CBSE Class 12 Physics 2025 question paper (55/7)
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 markTwo horizontal plates, separated by 1 cm, are arranged one above the other. A particle of mass 5 mg and charge 2 nC is released in air between the plates. The potential difference that should be applied to the plates so that the particle remains suspended between them, is :
Tap an option to check your answer.
- Q.21 markThe effective resistance between points A and B in the given circuit is :
Tap an option to check your answer.
- Q.31 markA rectangular coil of area A is kept in a uniform magnetic field such that the plane of the coil makes an angle with . The magnetic flux linked with the coil is :
Tap an option to check your answer.
- Q.41 markAn alternating current is given by . The least time the current takes to decrease from its maximum value to zero will be :
Tap an option to check your answer.
- Q.51 markA capacitor and an inductor are connected in series across an ac source of voltage of variable frequency. The frequency is increased continuously. The nature of the circuit before and after the resonance will be :
Tap an option to check your answer.
- Q.61 markA metal rod of length 50 cm is held vertically and moved with a velocity of 10 m/s towards east. The horizontal component of the Earth's magnetic field at the place is G. The emf induced across the ends of the rod is :
Tap an option to check your answer.
- Q.71 markThe dimensions of 'self-inductance' are :
Tap an option to check your answer.
- Q.81 markThe frequency of a photon of energy eV is :
Tap an option to check your answer.
- Q.91 markGermanium crystal is doped at room temperature with a minute quantity of boron. The charge carriers in the doped semiconductors will be :
Tap an option to check your answer.
- Q.101 markOut of the four options given, in which transition will the emitted photon have the maximum wavelength ?
Tap an option to check your answer.
- Q.111 markA p-n junction diode is forward biased. As a result,
Tap an option to check your answer.
- Q.121 markIsotones are the nuclides having :
Tap an option to check your answer.
- 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) : A charged particle is moving with velocity v in x-y plane, making an angle with x-axis. If a uniform magnetic field is applied in the region, along y-axis, the particle will move in a helical path with its axis parallel to x-axis. Reason (R) : The direction of the magnetic force acting on a charged particle moving in a magnetic field is along the velocity of the particle.
Tap an option to check your answer.
- Q.141 markAssertion (A) : A ray of light is incident normally on the face of a prism. The emergent ray will graze along the opposite face of the prism when the critical angle at glass-air interface is equal to the angle of the prism. Reason (R) : The refractive index of a prism depends on angle of the prism.
Tap an option to check your answer.
- Q.151 markAssertion (A) : EM waves do not require a medium for their propagation. Reason (R) : EM waves are transverse waves.
Tap an option to check your answer.
- Q.161 markAssertion (A) : The minimum negative potential applied to the anode in a photoelectric experiment at which photoelectric current becomes zero, is called cut-off voltage. Reason (R) : The threshold frequency for a metal is the minimum frequency of incident radiation below which emission of photoelectrons does not take place.
Tap an option to check your answer.
Section B
2 marks each
- Q.172 marksA cell of emf E and internal resistance r is connected across a resistor of variable resistance R. Show graphically the variation of (a) the terminal voltage across the cell, (b) the current supplied by the cell, with R as it is increased from 0 to the maximum value.
- Q.18 (a)2 marksUsing the mirror equation and the formula of magnification, deduce that "the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus."
OR
Q.18 (b)2 marksA convex lens of focal length 10 cm, a concave lens of focal length 15 cm and a third lens of unknown focal length are placed coaxially in contact. If the focal length of the combination is +12 cm, find the nature and focal length of the third lens, if all lenses are thin. Will the answer change if the lenses were thick ?- Q.192 marksWrite two differences in the patterns of double-slit interference experiment and single-slit diffraction experiment. Light waves from two pinholes illuminated by two sodium lamps do not produce interference patterns. Explain why.
- Q.202 marksDraw energy band diagrams of n-type and p-type semiconductors at temperature T > 0 K. Show the donor/acceptor energy levels with the order of difference of their energies from the bands.
- Q.212 marksBriefly explain how energy is produced in stars, giving two examples of the nuclear reactions involved.
Section C
3 marks each
- Q.223 marksThree cells A, B and C of emfs 2 V, 3 V and 5 V respectively are connected in parallel to each other. Their internal resistances are , and respectively. Calculate the currents flowing through the cells A, B and C.
- Q.23 (a)3 marks(i) Write Biot-Savart's law in vector form. (ii) Two identical circular coils A and B, each of radius R, carrying currents I and respectively, are placed concentrically in XY and YZ planes respectively. Find the magnitude and direction of the net magnetic field at their common centre.
