CBSE Class 12 Physics 2025 question paper (55/4)
Maximum marks 70 · Time 3 hours · 3 sets
Try each question first, then open its model answer. Where the paper offers a choice, both questions are shown with OR between them.
Section A
1 mark each
- Q.11 markA body acquires charge C. The mass of the body :
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- Q.21 markA current flows through a cylindrical conductor of radius R. The current density at a point in the conductor is (along its axis), here is a constant and r is distance from the axis of the conductor. The current flowing through the portion of the conductor from to is proportional to :
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- Q.31 markA particle having charge +q enters a uniform magnetic field as shown in the figure. The particle will describe :
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- Q.41 markA bar magnet is initially at right angles to a uniform magnetic field. The magnet is rotated till the torque acting on it becomes one-half of its initial value. The angle through which the bar magnet is rotated is :
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- Q.51 markWhich one out of the following materials is not paramagnetic ?
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- Q.61 markAn ammeter connected in series in an ac circuit reads 10 A. The maximum value of current at any instant in the circuit is :
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- Q.71 markThe amplitude of electric field in an electromagnetic wave in free space is 1000 . The amplitude of the magnetic field in this electromagnetic wave is :
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- Q.81 markThe magnification produced by a spherical mirror is . The mirror used and the nature of the image formed will be
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- Q.91 markChoose the correct statement :
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- Q.101 markA beam of red light and a beam of blue light have equal intensities. Which of the following statements is true ?
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- Q.111 markWhich of the following is an electrical conductor at room temperature ?
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- Q.121 markA long straight wire is held vertically and carries a steady current in upward direction. The shape of magnetic field lines produced by the current-carrying wire are :
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- Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.Q.131 markAssertion (A) : n-type semiconductor is not negatively charged. Reason (R) : Neutral pentavalent impurity atom doped in intrinsic semiconductor (neutral) donates its fifth unpaired electron to the crystal lattice and becomes a positive donor.
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- Q.141 markAssertion (A) : A series LCR circuit behaves as a pure resistive circuit at resonance. Reason (R) : At resonance, gives .
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- Q.151 markAssertion (A) : In double slit experiment if one slit is closed, diffraction pattern due to the other slit will appear on the screen. Reason (R) : For interference, at least two waves are required.
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- Q.161 markAssertion (A) : For monochromatic incident radiation, the emitted photoelectrons from a given metal have speed ranging from zero to a certain maximum value. Reason (R) : Each metal has a definite work function.
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Section B
2 marks each
- Q.17 (a)2 marksIn the given figure, three identical bulbs P, Q and S are connected to a battery. (i) Compare the brightness of bulbs P and Q with that of bulb S when key K is closed. (ii) Compare the brightness of the bulbs S and Q when the key K is opened. Justify your answer in both cases.
OR
Q.17 (b)2 marksTwo cells of emf 10 V each, two resistors of 20 and 10 and a bulb B of 10 resistance are connected together as shown in the figure. Find the current that flows through the bulb.- Q.182 marksFind the angle of diffraction (in degrees) for first secondary maximum of the pattern due to diffraction at a single slit. The width of the slit and wavelength of light used are mm and 550 nm, respectively.
- Q.192 marksAn equiconvex lens is made of glass of refractive index . If the focal length of the lens is cm, calculate the radius of curvature of its surfaces.
- Q.202 marksCalculate the mass of an -particle in atomic mass unit (u). Given, Mass of a normal helium atom = u Mass of carbon atom = kg
- Q.212 marksIn an intrinsic semiconductor, carrier's concentration is . On doping with impurity atoms, the hole concentration becomes . (a) Identify (i) the type of dopant and (ii) the extrinsic semiconductor so formed. (b) Calculate the electron concentration in the extrinsic semiconductor.
Section C
3 marks each
- Q.22 (a)3 marks(i) Derive an expression for the resistivity of a conductor in terms of number density of free electrons and relaxation time. (ii) The figure shows the plot of current through a cross-section of wire over two different time intervals. Compare the charges ( and ) that pass through the cross-section during these time intervals.
OR
Q.22 (b)3 marks(i) A battery of emf E and internal resistance r is connected to a variable external resistance R. (I) Obtain the expression for current I in the circuit and the value of maximum current the battery can supply. (II) Obtain the terminal voltage V across the battery and its maximum possible value. (ii) The above battery sends a current when and a current when . Obtain the internal resistance of the battery in terms of , , and .- Q.233 marks(a) Write vector form of Biot-Savart law. (b) Two insulated long straight wires, each carrying A current are kept along and axis as shown in the figure. Find the magnitude and direction of resultant magnetic field at point P (4m, 5m).
