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CBSE Class 12 Physics 2023 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

  1. Q.11 mark
    Two charges q1q_1 and q2q_2 are placed at the centres of two spherical conducting shells of radius r1r_1 and r2r_2 respectively. The shells are arranged such that their centres are d [ >(r1+r2)]d\,[\,>(r_1 + r_2)] distance apart. The force on q2q_2 due to q1q_1 is :

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  2. Q.21 mark
    An electron enters a uniform magnetic field with speed vv. It describes a semicircular path and comes out of the field. The final speed of the electron is :

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  3. Q.31 mark
    The magnetic field lines near a substance are as shown in the figure. The substance is :

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  4. Q.41 mark
    The figure shows variation of current (I) with time (t) in four devices P, Q, R and S. The device in which an alternating current flows is :

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  5. Q.51 mark
    The electromagnetic waves used in radar systems are :

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  6. Q.61 mark
    In a Young's double-slit experiment, the fringe width is found to be β\beta. If the entire apparatus is immersed in a liquid of refractive index μ\mu, the new fringe width will be :

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  7. Q.71 mark
    Photons of energy 3⋅23{\cdot}2 eV are incident on a photosensitive surface. If the stopping potential for the emitted electrons is 1⋅51{\cdot}5 V, the work function for the surface is :

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  8. Q.81 mark
    Which of the following statements is not true for nuclear forces ?

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  9. Q.91 mark
    The direction of induced current in the loop abc is :

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  10. Q.101 mark
    An ac voltage v=v0sin⁡ωtv = v_0 \sin \omega t is applied to a series combination of a resistor R and an element X. The instantaneous current in the circuit is I=I0sin⁡(ωt+π4)I = I_0 \sin\left(\omega t + \dfrac{\pi}{4}\right). Then which of the following is correct ?

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  11. Q.111 mark
    A plane wavefront is incident on a concave mirror of radius of curvature R. The radius of the refracted wavefront will be :

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  12. Q.121 mark
    A proton and an alpha particle have the same kinetic energy. The ratio of de Broglie wavelengths associated with the proton to that with the alpha particle is :

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  13. Q.131 mark
    The potential energy of an electron in the second excited state in hydrogen atom is :

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  14. Q.141 mark
    The difference in mass of 7X^{7}\mathrm{X} nucleus and total mass of its constituent nucleons is 21⋅0021{\cdot}00 u. The binding energy per nucleon for this nucleus is equal to the energy equivalent of :

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  15. Q.151 mark
    The threshold voltage for a p-n junction diode used in the circuit is 0⋅70{\cdot}7 V. The type of biasing and current in the circuit are :

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  16. Questions number 16 to 18 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.161 mark
    Assertion (A) : When three electric bulbs of power 200 W, 100 W and 50 W are connected in series to a source, the power consumed by the 50 W bulb is maximum. Reason (R) : In a series circuit, current is the same through each bulb, but the potential difference across each bulb is different.

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  17. Q.171 mark
    Assertion (A) : A current carrying square loop made of a wire of length L is placed in a magnetic field. It experiences a torque which is greater than the torque on a circular loop made of the same wire carrying the same current in the same magnetic field. Reason (R) : A square loop occupies more area than a circular loop, both made of wire of the same length.

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  18. Q.181 mark
    Assertion (A) : In 'n' type semiconductor, number density of electrons is greater than the number density of holes but the crystal maintains an overall charge neutrality. Reason (R) : The charge of electrons donated by donor atoms is just equal and opposite to that of the ionised donor.

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Section B

2 marks each

  1. Q.192 marks
    Two identical dipoles are arranged in x-y plane as shown in the figure. Find the magnitude and the direction of net electric field at the origin O.
  2. Q.202 marks
    Write two differences between the emf and terminal potential difference of a cell. What is the most important precaution that one should take while drawing current from a cell ?
  3. Q.212 marks
    A small magnetised needle P is placed at the origin of x-y plane with its magnetic moment pointing along the y-axis. Another identical magnetised needle Q is placed in two positions, one by one. Case 1 : at (a, 0) with its magnetic moment pointing along x-axis. Case 2 : at (0, a) with its magnetic moment pointing along y-axis. (a) In which case is the potential energy of P and Q minimum ? (b) In which case is P and Q not in equilibrium ? Justify your answers.
  4. Q.22 (a)2 marks
    What is a displacement current ? How is it different from a conduction current ?
  5. OR