OR
Q.23 (b)3 marks(i) A rectangular loop of sides and b carries a current I clockwise. Write the magnetic moment of the loop and show its direction in a diagram. (ii) The loop is placed in a uniform magnetic field and is free to rotate about an axis which is perpendicular to . Prove that the loop experiences no net force, but a torque .- Q.243 marks(a) State Faraday's law of electromagnetic induction and explain the role of negative sign in its expression. (b) Explain, with an example, that Lenz's law is consistent with the law of conservation of energy.
- Q.253 marks(a) Differentiate between 'conduction current' and 'displacement current', giving one similarity and one dissimilarity between them. (b) Explain the existence of electromagnetic waves in free space, using the concept of displacement current.
- Q.263 marks(a) Define 'work function' of a metal. How can its value be determined from a graph between stopping potential and frequency of the incident radiation ? (b) The work function of a metal is eV. A stopping potential of V is required to reduce the photocurrent to zero, in a photoelectric experiment. Calculate the wavelength of light used.
- Q.273 marksWrite the mathematical forms of three postulates of Bohr's theory of the hydrogen atom. Using them prove that, for an electron revolving in the orbit, (a) the radius of the orbit is proportional to , and (b) the total energy of the atom is proportional to .
- Q.283 marksExplain the process of formation of 'depletion layer' and 'potential barrier' in a p-n junction region of a diode, with the help of a suitable diagram. Which feature of junction diode makes it suitable for its use as a rectifier ?
Section D
1 mark each
- In a metallic conductor, an electron, moving due to thermal motion, suffers collisions with the heavy fixed ions but after collision, it will emerge out with the same speed but in random directions. If we consider all the electrons, their average velocity will be zero. When an electric field is applied, electrons move with an average velocity, known as drift velocity . The average time between successive collisions is known as relaxation time . The magnitude of drift velocity per unit electric field is called mobility . An expression for current through the conductor can be obtained in terms of drift velocity, number of electrons per unit volume (n), electronic charge (– e), and the cross-sectional area (A) of the conductor. This expression leads to an expression between current density and the electric field . Hence, an expression for resistivity of a metal is obtained. This expression helps us to understand increase in resistivity of a metal with increase in its temperature, in terms of change in the relaxation time and change in the number density of electrons (n).Q.29 (i)1 markConsider two cylindrical conductors A and B, made of the same metal connected in series to a battery. The length and the radius of B are twice that of A. If and are the mobility of electrons in A and B respectively, then is :
Tap an option to check your answer.
- Q.29 (ii)1 markA wire of length m and cross-sectional area m is connected to a battery of 2 V that maintains a current of A in it. The conductivity of the material of the wire (in ) is :
Tap an option to check your answer.
- Q.29 (iii)1 markThe temperature coefficient of resistance of nichrome is . In order to increase resistance of a nichrome wire by , the temperature of the wire should be increased by :
Tap an option to check your answer.
- Q.29 (iv) (a)1 markConsider the contribution of the following two factors I and II in resistivity of a metal : I. Relaxation time of electrons II. Number of electrons per unit volume The resistivity of a metal increases with increase in its temperature because :
Tap an option to check your answer.
OR
Q.29 (iv) (b)1 markA steady current flows in a copper wire of non-uniform cross-section. Consider the following three physical quantities : I. Electric field II. Current density III. Drift speed Then at the different points along the wire :Tap an option to check your answer.
- When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction is called the critical angle for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.Q.30 (i)1 markA small bulb is placed at the bottom of a tank containing a transparent liquid (refractive index n) to a depth H. The radius of the circular area of the surface of liquid, through which light from the bulb can emerge out, is R. Then is :
Tap an option to check your answer.
- Q.30 (ii) (a)1 markA parallel beam of light is incident on a face of a prism with refracting angle . The angle of minimum deviation is found to be . The refractive index of the material of the prism is close to :
Tap an option to check your answer.
OR
Q.30 (ii) (b)1 markThe angle of minimum deviation for a ray of light incident on a thin prism, made of crown glass (n = ) is . If the prism was made of dense flint glass (n = ) instead of crown glass, the angle of minimum deviation will :Tap an option to check your answer.
- Q.30 (iii)1 markAn object is placed in front of a convex spherical glass surface (n = and radius of curvature R) at a distance of 4R from it. As the object is moved slowly close to the surface, the image formed is :
Tap an option to check your answer.