- Q.243 marksTwo coils '1' and '2' are placed close to each other as shown in the figure. Find the direction of induced current in coil '1' in each of the following situations, justifying your answers : (a) Coil '2' is moving towards coil '1'. (b) Coil '2' is moving away from coil '1'. (c) The resistance connected with coil '2' is increased keeping both the coils stationary.
- Q.253 marks(a) State any three characteristics of electromagnetic waves. (b) Briefly explain how and where the displacement current exists during the charging of a capacitor.
- Q.263 marksA double slit set-up was initially placed in a tank filled with water and the interference pattern was obtained using a laser light. When water is replaced by a transparent liquid of refractive index , what will be the effect on the following ? (a) Speed, frequency and wavelength of the light of laser beam. (b) The fringe width, shape of interference fringes and shift in the position of central maximum.
- Q.273 marksExplain the following observations using Einstein's photoelectric equation : (a) Photoelectric emission does not occur from a surface when the frequency of the light incident on it is less than a certain minimum value. (b) It is the frequency, and not the intensity of the incident light which affects the maximum kinetic energy of the photoelectrons. (c) The cut-off voltage () versus frequency () of the incident light curve is a straight line with a slope .
- Q.283 marks(a) What are majority and minority charge carriers of p-type and n-type semiconductors ? (b) Explain briefly the formation of diffusion current and drift current in a p-n junction diode.
Section D
1 mark each
- A parallel plate capacitor consists of two conducting plates kept generally parallel to each other at a distance. When the capacitor is charged, the charge resides on the inner surfaces of the plates and an electric field is set up between them. Thus, electrostatic energy is stored in the capacitor. The figure shows three large square metallic plates, each of side 'L' held parallel and equidistant from each other. The space between and and and is completely filled with mica sheets of dielectric constant 'K'. The plate is connected to point A and other plates and are connected to point B. Point A is maintained at a positive potential with respect to point B and the potential difference between A and B is V.Q.29 (i)1 markThe capacitance of the system between A and B will be :
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- Q.29 (ii)1 markThe charge on plate is :
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- Q.29 (iii)1 markThe electric field in the region between and is :
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- Q.29 (iv) (a)1 markThe separation between the plates of same area () of a parallel plate air capacitor having capacitance equal to that of this system, will be :
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OR
Q.29 (iv) (b)1 markIf the source of potential difference applied between A and B is removed, and then A and B are connected by a conducting wire, the net charge on the system will be :Tap an option to check your answer.
- A hydrogen atom consists of an electron revolving in a circular orbit of radius r with certain velocity v around a proton located at the nucleus of the atom. The electrostatic force of attraction between the revolving electron and the proton provides the requisite centripetal force to keep it in the orbit. According to Bohr's model, an electron can revolve only in certain stable orbits. The angular momentum of the electron in these orbits is some integral multiple of , where h is the Planck's constant. Further, when an electron makes a transition from one orbit of higher energy to that of lower energy, a photon is emitted having energy equal to the difference between energies of the initial and final states. Assuming the mass and charge of an electron as m and e respectively, answer the following questions.Q.30 (i)1 markThe expression for the speed of electron v in terms of radius of the orbit (r) and physical constant () is :
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- Q.30 (ii)1 markThe total energy of the atom in terms of r and physical constant K is :
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- Q.30 (iii)1 markA photon of wavelength 500 nm is emitted when an electron makes a transition from one state to the other state in an atom. The change in the total energy of the electron and change in its kinetic energy in eV as per Bohr's model, respectively will be :
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- Q.30 (iv) (a)1 markIn Bohr's model of hydrogen atom, the frequency of revolution of electron in its orbit is proportional to :
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OR
Q.30 (iv) (b)1 markAn electron makes a transition from eV state to the ground state in hydrogen atom. Its radius of orbit changes by : (radius of orbit of electron in ground state = Å)Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) Two point charges +q and -q are held at (a, 0) and (-a, 0) in x-y plane. Obtain an expression for the net electric field due to the charges at a point (0, y). Hence, find electric field at a far off point (y >> a). (ii) Three point charges of -2 nC, -1 nC, and +5 nC are kept at the vertices A, B and C of an equilateral triangle of side m. Find the total amount of work done in shifting the charges from A to , B to and C to . Here , and are the midpoints of sides AB, BC and CA, respectively.
