis of energy bands, distinguish between a conductor, a semiconductor and an insulator. Draw their energy band diagrams.3-MARK ANSWER FRAME · UNIT XIVWhat is an intrinsic semiconductor? Explain how electrons and holes are produced in it and how they carry current. Draw its energy band diagram at T > 0 K.3-MARK ANSWER FRAME · UNIT XIVWhat are n-type and p-type semiconductors? How is each made? Draw their energy band diagrams and explain why each is electrically neutral.3-MARK ANSWER FRAME · UNIT XIVExplain, with a labelled diagram, the formation of the depletion region and the barrier potential in a p-n junction.3-MARK ANSWER FRAME · UNIT XIVExplain the effect of forward bias on a p-n junction. Draw its circuit diagram and its forward I-V characteristic, and mark the threshold voltage.5-MARK ANSWER FRAME · UNIT XIVDraw the circuit diagrams used to study the forward and reverse bias characteristics of a p-n junction diode. Draw the characteristics and explain their shape.5-MARK ANSWER FRAME · UNIT XIVWith the help of a labelled circuit diagram, explain the working of a full-wave rectifier. Draw its input and output waveforms.