- Q.30 (iv)1 markA double-convex lens, made of glass of refractive index , has focal length 10 cm. The radius of curvature of its each face, is :
Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) A parallel plate capacitor with plate area A and plate separation d has a capacitance . A slab of dielectric constant K having area A and thickness is inserted in the capacitor, parallel to the plates. Find the new value of its capacitance. (ii) You are provided with a large number of 1 identical capacitors and a power supply of 1200 V. The dielectric medium used in each capacitor can withstand up to 200 V only. Find the minimum number of capacitors and their arrangement, required to build a capacitor system of equivalent capacitance of 2 for use with this supply.
OR
Q.31 (b)5 marks(i) An electric dipole of dipole moment p consists of point charges q and – q, separated by 2a. Derive an expression for electric potential in terms of its dipole moment at a point at a distance x (>> a) from its centre and lying (I) along its axis, and (II) along its bisector line. (ii) An electric dipole of dipole moment Cm is placed in an electric field . Calculate the magnitude of the torque acting on it and the angle it makes with the x-axis, at this instant.- Q.32 (a)5 marks(i) With the help of a labelled diagram, explain the principle of working of a moving coil galvanometer. Write the purpose of using (i) radial magnetic field, and (ii) soft iron core, in it. (ii) Define current sensitivity of a galvanometer. "Increasing the current sensitivity may not necessarily increase the voltage sensitivity." Give reason.
OR
Q.32 (b)5 marks(i) (I) Write Ampere's circuital law in mathematical form and explain the terms used. (II) As the current carrying solenoid is made longer, the magnetic field produced outside it approaches zero. Why ? (III) A flexible loop of irregular shape carrying current when located in an external magnetic field, changes to a circular shape. Give reason. (ii) A galvanometer of resistance G is converted into a voltmeter to measure up to V volts, by connecting a resistance in series with the coil. If is replaced by , then it can only measure up to volt. Find the value of the resistance (in terms of and ) needed to convert it into a voltmeter that can read up to 2 V.- Q.33 (a)5 marks(i) Explain with the help of a labelled ray diagram the formation of final image by an astronomical telescope at infinity. Write the expression for its magnifying power. (ii) The total magnification produced by a compound microscope is 20. The magnification produced by the eyepiece is 5. When the microscope is focussed on a certain object, the distance between the objective and eyepiece is observed to be 14 cm. Calculate the focal lengths of the objective and the eyepiece. (Given that the least distance of distinct vision = 25 cm)
OR
Q.33 (b)5 marks(i) Two coherent light waves, each of intensity superpose each other and produce interference pattern on a screen. Obtain the expression for the resultant intensity at a point where the phase difference between the waves is . Write its maximum and minimum possible values. (ii) In a single slit diffraction experiment, the aperture of the slit is 3 mm and the separation between the slit and the screen is m. A monochromatic light of wavelength 600 nm is normally incident on the slit. Calculate the distance of (I) first order minimum, and (II) second order maximum, from the centre of the screen.
Section A
1 mark each
- Q.11 markThe electric field (E) and electric potential (V) at a point inside a charged hollow metallic sphere are respectively :
Tap an option to check your answer.
- Q.21 markThe dimensions of 'self-inductance' are :
Tap an option to check your answer.
- Q.31 markIn a circular loop of radius R, current I enters at point A and exits at point B, as shown in the figure. The value of the magnetic field at the centre O of the loop is :
Tap an option to check your answer.
- Q.41 markThe frequency of a photon of energy eV is :
Tap an option to check your answer.
- Q.51 markA metal rod of length 50 cm is held vertically and moved with a velocity of 10 m/s towards east. The horizontal component of the Earth's magnetic field at the place is G. The emf induced across the ends of the rod is :
Tap an option to check your answer.
- Q.61 markGermanium crystal is doped at room temperature with a minute quantity of boron. The charge carriers in the doped semiconductors will be :
Tap an option to check your answer.
- Q.71 markThe effective resistance between points A and B in the given circuit is :
Tap an option to check your answer.
- Q.81 markA capacitor and an inductor are connected in series across an ac source of voltage of variable frequency. The frequency is increased continuously. The nature of the circuit before and after the resonance will be :
Tap an option to check your answer.
- Q.91 markAn alternating current is given by . The least time the current takes to decrease from its maximum value to zero will be :
Tap an option to check your answer.
- Q.101 markThe mass numbers of two nuclei A and B are 27 and 64 respectively. The ratio of their radii will be :
Tap an option to check your answer.
- Q.111 markIsotones are the nuclides having :
Tap an option to check your answer.
- Q.121 markA p-n junction diode is forward biased. As a result,
Tap an option to check your answer.
- 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) : A ray of light is incident normally on the face of a prism. The emergent ray will graze along the opposite face of the prism when the critical angle at glass-air interface is equal to the angle of the prism. Reason (R) : The refractive index of a prism depends on angle of the prism.