    Q.22 (b)2 marks
    Write any two characteristics of an electromagnetic wave. Why are microwaves used in radar systems ?
  6. Q.232 marks
    The figure shows vm2v_m^2 versus 1λ\dfrac{1}{\lambda} graph for photoelectrons emitted from a surface where vmv_m is the maximum speed of electrons and λ\lambda is the wavelength of incident radiation. Using this graph and Einstein's photoelectric equation, obtain the expression for Planck's constant and work function of the surface.
  7. Q.242 marks
    Draw the graph showing the variation of binding energy per nucleon with mass number A of nuclei (2<A<170)(2 < A < 170). Use this graph to explain the release of energy in nuclear fission.
  8. Q.25 (a)2 marks
    Obtain an expression for electrostatic potential energy of a system of three charges qq, 2q2q and −3q-3q placed at the vertices of an equilateral triangle of side aa.
  9. OR

    Q.25 (b)2 marks
    Two small conducting balls A and B of radius r1r_1 and r2r_2 have charges q1q_1 and q2q_2 respectively. They are connected by a wire. Obtain the expression for charges on A and B, in equilibrium.

Section C

3 marks each

  1. Q.263 marks
    Two circular loops A and B, each of radius 3 m, are placed coaxially at a distance of 4 m. They carry currents of 3 A and 2 A in opposite directions respectively. Find the net magnetic field at the centre of loop A.
  2. Q.273 marks
    (a) The figure shows the variation of induced emf as a function of rate of change of current for two identical solenoids X and Y. One is air cored and the other is iron cored. Which one of them is iron cored ? Why ? (b) Obtain an expression for self-inductance of a long solenoid of length L and cross-sectional area A having N turns.
  3. Q.28 (a)3 marks
    A resistor of 30 Ω\Omega and a capacitor of 250π\dfrac{250}{\pi} μF\mu\mathrm{F} are connected in series to a 200 V, 50 Hz ac source. Calculate (i) the current in the circuit, and (ii) voltage drops across the resistor and the capacitor. (iii) Is the algebraic sum of these voltages more than the source voltage ? If yes, solve the paradox.
  4. OR

    Q.28 (b)3 marks
    A series LCR circuit with R = 20 Ω\Omega, L = 2 H and C = 50 μF\mu\mathrm{F} is connected to a 200 volts ac source of variable frequency. What is (i) the amplitude of the current, and (ii) the average power transferred to the circuit in one complete cycle, at resonance ? (iii) Calculate the potential drop across the capacitor.
  5. Q.29 (a)3 marks
    (i) In diffraction due to a single slit, the phase difference between light waves reaching a point on the screen is 5π5\pi. Explain whether a bright or a dark fringe will be formed at the point. (ii) What should the width (a) of each slit be to obtain eight maxima of two double-slit patterns (slit separation d) within the central maximum of the single slit pattern ? (iii) Draw the plot of intensity distribution in a diffraction pattern due to a single slit.
  6. OR

    Q.29 (b)3 marks
    (i) In a Young's double-slit experiment SS2−SS1=λ4\mathrm{SS_2} - \mathrm{SS_1} = \dfrac{\lambda}{4}, where S1\mathrm{S_1} and S2\mathrm{S_2} are the two slits as shown in the figure. Find the path difference (S2P−S1P)(\mathrm{S_2P} - \mathrm{S_1P}) for constructive and destructive interference at P. (ii) What is the effect on the interference fringes in a Young's double-slit experiment, if the monochromatic source S is replaced by a source of white light ?
  7. Q.303 marks
    Briefly explain Geiger-Marsden experiment. Show the variation of the number of particles scattered (N) with scattering angle (θ)(\theta) in this experiment. What is the main conclusion that can be inferred from this plot ?

Section D

5 marks each

  1. Q.31 (a)5 marks
    (i) Define mobility of electrons. Give its SI units. (ii) A steady current flows through a wire AB, as shown in the figure. What happens to the electric field and the drift velocity along the wire ? Justify your answer. (iii) Consider the circuit shown in the figure. Find the effective resistance of the circuit and the current drawn from the battery.
  2. OR