OR
Q.31 (b)5 marks(i) Show that Gauss's theorem is consistent with Coulomb's law. Using it, derive an expression for the electric field due to a uniformly charged thin spherical shell of radius r at a point at a distance y from the centre of the shell such that (I) , and (II) . (ii) A point charge of nC is kept at the origin of a three-dimensional coordinate system. Find the type and magnitude of the charge which should be kept at (0, 0, -6m) so that the potential due to the system becomes zero at (0, 0, 2m).- Q.32 (a)5 marks(i) State Lenz's law and explain how this law is a consequence of conservation of energy principle. (ii) A square shaped loop of side is initially lying outside a region of uniform magnetic field as shown in the figure. The loop is moved towards right with a constant velocity till it goes out of the region of magnetic field. (I) What will be the directions of induced current when the loop enters the field and when it leaves the field ? (II) Draw the plots showing the variation of magnetic flux linked with the loop with time t and variation of induced emf E with time t. Mark the relevant values of E, and t on the graphs.
OR
Q.32 (b)5 marks(i) Differentiate between peak and rms values of alternating current. How are they related ? (ii) A current element X is connected across an ac source of emf . It is found that the voltage leads the current in phase by radian. If element X was replaced by element Y, the voltage lags behind the current in phase by radian. (I) Identify elements X and Y by drawing phasor diagrams. (II) Obtain the condition of resonance when both elements X and Y are connected in series to the source and obtain expression for resonant frequency. What is the impedance value in this case ?- Q.33 (a)5 marks(i) An object is placed 30 cm from a thin convex lens of focal length 10 cm. The lens forms a sharp image on a screen. If a thin concave lens is placed in contact with the convex lens, the sharp image on the screen is formed when the screen is moved by 45 cm from its initial position. Calculate the focal length of the concave lens. (ii) Calculate the angle of minimum deviation of an equilateral prism. The refractive index of the prism is . Calculate the angle of incidence for this case of minimum deviation also.
OR
Q.33 (b)5 marks(i) A physics teacher wants to demonstrate interference with the help of double slit experiment using a laser beam of 633 nm wavelength. Since the hall is large enough, interference pattern is formed on the wall m from the slits. For clear and comfortable view by all the students they want the fringe width 5 mm. (I) Find the slit separation for obtaining the desired interference pattern. (II) How far will the first minimum be from the central maximum ? (ii) A parallel beam of light of wavelength 650 nm passes through a slit of width mm. The diffraction pattern is obtained on a screen kept 60 cm away from the slit. Find the distance between first order minima on both sides of the central maximum.
Section A
1 mark each
- Q.11 markAn electric dipole of dipole moment Cm lies along x-axis. An electric field of magnitude is switched on at an instant in the region. The unit vector along the electric field is . The magnitude of the torque acting on the dipole at that instant is :
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- Q.21 markWhen the switch of the circuit is turned on, the filament of the bulb glows instantaneously because :
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- Q.31 markA particle with charge q moving with velocity enters a region with magnetic field . The magnitude of force experienced by the particle is :
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- Q.41 markA bar magnet is initially at right angles to a uniform magnetic field. The magnet is rotated till the torque acting on it becomes one-half of its initial value. The angle through which the bar magnet is rotated is :
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- Q.51 markThe materials having negative magnetic susceptibility are :
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- Q.61 markWhen current in a coil changes at a steady rate from 8 A to 6 A in 4 ms, an emf of V is induced in it. The value of self-inductance of the coil is :
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- Q.71 markThe electric field in space between the plates of a parallel plate capacitor (each of area ) is changing at the rate of . The displacement current between the plates of the capacitor is :
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- Q.81 markA long straight wire is held vertically and carries a steady current in upward direction. The shape of magnetic field lines produced by the current-carrying wire are :
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- Q.91 markWhich of the following is an electrical conductor at room temperature ?
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- Q.101 markThe magnification produced by a spherical mirror is . The mirror used and the nature of the image formed will be
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- Q.111 markChoose the correct statement :
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- Q.121 markA beam of red light and a beam of blue light have equal intensities. Which of the following statements is true ?