Tap an option to check your answer.
- Q.141 markAssertion (A) : A charged particle is moving with velocity v in x-y plane, making an angle with x-axis. If a uniform magnetic field is applied in the region, along y-axis, the particle will move in a helical path with its axis parallel to x-axis. Reason (R) : The direction of the magnetic force acting on a charged particle moving in a magnetic field is along the velocity of the particle.
Tap an option to check your answer.
- Q.151 markAssertion (A) : The minimum negative potential applied to the anode in a photoelectric experiment at which photoelectric current becomes zero, is called cut-off voltage. Reason (R) : The threshold frequency for a metal is the minimum frequency of incident radiation below which emission of photoelectrons does not take place.
Tap an option to check your answer.
- Q.161 markAssertion (A) : EM waves do not require a medium for their propagation. Reason (R) : EM waves are transverse waves.
Tap an option to check your answer.
Section B
2 marks each
- Q.172 marksTwo wires made of the same material have the same length () but different cross-sectional areas and . They are connected together with a cell of voltage V. Find the ratio of the drift velocities of free electrons in the two wires when they are joined in (i) series, and (ii) parallel.
- Q.182 marksDraw energy band diagrams of n-type and p-type semiconductors at temperature T > 0 K. Show the donor/acceptor energy levels with the order of difference of their energies from the bands.
- Q.192 marksThe ratio of the intensities at maxima to minima in Young's double-slit experiment is 25 : 9. Calculate the ratio of intensities of the interfering waves.
- Q.20 (a)2 marksUsing the mirror equation and the formula of magnification, deduce that "the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus."
OR
Q.20 (b)2 marksA convex lens of focal length 10 cm, a concave lens of focal length 15 cm and a third lens of unknown focal length are placed coaxially in contact. If the focal length of the combination is +12 cm, find the nature and focal length of the third lens, if all lenses are thin. Will the answer change if the lenses were thick ?- Q.212 marksCalculate the binding energy per nucleon (in MeV) of a helium nucleus . Given : u u u MeV/c
Section C
3 marks each
- Q.223 marksWrite the mathematical forms of three postulates of Bohr's theory of the hydrogen atom. Using them prove that, for an electron revolving in the orbit, (a) the radius of the orbit is proportional to , and (b) the total energy of the atom is proportional to .
- Q.233 marks(a) Briefly explain Einstein's photoelectric equation. (b) Four metals with their work functions are listed below : K = eV, Na = eV, Mo = eV and Ni = eV. The radiation of wavelength 330 nm from a laser source placed 1 m away, falls on these metals. Which of these metals will not show photoelectric emission ? What will happen if the laser source is brought closer to a distance of 50 cm ?
- Q.24 (a)3 marks(i) Write Biot-Savart's law in vector form. (ii) Two identical circular coils A and B, each of radius R, carrying currents I and respectively, are placed concentrically in XY and YZ planes respectively. Find the magnitude and direction of the net magnetic field at their common centre.
OR
Q.24 (b)3 marks(i) A rectangular loop of sides and b carries a current I clockwise. Write the magnetic moment of the loop and show its direction in a diagram. (ii) The loop is placed in a uniform magnetic field and is free to rotate about an axis which is perpendicular to . Prove that the loop experiences no net force, but a torque .- Q.253 marks(a) How are electromagnetic waves produced ? (b) Write the wavelength range and one use of : (i) Microwaves, and (ii) Ultraviolet waves.
- Q.263 marks(a) Two concentric circular coils of radii and are placed coaxially with their centres coinciding. If a current I is passed through the outer coil, obtain the expression for mutual inductance of the arrangement. (b) The current in a solenoid decreases steadily from 6 mA to 2 mA in 50 ms. If an average emf of V is induced, find the self-inductance of the solenoid.
- Q.273 marksExplain the process of formation of 'depletion layer' and 'potential barrier' in a p-n junction region of a diode, with the help of a suitable diagram. Which feature of junction diode makes it suitable for its use as a rectifier ?
- Q.283 marksTwo point charges of and are located in free space at and respectively. (a) Calculate the amount of work done to separate the two charges at infinite distance. (b) If this system of charges was initially kept in an electric field , where N C m, calculate the electrostatic potential energy of the system.
Section D
1 mark each
- When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction is called the critical angle for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.Q.29 (i)1 markA small bulb is placed at the bottom of a tank containing a transparent liquid (refractive index n) to a depth H. The radius of the circular area of the surface of liquid, through which light from the bulb can emerge out, is R. Then is :
Tap an option to check your answer.
- Q.29 (ii) (a)1 markA parallel beam of light is incident on a face of a prism with refracting angle . The angle of minimum deviation is found to be . The refractive index of the material of the prism is close to :
Tap an option to check your answer.