    Q.31 (b)5 marks
    (i) Define electrical conductivity of a wire. Give its SI unit. (ii) High current is to be drawn safely from (1) a low-voltage battery, and (2) a high-voltage battery. What can you say about the internal resistance of the two batteries ? (iii) Calculate the total energy supplied by the batteries to the circuit shown in the figure, in one minute.
  3. Q.32 (a)5 marks
    (i) Draw a ray diagram to show how the final image is formed at infinity in an astronomical refracting telescope. Obtain an expression for its magnifying power. (ii) Two thin lenses L1\mathrm{L_1} and L2\mathrm{L_2}, L1\mathrm{L_1} being a convex lens of focal length 24 cm and L2\mathrm{L_2} a concave lens of focal length 18 cm are placed coaxially at a separation of 45 cm. A 1 cm tall object is placed in front of the lens L1\mathrm{L_1} at a distance of 36 cm. Find the location and height of the image formed by the combination.
  4. OR

    Q.32 (b)5 marks
    (i) Explain the working principle of an optical fibre with the help of a diagram. Mention one use of a light pipe. (ii) A ray of light is incident at an angle of 60° on one face of a prism with the prism angle A = 60°. The ray passes symmetrically through the prism. Find the angle of minimum deviation (δm)(\delta_m) and refractive index of the material of the prism. If the prism is immersed in water, how will δm\delta_m be affected ? Justify your answer.
  5. Q.33 (a)5 marks
    (i) A germanium crystal is doped with antimony. With the help of energy-band diagram, explain how the conductivity of the doped crystal is affected. (ii) Briefly explain the two processes involved in the formation of a p-n junction. (iii) What will the effect of (1) forward biasing, and (2) reverse biasing be on the width of depletion layer in a p-n junction diode ?
  6. OR

    Q.33 (b)5 marks
    (i) With the help of a circuit diagram, briefly explain the working of a full-wave rectifier using p-n junction diodes. (ii) Draw V – I characteristics of a p-n junction diode. Explain how these characteristics make a diode suitable for rectification. (iii) Carbon and silicon have the same lattice structure. Then why is carbon an insulator but silicon a semiconductor ?

Section E

  1. Electrostatics deals with the study of forces, fields and potentials arising from static charges. Force and electric field, due to a point charge is basically determined by Coulomb's law. For symmetric charge configurations, Gauss's law, which is also based on Coulomb's law, helps us to find the electric field. A charge/a system of charges like a dipole experience a force/torque in an electric field. Work is required to be done to provide a specific orientation to a dipole with respect to an electric field.
    Q.34 (a)1 mark
    Consider a uniformly charged thin conducting shell of radius R. Plot a graph showing the variation of ∣E⃗∣|\vec{\mathrm{E}}| with distance r from the centre, for points 0≤r≤3R0 \le r \le 3\mathrm{R}.
  2. Q.34 (b)1 mark
    The figure shows the variation of potential V with 1r\dfrac{1}{r} for two point charges Q1\mathrm{Q_1} and Q2\mathrm{Q_2}, where V is the potential at a distance r due to a point charge. Find Q1Q2\dfrac{\mathrm{Q_1}}{\mathrm{Q_2}}.
  3. Q.34 (c)2 marks
    An electric dipole of dipole moment of 6×10−76 \times 10^{-7} C-m is kept in a uniform electric field of 10410^4 N/C such that the dipole moment and the electric field are parallel. Calculate the potential energy of the dipole.
  4. OR

    Q.34 (c) OR2 marks
    An electric dipole of dipole moment p⃗\vec{p} is initially kept in a uniform electric field E⃗\vec{E} such that p⃗\vec{p} is perpendicular to E⃗\vec{E}. Find the amount of work done in rotating the dipole to a position at which p⃗\vec{p} becomes antiparallel to E⃗\vec{E}.
  5. The lens maker's formula is useful to design lenses of desired focal lengths using surfaces of suitable radii of curvature. The focal length also depends on the refractive index of the material of the lens and the surrounding medium. The refractive index depends on the wavelength of the light used. The power of a lens is related to its focal length.
    Q.35 (a)1 mark
    How will the power of a lens be affected with an increase of wavelength of light ?
  6. Q.35 (b)1 mark
    The radius of curvature of two surfaces of a convex lens is R each. For what value of μ\mu of its material will its focal length become equal to R ?
  7. Q.35 (c)2 marks
    The focal length of a concave lens of μ=1⋅5\mu = 1{\cdot}5 is 20 cm in air. It is completely immersed in water of μ=43\mu = \dfrac{4}{3}. Calculate its focal length in water.
  8. OR

    Q.35 (c) OR2 marks
    An object is placed in front of a lens which forms its erect image of magnification 3. The power of the lens is 5 D. Calculate the distance of the object and the image from the lens.