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- Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.Q.131 markAssertion (A) : For monochromatic incident radiation, the emitted photoelectrons from a given metal have speed ranging from zero to a certain maximum value. Reason (R) : Each metal has a definite work function.
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- Q.141 markAssertion (A) : In double slit experiment if one slit is closed, diffraction pattern due to the other slit will appear on the screen. Reason (R) : For interference, at least two waves are required.
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- Q.151 markAssertion (A) : A series LCR circuit behaves as a pure resistive circuit at resonance. Reason (R) : At resonance, gives .
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- Q.161 markAssertion (A) : n-type semiconductor is not negatively charged. Reason (R) : Neutral pentavalent impurity atom doped in intrinsic semiconductor (neutral) donates its fifth unpaired electron to the crystal lattice and becomes a positive donor.
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Section B
2 marks each
- Q.172 marksIn an intrinsic semiconductor, carrier's concentration is . On doping with impurity atoms, the hole concentration becomes . (a) Identify (i) the type of dopant and (ii) the extrinsic semiconductor so formed. (b) Calculate the electron concentration in the extrinsic semiconductor.
- Q.182 marksIn a double slit experiment, the two slits are mm apart. The slits are illuminated by a mixture of lights of wavelengths of 600 nm and 400 nm and the interference pattern is observed on a screen m away from the slits. Find the minimum distance of the point from the central maximum at which bright fringes of the interference patterns of the two wavelengths coincide.
- Q.192 marksFind the focal length of plano-convex lens of refractive index and radius of curvature 10 cm when it is immersed in a liquid of refractive index .
- Q.202 marksFind the ratio of minimum to maximum wavelength of radiations emitted when electron jumps from higher energy state into ground state of hydrogen atom.
- Q.21 (a)2 marksIn the given figure, three identical bulbs P, Q and S are connected to a battery. (i) Compare the brightness of bulbs P and Q with that of bulb S when key K is closed. (ii) Compare the brightness of the bulbs S and Q when the key K is opened. Justify your answer in both cases.
OR
Q.21 (b)2 marksTwo cells of emf 10 V each, two resistors of 20 and 10 and a bulb B of 10 resistance are connected together as shown in the figure. Find the current that flows through the bulb.
Section C
3 marks each
- Q.223 marksExplain the following observations using Einstein's photoelectric equation : (a) Photoelectric emission does not occur from a surface when the frequency of the light incident on it is less than a certain minimum value. (b) It is the frequency, and not the intensity of the incident light which affects the maximum kinetic energy of the photoelectrons. (c) The cut-off voltage () versus frequency () of the incident light curve is a straight line with a slope .
- Q.233 marks(a) A charged particle q moving with a velocity is subjected to a uniform magnetic field acting perpendicular to . If a uniform electric field is also set up in the region along the direction of , describe the path followed by the particle and draw its shape. (b) How will the magnetic field inside a long solenoid be affected when : (i) the radius of the turns of the solenoid is increased, (ii) the length of solenoid as well as the total number of its turns are doubled ?
- Q.243 marks(a) Differentiate between magnetic flux through an area and magnetic field at a point. (b) A bar magnet is held with its length along the axis of a closed coil. Initially the south pole of the magnet faces the coil. If the magnet is moved towards the coil, explain how a current is induced in the coil and in what direction.
- Q.253 marks(a) State any three characteristics of electromagnetic waves. (b) Briefly explain how and where the displacement current exists during the charging of a capacitor.
- Q.263 marks(a) Define 'wavefront' of a light wave. A plane wavefront is refracted from a convex lens. Draw the shape of the refracted wavefront. (b) A plane wave travelling in a medium is incident on a plane surface separating this medium from a rarer medium. Draw a diagram to show refraction of the wave. Hence, verify Snell's law.
- Q.273 marks(a) What are majority and minority charge carriers of p-type and n-type semiconductors ? (b) Explain briefly the formation of diffusion current and drift current in a p-n junction diode.
- Q.28 (a)3 marks(i) Derive an expression for the resistivity of a conductor in terms of number density of free electrons and relaxation time. (ii) The figure shows the plot of current through a cross-section of wire over two different time intervals. Compare the charges ( and ) that pass through the cross-section during these time intervals.
OR
Q.28 (b)3 marks(i) A battery of emf E and internal resistance r is connected to a variable external resistance R. (I) Obtain the expression for current I in the circuit and the value of maximum current the battery can supply. (II) Obtain the terminal voltage V across the battery and its maximum possible value. (ii) The above battery sends a current when and a current when . Obtain the internal resistance of the battery in terms of , , and .
