**We have collection of most prospecting numerical problems for CBSE 2023. Solve at least these problems before appearing in Board exam.**

Q1. (a)An infinite line charge produces a field of 9 x 10^{4} N/c at a distance of 2 cm. Calculate linear charge density.

(b)The electric field components in Fig. are *Ex *– = a *x*1/2 , *E*z= 0, in which given by a = 800 N/Cm^{2} . Calculate (i) the flux φE through the cube and (ii) the charge within the cube. Assume that *a *= 0.1 m.

Q2. (a) An electric dipole with dipole moment 4 x 10^{-9} Cm is aligned at 30^{0} with the direction of a uniform electric field of magnitude 5 x 10^{4} N/C. Calculate the magnitude of the torque acting on the dipole.

(b) A point charge of 2 micro coulomb is at the centre of cubic Gaussian surface 9 cm on edge. What is net flux through the surface.

Q3 (a) A 600pF capacitor is connected by a 200 V supply. It is then disconnected and is connected to another uncharged capacitor of same value. How much energy is lost in this process?

(b) A particle of mass *m *and charge (–*q*) enters the region between the two charge plates show that vertical deflection *y *= *qE L*^{2} / 2*mvx*^{2} where Vx is velocity in x direction L is length of plates.

Q4. (a) A parallel plate capacitor is charged by battery. When the battery is disconnected and a dielectric slab is then inserted in the space between the plates, explain what changes if any occur in the value of

- (I) capacitance
- (ii) potential difference
- (iii) electric field
- (iv) energy stored.

(b) in the above question how the changes will occur if battery remain connected.

Q5. (a) In the circuit shown in fig. E, F, G and H are cells of emf 2, 1, 3 and 1 volts and their internal resistances are 2, 1, 3 and 1 ohm respectively. Calculate –

- the potential difference between B and D and
- the potential difference across the terminals of each of the cells G and H.

(b) Find equivalent resistance and current in following diagram

(c ) Find current through 1 ohm and potential difference across EF

Q6. (a) A battery of emf 10 V and internal resistance 3 ohm is connected to a resistor. If the current in the circuit is 0.5 A what is resistance of the resistor? What is terminal voltage of the battery when circuit is closed ?

(b) A silver wire has a resistance of 2.1 ohm at 27.5 ^{0} C and 2.7 ohm at 100^{0} C. Determine the temperature coefficient of silver.

Q7. (a) A wire has a resistance of 16 ohm. It is melted and drawn in to a wire of half its length. Calculate the resistance of the new wire. What is % change in its resistance?

(b) How many electrons pass through a lamp in one minute if current is 300mA?

Q8 (a) Fig. shows two current carrying wires 1 and 2. Find the magnitudes and directions of the magnetic field at points *P*, *Q *and *R*.

(b)Two concentric circular coils X and Y of radii 16 cm and 10 cm respectively lie in the same vertical plane containing the north-south direction. Coil X has 20 turns and carries a current of 16 A; coil Y has 25 turns and carries a current of 18A. The sense of the current in X is anticlockwise, and in Y clockwise, for an observer looking at the coils facing west. Give the magnitude and direction of the net magnetic field due to the coils at their centre. (15.7 ×10^{-4} T) towards east

Q9. (a) A galvanometer with a coil of resistance 12 ohm shows full scale deflection for a current of 2.5 mA. How will you convert the meter in to

- (i) an ammeter of range 0 to 5amp
- (ii) a voltmeter of range 0 to 10 V.

(b) A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of solenoid is 1.8 cm. If the current carried is 8.0A, estimate the magnitude of B inside the solenoid near its center. (2.5 ×10^{-2} T )

Q10. (a) A Narrow beam of protons and deuterons, each having the same momentum, enter a region of uniform magnetic field directed perpendicular to their direction of momentum. What would be the ratio of the circular paths described by them?

(b) Two moving coil meters M1 and M2 have the following particulars

R1 = 10Ω | N1 = 30 | A1 = 3.6×10^{-3} m^{2} | B1 = 0.25 T |

R2 = 14Ω | N2 = 42 | A2 = 1.8×10^{-3} m^{2} | B2 = 0.50 T |

Determine the ratio of (a) Current Sensitivity (b ) Voltage Sensitivity.

Q11. (a) Figure shows a rectangular conductor *PQRS *in which the conductor *PQ *is free to move in a uniform magnetic field *B *perpendicular to the plane of the paper. The field extends from *x *= 0 to *x *= *b *and is zero for *x *> *b. *Assume that only the arm *PQ *is pulled outward from *x *= 0 to *x *= 2b and is then moved backward to *x *= 0 with constant speed *v, *obtain the expressions for the flux and the induced emf. Sketch the variations of these quantities with distance 0 <= *x *<= 2*b*.

(b) Current is the circuit falls from 5 A to 0 A in 0.1 sec. If an average emf of 200 V induced, give an estimate of the self-inductance.

(c) 1 m long metallic rod is rotated with an angular frequency of 400 rad/sec about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. If Magnetic field is 0.5 T find emf developed between the centre and the ring

Q12. (a) In a series LCR circuit connected to a variable frequency 230 V with L = 5.0 H, C = 80mF, R = 40W. Determine the source frequency which drives the circuit in resonance. Obtain the impedance of the circuit and the amplitude of current at resonating freq. determine the r.m.f. potential across the three elements.