OR
Q.29 (ii) (b)1 markThe angle of minimum deviation for a ray of light incident on a thin prism, made of crown glass (n = ) is . If the prism was made of dense flint glass (n = ) instead of crown glass, the angle of minimum deviation will :Tap an option to check your answer.
- Q.29 (iii)1 markAn object is placed in front of a convex spherical glass surface (n = and radius of curvature R) at a distance of 4R from it. As the object is moved slowly close to the surface, the image formed is :
Tap an option to check your answer.
- Q.29 (iv)1 markA double-convex lens, made of glass of refractive index , has focal length 10 cm. The radius of curvature of its each face, is :
Tap an option to check your answer.
- In a metallic conductor, an electron, moving due to thermal motion, suffers collisions with the heavy fixed ions but after collision, it will emerge out with the same speed but in random directions. If we consider all the electrons, their average velocity will be zero. When an electric field is applied, electrons move with an average velocity, known as drift velocity . The average time between successive collisions is known as relaxation time . The magnitude of drift velocity per unit electric field is called mobility . An expression for current through the conductor can be obtained in terms of drift velocity, number of electrons per unit volume (n), electronic charge (– e), and the cross-sectional area (A) of the conductor. This expression leads to an expression between current density and the electric field . Hence, an expression for resistivity of a metal is obtained. This expression helps us to understand increase in resistivity of a metal with increase in its temperature, in terms of change in the relaxation time and change in the number density of electrons (n).Q.30 (i)1 markConsider two cylindrical conductors A and B, made of the same metal connected in series to a battery. The length and the radius of B are twice that of A. If and are the mobility of electrons in A and B respectively, then is :
Tap an option to check your answer.
- Q.30 (ii)1 markA wire of length m and cross-sectional area m is connected to a battery of 2 V that maintains a current of A in it. The conductivity of the material of the wire (in ) is :
Tap an option to check your answer.
- Q.30 (iii)1 markThe temperature coefficient of resistance of nichrome is . In order to increase resistance of a nichrome wire by , the temperature of the wire should be increased by :
Tap an option to check your answer.
- Q.30 (iv) (a)1 markConsider the contribution of the following two factors I and II in resistivity of a metal : I. Relaxation time of electrons II. Number of electrons per unit volume The resistivity of a metal increases with increase in its temperature because :
Tap an option to check your answer.
OR
Q.30 (iv) (b)1 markA steady current flows in a copper wire of non-uniform cross-section. Consider the following three physical quantities : I. Electric field II. Current density III. Drift speed Then at the different points along the wire :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) Explain with the help of a labelled ray diagram the formation of final image by an astronomical telescope at infinity. Write the expression for its magnifying power. (ii) The total magnification produced by a compound microscope is 20. The magnification produced by the eyepiece is 5. When the microscope is focussed on a certain object, the distance between the objective and eyepiece is observed to be 14 cm. Calculate the focal lengths of the objective and the eyepiece. (Given that the least distance of distinct vision = 25 cm)
OR
Q.31 (b)5 marks(i) Two coherent light waves, each of intensity superpose each other and produce interference pattern on a screen. Obtain the expression for the resultant intensity at a point where the phase difference between the waves is . Write its maximum and minimum possible values. (ii) In a single slit diffraction experiment, the aperture of the slit is 3 mm and the separation between the slit and the screen is m. A monochromatic light of wavelength 600 nm is normally incident on the slit. Calculate the distance of (I) first order minimum, and (II) second order maximum, from the centre of the screen.- Q.32 (a)5 marks(i) A parallel plate capacitor with plate area A and plate separation d has a capacitance . A slab of dielectric constant K having area A and thickness is inserted in the capacitor, parallel to the plates. Find the new value of its capacitance. (ii) You are provided with a large number of 1 identical capacitors and a power supply of 1200 V. The dielectric medium used in each capacitor can withstand up to 200 V only. Find the minimum number of capacitors and their arrangement, required to build a capacitor system of equivalent capacitance of 2 for use with this supply.
OR
Q.32 (b)5 marks(i) An electric dipole of dipole moment p consists of point charges q and – q, separated by 2a. Derive an expression for electric potential in terms of its dipole moment at a point at a distance x (>> a) from its centre and lying (I) along its axis, and (II) along its bisector line. (ii) An electric dipole of dipole moment Cm is placed in an electric field . Calculate the magnitude of the torque acting on it and the angle it makes with the x-axis, at this instant.- Q.33 (a)5 marks(i) With the help of a labelled diagram, explain the principle of working of a moving coil galvanometer. Write the purpose of using (i) radial magnetic field, and (ii) soft iron core, in it. (ii) Define current sensitivity of a galvanometer. "Increasing the current sensitivity may not necessarily increase the voltage sensitivity." Give reason.