Section D
1 mark each
- A hydrogen atom consists of an electron revolving in a circular orbit of radius r with certain velocity v around a proton located at the nucleus of the atom. The electrostatic force of attraction between the revolving electron and the proton provides the requisite centripetal force to keep it in the orbit. According to Bohr's model, an electron can revolve only in certain stable orbits. The angular momentum of the electron in these orbits is some integral multiple of , where h is the Planck's constant. Further, when an electron makes a transition from one orbit of higher energy to that of lower energy, a photon is emitted having energy equal to the difference between energies of the initial and final states. Assuming the mass and charge of an electron as m and e respectively, answer the following questions.Q.29 (i)1 markThe expression for the speed of electron v in terms of radius of the orbit (r) and physical constant () is :
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- Q.29 (ii)1 markThe total energy of the atom in terms of r and physical constant K is :
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- Q.29 (iii)1 markA photon of wavelength 500 nm is emitted when an electron makes a transition from one state to the other state in an atom. The change in the total energy of the electron and change in its kinetic energy in eV as per Bohr's model, respectively will be :
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- Q.29 (iv) (a)1 markIn Bohr's model of hydrogen atom, the frequency of revolution of electron in its orbit is proportional to :
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OR
Q.29 (iv) (b)1 markAn electron makes a transition from eV state to the ground state in hydrogen atom. Its radius of orbit changes by : (radius of orbit of electron in ground state = Å)Tap an option to check your answer.
- A parallel plate capacitor consists of two conducting plates kept generally parallel to each other at a distance. When the capacitor is charged, the charge resides on the inner surfaces of the plates and an electric field is set up between them. Thus, electrostatic energy is stored in the capacitor. The figure shows three large square metallic plates, each of side 'L' held parallel and equidistant from each other. The space between and and and is completely filled with mica sheets of dielectric constant 'K'. The plate is connected to point A and other plates and are connected to point B. Point A is maintained at a positive potential with respect to point B and the potential difference between A and B is V.Q.30 (i)1 markThe capacitance of the system between A and B will be :
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- Q.30 (ii)1 markThe charge on plate is :
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- Q.30 (iii)1 markThe electric field in the region between and is :
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- Q.30 (iv) (a)1 markThe separation between the plates of same area () of a parallel plate air capacitor having capacitance equal to that of this system, will be :
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OR
Q.30 (iv) (b)1 markIf the source of potential difference applied between A and B is removed, and then A and B are connected by a conducting wire, the net charge on the system will be :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) State Lenz's law and explain how this law is a consequence of conservation of energy principle. (ii) A square shaped loop of side is initially lying outside a region of uniform magnetic field as shown in the figure. The loop is moved towards right with a constant velocity till it goes out of the region of magnetic field. (I) What will be the directions of induced current when the loop enters the field and when it leaves the field ? (II) Draw the plots showing the variation of magnetic flux linked with the loop with time t and variation of induced emf E with time t. Mark the relevant values of E, and t on the graphs.
OR
Q.31 (b)5 marks(i) Differentiate between peak and rms values of alternating current. How are they related ? (ii) A current element X is connected across an ac source of emf . It is found that the voltage leads the current in phase by radian. If element X was replaced by element Y, the voltage lags behind the current in phase by radian. (I) Identify elements X and Y by drawing phasor diagrams. (II) Obtain the condition of resonance when both elements X and Y are connected in series to the source and obtain expression for resonant frequency. What is the impedance value in this case ?- Q.32 (a)5 marks(i) An object is placed 30 cm from a thin convex lens of focal length 10 cm. The lens forms a sharp image on a screen. If a thin concave lens is placed in contact with the convex lens, the sharp image on the screen is formed when the screen is moved by 45 cm from its initial position. Calculate the focal length of the concave lens. (ii) Calculate the angle of minimum deviation of an equilateral prism. The refractive index of the prism is . Calculate the angle of incidence for this case of minimum deviation also.