(b) A voltage of 283 peak value and 50 HZ is applied to a series LCR circuit in which R = 3W, L = 25.48 mH and C = 796 mF. Find

- (a) The impedance of the circuit
- (b) Phase different between voltage and current.
- (c) The power dissipation
- (d) Power factor
- (e) What is the frequency of the source at which resonance occurs.
- (f) Calculate the impedance, current and the power at resonant condition.

Q13. (a) A power transmission line feeds input power at 2300V to a step-down transformer with primary winding 4000 terms. What should be the number of term in the secondary in order to get output at 230V?

(b) A 60 micro farad capacitor is connected to a 110V,60Hz ac supply. Determine the rms value of current in the circuit. Also calculate power absorbed by the circuit in a complete cycle.

Q14. (a) A beam of light converges to a point P. A lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) convex lens of focal length 20 cm (b) a concave lens of focal length 16 cm.

(b) Three thin lenses, each of focal length 20 cm are aligned on a common axis. Find the position of image of a small object on the axis, 60cm to the left of first lens if the distance between two consecutive lens is 30 cm.

(c) Find the position of image formed of an object O by the lens combination given whose details is given as under.

Three lenses of focal length +10 cm, -10cm and +30cm. object is placed in front of first lens at 30cm,separation between first and second lens is 5cm and second and third lens is 10cm.

Q15. (a)A ray of light passing through an equilateral prism from air undergoes minimum deviation when angle of incidence is 3/4^{th} of the angle of prism Calculate the speed of light in the prism.

(b) At what angle should a ray of light be incident on the face of a prism of refracting angle 60^{0} so that it just suffers total internal reflection at the outer face if refractive index of prism is 3/2 critical angle is 41 degree and sin 19^{0} =0.3.

Q16. (a)A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20 cm. Calculate the focal length of the lens used.

(b) Two lenses of power 10D and -5D are placed in contact. Calculate the power of lens combination. Where should an object be held from lens ,so as to obtain a virtual image of magnification 2 ( P= 5 D ) u= -10cm

(c) Double convex lens are to be manufactured from a glass of refractive index 1.5 with both faces of same radius of curvature. Find radius of curvature required if the focal length is to be 20 cm?

Q17. (a) A compound microscope uses an objective lens of focal length 4 cm and eye piece lens of focal length 10 cm. An object is placed at 6 cm from the objective lens. Calculate the magnification power of the compound microscope. Also calculate length of the microscope.

(b) An astronomical telescope having magnifying power of 5 consists of two thin lenses 0.24m apart. Find the focal length of lenses.

Q18. (a) In Young’s double slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is λ is K unit. Find out intensity of light at a point where path difference is λ/3.

(b) Find the ratio of intensities at two points in a screen in YDS when waves from the two slits have path difference of (I ) λ/2 (ii) λ/4.

Q19. (a) A beam of light consisting two wavelength 800nm and 600 nm is used to obtain the interference fringes. On a screen placed 1.4m away. If the two slits are separated by 0.28 mm, calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide.

(b) Green light of wavelength 5100 A^{0} from a narrow slit is incident on a double slit. If the overall separation of 10 fringes is 2 cm on a screen 200cm away. Find the slit separation.

Q20. (a) A width a is illuminated by light of wavelength 700nm. What will be the value of slit width a when (i) first minimum falls at an angle of diffraction 30^{0} (ii) first maximum falls at an angle of diffraction 30^{0}.

(b) Two plane monochromatic wave propagating in the same direction with amplitude A and 2A and differing in phase by л/3 super impose. Calculate the amplitude of resultant wave.

Q21. (a) The work function of the following metals is given Na =2.75eV, K= 2.30eV, Mo= 4.17eV Ni= 5.15eV Which of these metals will not show a photoelectric emission for 3300 A^{0}.

(b)The work function of cesium metal is 2.14eV. When light of frequency 6 × 10^{14} Hz is incident on the metal surface, photoemission of electron occurs. What is the

- Maximum kinetic energy of the emitted electrons?
- Stopping potential
- Maximum speed of emitted electrons

Q22. (a) In a Geiger Marsden experiment, what is the distance of closest approach to the nucleus of a 5 MeV alpha particle before it comes momentarily to rest and reverse its direction

(b)The energy level diagram of an element is given below. Identify, by doing necessary calculations, which transition corresponds to the emission of a spectral line of wavelength 102.7 nm.

Q24. (a) If 200 MeV energy is released in the fission of a single nucleus of U-235. How many fission must occur to produce a power of 1 KW.

(b) A neutron is absorbed by a _{3}Li^{6} with subsequent emission of an alpha particle. Write the corresponding nuclear reaction . Calculate the energy released in this reaction **Given ( m(Li-6 =6.015126amu) m(He-4 =4.0026044amu) , m( n-1 =1.008665amu) m(H-3= 3.01604amu)**.

(c) Compare the energy released by fusion of 1 kg of hydrogen and fission of 1 kg of U-235 if energy per fusion of hydrogen is 26 MeV and energy per fission of U-235 is 200 MevI

Q25. (a)What is out put frequency in rectifier if input frequency is 50 Hz when we have

- (i) half wave rectification
- (ii) full wave rectification

(b) Calculate Current in the circuit