OR
Q.33 (b)5 marks(i) (I) Write Ampere's circuital law in mathematical form and explain the terms used. (II) As the current carrying solenoid is made longer, the magnetic field produced outside it approaches zero. Why ? (III) A flexible loop of irregular shape carrying current when located in an external magnetic field, changes to a circular shape. Give reason. (ii) A galvanometer of resistance G is converted into a voltmeter to measure up to V volts, by connecting a resistance in series with the coil. If is replaced by , then it can only measure up to volt. Find the value of the resistance (in terms of and ) needed to convert it into a voltmeter that can read up to 2 V.
Section A
1 mark each
- Q.11 markIn the circuit shown, the charge on the left plate of 20 capacitor is . The charge on the right plate of the 12 capacitor is :
Tap an option to check your answer.
- Q.21 markGermanium crystal is doped at room temperature with a minute quantity of boron. The charge carriers in the doped semiconductors will be :
Tap an option to check your answer.
- Q.31 markA steady current I is passed through a conductor at room temperature for time t. It is observed that its temperature rises by C. If 2I current is passed through the conductor (at room temperature) for the same duration, the rise in its temperature will be approximately :
Tap an option to check your answer.
- Q.41 markThe dimensions of 'self-inductance' are :
Tap an option to check your answer.
- Q.51 markIsotones are the nuclides having :
Tap an option to check your answer.
- Q.61 markA metal rod of length 50 cm is held vertically and moved with a velocity of 10 m/s towards east. The horizontal component of the Earth's magnetic field at the place is G. The emf induced across the ends of the rod is :
Tap an option to check your answer.
- Q.71 markThe frequency of a photon of energy eV is :
Tap an option to check your answer.
- Q.81 markAn alternating current is given by . The least time the current takes to decrease from its maximum value to zero will be :
Tap an option to check your answer.
- Q.91 markA rectangular coil of area A is kept in a uniform magnetic field such that the plane of the coil makes an angle with . The magnetic flux linked with the coil is :
Tap an option to check your answer.
- Q.101 markThe minimum energy required to free the electron from the ground state of the hydrogen atom is :
Tap an option to check your answer.
- Q.111 markA capacitor and an inductor are connected in series across an ac source of voltage of variable frequency. The frequency is increased continuously. The nature of the circuit before and after the resonance will be :
Tap an option to check your answer.
- Q.121 markA p-n junction diode is forward biased. As a result,
Tap an option to check your answer.
- 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) : EM waves do not require a medium for their propagation. Reason (R) : EM waves are transverse waves.
Tap an option to check your answer.
- Q.141 markAssertion (A) : A charged particle is moving with velocity v in x-y plane, making an angle with x-axis. If a uniform magnetic field is applied in the region, along y-axis, the particle will move in a helical path with its axis parallel to x-axis. Reason (R) : The direction of the magnetic force acting on a charged particle moving in a magnetic field is along the velocity of the particle.
Tap an option to check your answer.
- Q.151 markAssertion (A) : The minimum negative potential applied to the anode in a photoelectric experiment at which photoelectric current becomes zero, is called cut-off voltage. Reason (R) : The threshold frequency for a metal is the minimum frequency of incident radiation below which emission of photoelectrons does not take place.
Tap an option to check your answer.
- Q.161 markAssertion (A) : A ray of light is incident normally on the face of a prism. The emergent ray will graze along the opposite face of the prism when the critical angle at glass-air interface is equal to the angle of the prism. Reason (R) : The refractive index of a prism depends on angle of the prism.
Tap an option to check your answer.
Section B
2 marks each
- Q.172 marksCalculate the value of the current passing through the battery in the given circuit diagram.
- Q.182 marksIn a Young's double-slit experiment, the intensity at the central maximum in the interference pattern on the screen is . Find the intensity at a point on the screen where the path difference between the interfering waves is .
- Q.192 marksDefine the 'distance of closest approach'. An -particle of kinetic energy K is bombarded on a thin gold foil. Derive an expression for the 'distance of closest approach'.
- Q.20 (a)2 marksUsing the mirror equation and the formula of magnification, deduce that "the virtual image produced by a convex mirror is always diminished in size and is located between the pole and the focus."