OR
Q.32 (b)5 marks(i) A physics teacher wants to demonstrate interference with the help of double slit experiment using a laser beam of 633 nm wavelength. Since the hall is large enough, interference pattern is formed on the wall m from the slits. For clear and comfortable view by all the students they want the fringe width 5 mm. (I) Find the slit separation for obtaining the desired interference pattern. (II) How far will the first minimum be from the central maximum ? (ii) A parallel beam of light of wavelength 650 nm passes through a slit of width mm. The diffraction pattern is obtained on a screen kept 60 cm away from the slit. Find the distance between first order minima on both sides of the central maximum.- Q.33 (a)5 marks(i) Two point charges +q and -q are held at (a, 0) and (-a, 0) in x-y plane. Obtain an expression for the net electric field due to the charges at a point (0, y). Hence, find electric field at a far off point (y >> a). (ii) Three point charges of -2 nC, -1 nC, and +5 nC are kept at the vertices A, B and C of an equilateral triangle of side m. Find the total amount of work done in shifting the charges from A to , B to and C to . Here , and are the midpoints of sides AB, BC and CA, respectively.
OR
Q.33 (b)5 marks(i) Show that Gauss's theorem is consistent with Coulomb's law. Using it, derive an expression for the electric field due to a uniformly charged thin spherical shell of radius r at a point at a distance y from the centre of the shell such that (I) , and (II) . (ii) A point charge of nC is kept at the origin of a three-dimensional coordinate system. Find the type and magnitude of the charge which should be kept at (0, 0, -6m) so that the potential due to the system becomes zero at (0, 0, 2m).
Section A
1 mark each
- Q.11 markTwo point charges Q and – q are held 'r' distance apart in free space. A uniform electric field is applied in the region perpendicular to the line joining the two charges. Which one of the following angles will the direction of the net force acting on charge – q make with the line joining Q and – q ?
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- Q.21 markThree wires A, B and C of the same material have lengths and area of cross-sections as , and , respectively. If the resistances of these wires are , and respectively, then :
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- Q.31 markA particle of mass m and charge q moves along y-axis in a region in which a uniform magnetic field is pointing along x-axis. The Lorentz force acting on the charge will point along :
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- Q.41 markA bar magnet is initially at right angles to a uniform magnetic field. The magnet is rotated till the torque acting on it becomes one-half of its initial value. The angle through which the bar magnet is rotated is :
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- Q.51 markWhich of the following substances has magnetic permeability less than that of free space ?
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- Q.61 markThe magnetic flux linked with a closed coil (in Wb) varies with time t (in s) as . If the resistance of the circuit is 14 , the magnitude of induced current in the coil at t = 1 s will be :
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- Q.71 markIn an electromagnetic wave travelling in free space, the amplitude of magnetic field is T. The amplitude of its electric field is :
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- Q.81 markA long straight wire is held vertically and carries a steady current in upward direction. The shape of magnetic field lines produced by the current-carrying wire are :
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- Q.91 markThe magnification produced by a spherical mirror is . The mirror used and the nature of the image formed will be
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- Q.101 markChoose the correct statement :
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- Q.111 markA beam of red light and a beam of blue light have equal intensities. Which of the following statements is true ?
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- Q.121 markWhich of the following is an electrical conductor at room temperature ?
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- Questions number 13 to 16 are Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.Q.131 markAssertion (A) : In double slit experiment if one slit is closed, diffraction pattern due to the other slit will appear on the screen. Reason (R) : For interference, at least two waves are required.
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- Q.141 markAssertion (A) : For monochromatic incident radiation, the emitted photoelectrons from a given metal have speed ranging from zero to a certain maximum value. Reason (R) : Each metal has a definite work function.
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- Q.151 markAssertion (A) : n-type semiconductor is not negatively charged. Reason (R) : Neutral pentavalent impurity atom doped in intrinsic semiconductor (neutral) donates its fifth unpaired electron to the crystal lattice and becomes a positive donor.
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- Q.161 markAssertion (A) : A series LCR circuit behaves as a pure resistive circuit at resonance. Reason (R) : At resonance, gives .
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Section B
2 marks each
- Q.172 marksIn an intrinsic semiconductor, carrier's concentration is . On doping with impurity atoms, the hole concentration becomes . (a) Identify (i) the type of dopant and (ii) the extrinsic semiconductor so formed. (b) Calculate the electron concentration in the extrinsic semiconductor.
- Q.182 marksIn Young's double slit experiment, the screen is moved 30 cm towards the slits. As a consequence, the fringe width of the pattern changes by mm. If the slits separation used is 2 mm, calculate the wavelength of light used in the experiment.
