**Instructions:**

1. Section-A Q. no. 1-8 carry 1 mark each.

2. Section-B Q. no. 9-18 carry 2 marks each.

3. Section-C Q. no. 19-27 carry 3 marks each.

4. Section-D Q. no. 28-30 carry 5 marks each.

2. Section-B Q. no. 9-18 carry 2 marks each.

3. Section-C Q. no. 19-27 carry 3 marks each.

4. Section-D Q. no. 28-30 carry 5 marks each.

**Section-A**

**1. S**

_{1}and S_{2}are two hollow concentric spheres enclosing charges q and 2q respectively.**(i) What is the ratio of electric flux through S**

_{1}and S_{2}?**(ii) How will the electric flux through sphere S**

_{1}change is a medium of dielectric constant 5 is introduced in the sphere S_{1}in place of air ?**Ans.**(i)

(ii)

**2. For the potentiometer circuit shown in the figure, points X and Y represent the two terminals of an unknown emf E’. A student observed that when the jockey is moved from the end A to the end B, deflection in galvanometer remains in same direction. What may be two possible faults?**

**Ans.**Two possible faults may be

(a) E < ε

(b) Polarity of terminals X and Y are not connected correctly

**3. Define 1mH Inductance.**

**Ans.**As Φ = LI ⇒ when one miliwebere flux changes due to flow of unit current through a coil then the flux linked will be one milihenery.

**4. Derive an expression for capacitance of a parallel plate capacitor.**

**Ans.**Electric field between the plates of capacitor of charge q and area of crossection A is given as E = σ/∈

_{0}

∴ P.D between the plates V = σ/∈

_{0 }
∴

_{ }capacitance**5. How does the intensity of magnetization of paramagnetic sample vary with temperature ?**

**Ans.**

**6. A circular coil of N turn and radius R is kept normal to a magnetic field given by B=B**

_{o }cos wt. State the rule which helps to detect the direction of induced current?**Ans.**Lenz’ law. As accorong to law, induced current will be such that it opposes the cause by which it is induced.

**7. A bulb of resistor 10? connected to an Inductor of inductance L is in series with an a.c. source marked 100v 50Hz. If phase angle between the voltage and current is π/4 radian. Calculate the value of L.**

**Ans.**as Φ = π/4, R = 10Ω f = 50Hz

tanΦ = X

_{L}/R ⇒ tanπ/4 = 2πfL/R
⇒ 2πfL = R ⇒ L = R/2πf = 0.3henery

**8. An electron and a proton have same De broglie wavelength associated with them. How are their Kinetic energies related to each other ?**

**Ans.**

**SECTION-B**

**9. Two radioactive nuclei X & Y initially contain an equal number of atoms. Their half life is 1 hour and 2 hour respectively. Calculate the ratio of their rates of disintegration after two hours.**

**Ans.**Given N

_{ox}= N

_{oy }= N

_{o}

T

_{y2x}= IH, T_{y2y }= 2H.**10. A message signal of frequency 15 KHz. and peak voltage of 5 volts is used to modulation a carrier of frequency 1 MHz . and peak voltage 20 volt .Determine the modulation index and the side bands.**

**Ans.**

Side base band .1MHz +15 KHz and 1MHz - 15 KHz

i.e. 1.015 MHz and 0.985 MHz.

**11. Two rectangular metal plates, each of area A are kept parallel to each other at a distance ‘d’ apart to form a parallel plate capacitor. If the area of each of the plates is doubled and their distance of separation decreases to 1/2 of its initial value. Calculate the ratio of their capacitance in the two cases?**

**Ans.**Capacitance of parallel capacitor is given as C =

_{ }

C

C

_{Initial}= C_{1}= andC

_{final }= C_{2}=
=

**12. Show that energy stored in a parallel plate capacitor is 1/2CV**

^{2}.**Ans.**Graphically variation of stored charged on plate of capacitor & P.D between the plate is shown in figure

Area of ΔOAB =

**13. A conductor of length ‘l’ connected to a d.c. source of potential V. If the length of the conductor is tripled by streching it keeping ‘V’ constant. Explain how do the following factors vary in the conductor? (2 marks)**

**(1) Drift speed of electrons**

**(2) Resistence**

**(3) Resistivity**

**Ans.**(1)

(2) R:- increases 9 times as R α n

^{2}.
(3) ρ :- No effect.

**14. Distinguish between paramagnetic, diamagnetic and ferromagnetic material.**

**Ans.**

Diamagnetic |
Paramagnetic |
Feromagnetic |

If kept near a magnet, materials are freely repelled. |
Feebly attracted. |
Strongly attracted. |

χ : negative & small. |
χ : positive and small. |
χ: positive and large. |

μ : Slightly less than one. |
μ : Slightly more than one. |
μ : Quite larger than one. |

**15. A particle of mass ‘m’ with charge ‘q’ moving with a uniform speed ? normal to a uniform magnetic field B, describes a circular path of radius r. Describe an expression for the (i) time period of revolution & (ii) Kinetic energy of the particle.**

**Ans.**As

It follow a circular path

Time to complete one circular path

and

**16. Draw a schematic arrangement of Geiger-Marsden experimental setup. How does it explain the size of nucleus.**

**Ans.**The fact that only a small fraction of incident particles rebound back that number of α particles undergoing head on collision is small this leads the mass confined in small region.