OR
Q.20 (b)2 marksA convex lens of focal length 10 cm, a concave lens of focal length 15 cm and a third lens of unknown focal length are placed coaxially in contact. If the focal length of the combination is +12 cm, find the nature and focal length of the third lens, if all lenses are thin. Will the answer change if the lenses were thick ?- Q.212 marksDraw energy band diagrams of n-type and p-type semiconductors at temperature T > 0 K. Show the donor/acceptor energy levels with the order of difference of their energies from the bands.
Section C
3 marks each
- Q.223 marksExplain the process of formation of 'depletion layer' and 'potential barrier' in a p-n junction region of a diode, with the help of a suitable diagram. Which feature of junction diode makes it suitable for its use as a rectifier ?
- Q.233 marksAn electric field given by : for x > 0 for x < 0 exists in a region. A right circular cylinder of length 10 cm and radius 2 cm, is placed in the region such that its axis coincides with x-axis and its two faces are at x = 5 cm and x = 5 cm. Calculate : (a) the net outward flux through the cylinder, and (b) the net charge inside the cylinder.
- Q.243 marksAnswer the following, giving reasons : (a) The maximum kinetic energy of the photoelectrons is independent of the intensity of incident radiation. (b) Photoelectric current increases with the increase in the intensity of the incident radiation. (c) The stopping potential varies linearly with the frequency of the incident radiation for a given photosensitive surface.
- Q.25 (a)3 marks(i) Write Biot-Savart's law in vector form. (ii) Two identical circular coils A and B, each of radius R, carrying currents I and respectively, are placed concentrically in XY and YZ planes respectively. Find the magnitude and direction of the net magnetic field at their common centre.
OR
Q.25 (b)3 marks(i) A rectangular loop of sides and b carries a current I clockwise. Write the magnetic moment of the loop and show its direction in a diagram. (ii) The loop is placed in a uniform magnetic field and is free to rotate about an axis which is perpendicular to . Prove that the loop experiences no net force, but a torque .- Q.263 marksName the electromagnetic radiations and write their frequency range : (a) Used to take the photograph of the bones (b) Produced by hot bodies (c) Used in television communication systems
- Q.273 marksAn ac source of voltage is connected to a circuit element X. It is observed that the current flowing through X varies as . (a) Identify the element X and write the expression for its reactance. (b) Plot a graph to show the variation of reactance of the element with the frequency of the applied voltage. (c) Draw plots showing the variation of voltage and current with time over one cycle of applied ac.
- Q.283 marksWrite the mathematical forms of three postulates of Bohr's theory of the hydrogen atom. Using them prove that, for an electron revolving in the orbit, (a) the radius of the orbit is proportional to , and (b) the total energy of the atom is proportional to .
Section D
1 mark each
- In a metallic conductor, an electron, moving due to thermal motion, suffers collisions with the heavy fixed ions but after collision, it will emerge out with the same speed but in random directions. If we consider all the electrons, their average velocity will be zero. When an electric field is applied, electrons move with an average velocity, known as drift velocity . The average time between successive collisions is known as relaxation time . The magnitude of drift velocity per unit electric field is called mobility . An expression for current through the conductor can be obtained in terms of drift velocity, number of electrons per unit volume (n), electronic charge (– e), and the cross-sectional area (A) of the conductor. This expression leads to an expression between current density and the electric field . Hence, an expression for resistivity of a metal is obtained. This expression helps us to understand increase in resistivity of a metal with increase in its temperature, in terms of change in the relaxation time and change in the number density of electrons (n).Q.29 (i) (a)1 markConsider the contribution of the following two factors I and II in resistivity of a metal : I. Relaxation time of electrons II. Number of electrons per unit volume The resistivity of a metal increases with increase in its temperature because :
Tap an option to check your answer.
OR
Q.29 (i) (b)1 markA steady current flows in a copper wire of non-uniform cross-section. Consider the following three physical quantities : I. Electric field II. Current density III. Drift speed Then at the different points along the wire :Tap an option to check your answer.
- Q.29 (ii)1 markThe temperature coefficient of resistance of nichrome is . In order to increase resistance of a nichrome wire by , the temperature of the wire should be increased by :
Tap an option to check your answer.
- Q.29 (iii)1 markA wire of length m and cross-sectional area m is connected to a battery of 2 V that maintains a current of A in it. The conductivity of the material of the wire (in ) is :
Tap an option to check your answer.
- Q.29 (iv)1 markConsider two cylindrical conductors A and B, made of the same metal connected in series to a battery. The length and the radius of B are twice that of A. If and are the mobility of electrons in A and B respectively, then is :
Tap an option to check your answer.