- Q.192 marksThe two surfaces of a biconvex lens are of radius of curvature 'R' each. Obtain the condition under which its focal length 'f' be equal to 'R'. If one of the two surfaces of this lens is made plane, what will be the new focal length of the lens ?
- Q.202 marksIn Bohr's model of hydrogen atom, find the percentage change in the radius of its orbit when an electron makes a transition from n = 3 state to n = 2 state.
- Q.21 (a)2 marksIn the given figure, three identical bulbs P, Q and S are connected to a battery. (i) Compare the brightness of bulbs P and Q with that of bulb S when key K is closed. (ii) Compare the brightness of the bulbs S and Q when the key K is opened. Justify your answer in both cases.
OR
Q.21 (b)2 marksTwo cells of emf 10 V each, two resistors of 20 and 10 and a bulb B of 10 resistance are connected together as shown in the figure. Find the current that flows through the bulb.
Section C
3 marks each
- Q.223 marks(a) What are majority and minority charge carriers of p-type and n-type semiconductors ? (b) Explain briefly the formation of diffusion current and drift current in a p-n junction diode.
- Q.233 marks(a) In which cases does a charged particle not experience a force in a magnetic field ? (b) A square loop MNPK of side '' carrying a current '' is kept close to a long straight wire in the same plane and the wire carries a steady current as shown in the figure. Obtain the magnitude of magnetic force exerted by the wire on the loop.
- Q.243 marks(a) Obtain an expression for the self-inductance of a long solenoid of length '', cross-sectional area 'A' and having 'N' turns. (b) The figure shows the plot of magnitude of induced emf () versus the rate of change of current in two coils '1' and '2'. Which coil has greater value of self-inductance and why ?
- Q.253 marksExplain the following observations using Einstein's photoelectric equation : (a) Photoelectric emission does not occur from a surface when the frequency of the light incident on it is less than a certain minimum value. (b) It is the frequency, and not the intensity of the incident light which affects the maximum kinetic energy of the photoelectrons. (c) The cut-off voltage () versus frequency () of the incident light curve is a straight line with a slope .
- Q.263 marks(a) Write the conditions under which two light waves originating from two coherent sources can interfere each other (i) constructively, and (ii) destructively, in terms of wavelength. Can these be applied for two lights originating from two sodium lamps ? Give reason. (b) Monochromatic light of green colour is used in Young's double slit experiment and an interference pattern is observed on a screen. If the green light is replaced by red monochromatic light of the same intensity, how will the fringe width of interference pattern be affected ? Justify your answer.
- Q.27 (a)3 marks(i) Derive an expression for the resistivity of a conductor in terms of number density of free electrons and relaxation time. (ii) The figure shows the plot of current through a cross-section of wire over two different time intervals. Compare the charges ( and ) that pass through the cross-section during these time intervals.
OR
Q.27 (b)3 marks(i) A battery of emf E and internal resistance r is connected to a variable external resistance R. (I) Obtain the expression for current I in the circuit and the value of maximum current the battery can supply. (II) Obtain the terminal voltage V across the battery and its maximum possible value. (ii) The above battery sends a current when and a current when . Obtain the internal resistance of the battery in terms of , , and .- Q.283 marks(a) State any three characteristics of electromagnetic waves. (b) Briefly explain how and where the displacement current exists during the charging of a capacitor.
Section D
1 mark each
- A hydrogen atom consists of an electron revolving in a circular orbit of radius r with certain velocity v around a proton located at the nucleus of the atom. The electrostatic force of attraction between the revolving electron and the proton provides the requisite centripetal force to keep it in the orbit. According to Bohr's model, an electron can revolve only in certain stable orbits. The angular momentum of the electron in these orbits is some integral multiple of , where h is the Planck's constant. Further, when an electron makes a transition from one orbit of higher energy to that of lower energy, a photon is emitted having energy equal to the difference between energies of the initial and final states. Assuming the mass and charge of an electron as m and e respectively, answer the following questions.Q.29 (i)1 markThe expression for the speed of electron v in terms of radius of the orbit (r) and physical constant () is :
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- Q.29 (ii)1 markThe total energy of the atom in terms of r and physical constant K is :
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- Q.29 (iii)1 markA photon of wavelength 500 nm is emitted when an electron makes a transition from one state to the other state in an atom. The change in the total energy of the electron and change in its kinetic energy in eV as per Bohr's model, respectively will be :
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- Q.29 (iv) (a)1 markIn Bohr's model of hydrogen atom, the frequency of revolution of electron in its orbit is proportional to :
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OR
Q.29 (iv) (b)1 markAn electron makes a transition from eV state to the ground state in hydrogen atom. Its radius of orbit changes by : (radius of orbit of electron in ground state = Å)Tap an option to check your answer.
- A parallel plate capacitor consists of two conducting plates kept generally parallel to each other at a distance. When the capacitor is charged, the charge resides on the inner surfaces of the plates and an electric field is set up between them. Thus, electrostatic energy is stored in the capacitor. The figure shows three large square metallic plates, each of side 'L' held parallel and equidistant from each other. The space between and and and is completely filled with mica sheets of dielectric constant 'K'. The plate is connected to point A and other plates and are connected to point B. Point A is maintained at a positive potential with respect to point B and the potential difference between A and B is V.Q.30 (i)1 markThe capacitance of the system between A and B will be :
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- Q.30 (ii)1 markThe charge on plate is :
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- Q.30 (iii)1 markThe electric field in the region between and is :
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- Q.30 (iv) (a)1 markThe separation between the plates of same area () of a parallel plate air capacitor having capacitance equal to that of this system, will be :
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OR
Q.30 (iv) (b)1 markIf the source of potential difference applied between A and B is removed, and then A and B are connected by a conducting wire, the net charge on the system will be :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) An object is placed 30 cm from a thin convex lens of focal length 10 cm. The lens forms a sharp image on a screen. If a thin concave lens is placed in contact with the convex lens, the sharp image on the screen is formed when the screen is moved by 45 cm from its initial position. Calculate the focal length of the concave lens. (ii) Calculate the angle of minimum deviation of an equilateral prism. The refractive index of the prism is . Calculate the angle of incidence for this case of minimum deviation also.
OR
Q.31 (b)5 marks(i) A physics teacher wants to demonstrate interference with the help of double slit experiment using a laser beam of 633 nm wavelength. Since the hall is large enough, interference pattern is formed on the wall m from the slits. For clear and comfortable view by all the students they want the fringe width 5 mm. (I) Find the slit separation for obtaining the desired interference pattern. (II) How far will the first minimum be from the central maximum ? (ii) A parallel beam of light of wavelength 650 nm passes through a slit of width mm. The diffraction pattern is obtained on a screen kept 60 cm away from the slit. Find the distance between first order minima on both sides of the central maximum.- Q.32 (a)5 marks(i) Two point charges + q and – q are held at (a, 0) and (– a, 0) in x-y plane. Obtain an expression for the net electric field due to the charges at a point (0, y). Hence, find electric field at a far off point (y >> a). (ii) Three point charges of – 2 nC, – 1 nC, and + 5 nC are kept at the vertices A, B and C of an equilateral triangle of side m. Find the total amount of work done in shifting the charges from A to , B to and C to . Here , and are the midpoints of sides AB, BC and CA, respectively.
OR
Q.32 (b)5 marks(i) Show that Gauss's theorem is consistent with Coulomb's law. Using it, derive an expression for the electric field due to a uniformly charged thin spherical shell of radius r at a point at a distance y from the centre of the shell such that (I) , and (II) . (ii) A point charge of nC is kept at the origin of a three-dimensional coordinate system. Find the type and magnitude of the charge which should be kept at (0, 0, – 6m) so that the potential due to the system becomes zero at (0, 0, 2m).- Q.33 (a)5 marks(i) State Lenz's law and explain how this law is a consequence of conservation of energy principle. (ii) A square shaped loop of side is initially lying outside a region of uniform magnetic field as shown in the figure. The loop is moved towards right with a constant velocity till it goes out of the region of magnetic field. (I) What will be the directions of induced current when the loop enters the field and when it leaves the field ? (II) Draw the plots showing the variation of magnetic flux linked with the loop with time t and variation of induced emf E with time t. Mark the relevant values of E, and t on the graphs.
OR
Q.33 (b)5 marks(i) Differentiate between peak and rms values of alternating current. How are they related ? (ii) A current element X is connected across an ac source of emf . It is found that the voltage leads the current in phase by radian. If element X was replaced by element Y, the voltage lags behind the current in phase by radian. (I) Identify elements X and Y by drawing phasor diagrams. (II) Obtain the condition of resonance when both elements X and Y are connected in series to the source and obtain expression for resonant frequency. What is the impedance value in this case ?