- When light travels from an optically denser medium to an optically rarer medium, at the interface it is partly reflected back into the same medium and partly refracted to the second medium. The angle of incidence corresponding to an angle of refraction is called the critical angle for the given pair of media. This angle is related to the refractive index of medium 1 with respect to medium 2. Refraction of light through a prism involves refraction at two plane interfaces. A relation for the refractive index of the material of the prism can be obtained in terms of the refracting angle of the prism and the angle of minimum deviation. For a thin prism, this relation reduces to a simple equation. Laws of refraction are also valid for refraction of light at a spherical interface. When an object is placed in front of a spherical surface separating two media, its image is formed. A relation between object and image distance, in terms of refractive indices of two media and the radius of curvature of the spherical surface can be obtained. Using this relation for two surfaces of a lens, 'lens maker formula' is obtained.Q.30 (i)1 markAn object is placed in front of a convex spherical glass surface (n = and radius of curvature R) at a distance of 4R from it. As the object is moved slowly close to the surface, the image formed is :
Tap an option to check your answer.
- Q.30 (ii)1 markA double-convex lens, made of glass of refractive index , has focal length 10 cm. The radius of curvature of its each face, is :
Tap an option to check your answer.
- Q.30 (iii)1 markA small bulb is placed at the bottom of a tank containing a transparent liquid (refractive index n) to a depth H. The radius of the circular area of the surface of liquid, through which light from the bulb can emerge out, is R. Then is :
Tap an option to check your answer.
- Q.30 (iv) (a)1 markA parallel beam of light is incident on a face of a prism with refracting angle . The angle of minimum deviation is found to be . The refractive index of the material of the prism is close to :
Tap an option to check your answer.
OR
Q.30 (iv) (b)1 markThe angle of minimum deviation for a ray of light incident on a thin prism, made of crown glass (n = ) is . If the prism was made of dense flint glass (n = ) instead of crown glass, the angle of minimum deviation will :Tap an option to check your answer.
Section E
5 marks each
- Q.31 (a)5 marks(i) With the help of a labelled diagram, explain the principle of working of a moving coil galvanometer. Write the purpose of using (i) radial magnetic field, and (ii) soft iron core, in it. (ii) Define current sensitivity of a galvanometer. "Increasing the current sensitivity may not necessarily increase the voltage sensitivity." Give reason.
OR
Q.31 (b)5 marks(i) (I) Write Ampere's circuital law in mathematical form and explain the terms used. (II) As the current carrying solenoid is made longer, the magnetic field produced outside it approaches zero. Why ? (III) A flexible loop of irregular shape carrying current when located in an external magnetic field, changes to a circular shape. Give reason. (ii) A galvanometer of resistance G is converted into a voltmeter to measure up to V volts, by connecting a resistance in series with the coil. If is replaced by , then it can only measure up to volt. Find the value of the resistance (in terms of and ) needed to convert it into a voltmeter that can read up to 2 V.- Q.32 (a)5 marks(i) Explain with the help of a labelled ray diagram the formation of final image by an astronomical telescope at infinity. Write the expression for its magnifying power. (ii) The total magnification produced by a compound microscope is 20. The magnification produced by the eyepiece is 5. When the microscope is focussed on a certain object, the distance between the objective and eyepiece is observed to be 14 cm. Calculate the focal lengths of the objective and the eyepiece. (Given that the least distance of distinct vision = 25 cm)
OR
Q.32 (b)5 marks(i) Two coherent light waves, each of intensity superpose each other and produce interference pattern on a screen. Obtain the expression for the resultant intensity at a point where the phase difference between the waves is . Write its maximum and minimum possible values. (ii) In a single slit diffraction experiment, the aperture of the slit is 3 mm and the separation between the slit and the screen is m. A monochromatic light of wavelength 600 nm is normally incident on the slit. Calculate the distance of (I) first order minimum, and (II) second order maximum, from the centre of the screen.- Q.33 (a)5 marks(i) A parallel plate capacitor with plate area A and plate separation d has a capacitance . A slab of dielectric constant K having area A and thickness is inserted in the capacitor, parallel to the plates. Find the new value of its capacitance. (ii) You are provided with a large number of 1 identical capacitors and a power supply of 1200 V. The dielectric medium used in each capacitor can withstand up to 200 V only. Find the minimum number of capacitors and their arrangement, required to build a capacitor system of equivalent capacitance of 2 for use with this supply.
OR
Q.33 (b)5 marks(i) An electric dipole of dipole moment p consists of point charges q and – q, separated by 2a. Derive an expression for electric potential in terms of its dipole moment at a point at a distance x (>> a) from its centre and lying (I) along its axis, and (II) along its bisector line. (ii) An electric dipole of dipole moment Cm is placed in an electric field . Calculate the magnitude of the torque acting on it and the angle it makes with the x-axis, at this instant.