**17. Calculate the maximum kinetic energy of α particle emitted during α-decay of**

_{92}U^{238}→_{90}Th^{234 }+_{2}He^{4}**M(**

_{92}U^{238}) = 238.05079U, M(_{90}Th^{234}) = 234.04363U, M(_{2}He^{4}) = 4.00260U**Ans.**Δm = [ M(u) - M(th) - M(He) ]

= (238.05079 – 234.04363 – 4.00560)

= 0.00456 U

Q = 0.00456 x 931 mev

**18. State the laws of Photoelectric effect. Explain it on the basis of Einstein equation.**

**Ans.**Laws : -

(i) It is an instantaneous process

(ii) No Photo emission takes place below threshold frequency of material, no matter how intense the incident beam.

(iii)
The maximum photo current (saturation current ) does not depends upon
stopping potential or frequency but depends on intensity of incident
radiation.

(iv) Stopping potential is independent on intensity of incident radiation.

**SECTION-C**

**19. Explain with the help of a labeled diagram the underlying the principle and working of a step down transformer.**

**Ans.**

**Principle**– It works on the principle of mutual induction i.e. when a magnetic flux linked with a coil changes an emf is induced in another coil which is placed closer to first one.

**Working**– when a.c. signal is applied in primary (p) coil, the flux linked with primary and secondary coil will be given as

Φ

_{S}= N_{S}BA and
Φ

_{P}= N_{P}BA
emf induced in secondary will be given as

As Ns < Np ⇒ Es < Ep

**20. The magnitude of magnetic field in a plane e.m. wave is given as B**

_{X}= 0, B_{Y}= 2 x 10^{-7}sin(0.5 x 10^{3 }x + 1.5 x 10^{11}t)T.**(a) Determine the wavelength and frequency of wave.**

**(b) Write an expression for the electric field.**

**Ans.**B

_{Y}= B

_{O}sin (1.5 x 10

^{11}t + 0.5 x 10

^{3}x)T

B

_{O }= 2 x 10^{-7}T, ω = 2πν = 1.5 x 10^{11}
ω = 1.5 x 10

K = 0.5 x 10

^{11}⇒K = 0.5 x 10

^{3}
E

_{X}= 0 , E_{Y}= 0, E_{Z}= CB_{O }sin (1.5 x 10^{11}t + 0.5 x 10^{3}x)
E

_{Z}= 60 sin (1.5x 10^{11}t + 0.5 x 10^{3}x)**21. The energy level of an element are given below. Which corresponds to emission of spectral line of wavelength 482nm?**

**Ans.**

For ‘B’ Transition ΔE = 3.4 – 0.85

= 2.55 very closer

= 2.55 very closer

‘B’ is possible

**23. Why do we require modulation? Explain the AM with block diagram.**

**Ans.**As for Transmission of signals .Size of antenna , which is too large.

Hence
to reduce the size of antenna , Frequency (Other characteristics such
as amplitude, phase, should be modified, and the process is known as
modulation.

**24. Define coefficient of mutual inductance of two coils. A secondary coil of n**

_{2}turns is wound on a long solenoid of area of cross section A having a primary coil of n_{1}turns per unit length. What is the mutual inductance of the two coils ?**Ans. Mutual inductance:**Mutual inductance is numerically equal to the induced emf produced in coil when the rate of change of current is unity in the neighboring coil.

**Derivation:**

Let n

_{1}= Number of turns per unit length in first and

n

_{2}= Number of turns per unit length in secondary coil

Φ

_{21}= M

_{21}I

_{1}

= N

_{2}BA

= N2(µ

_{0}n

_{1}I

_{1}) A ----------------(1)

⇒M

_{21}I

_{1}= µ

_{0}N

_{1}N

_{2}I

_{1}A / L

⇒ M

_{21}= µ

_{0}n

_{1}n

_{2}AL

Similarly M

_{12}= n

_{1}n

_{2}AL

**25. Find the value of unknown resistance X in the following circuit, if no current flows through the section AO. Also calculate the current drawn by the circuit from the battery of emf CV.**

**Ans.**

As

Now 2Ω & 4Ω are connected in series and 3Ω & 6Ω are connected in series and combination is connected in parallel with battery.

**26. The following data was obtained for the dependence of the magnitude of electric field with distance, from a reference point o, with in the charge distribution in shaded region.**

**(I) Identify the charge distribution**

**(II) Identify the location points A B C and A**

^{1}B^{1}C^{1}**Ans.**

E Varies inversely to cube of distance Charge distribution should be Dipole , as due to dipole E α 1/r

^{3}
Hence A,B,C lies on axis & A

^{1},B^{1},C^{1}on Bisector.**27. A short bar magnet which is placed with its axis at 30**

^{o}experiences a torque of 0.016Nm in an external field of 800G.**(i) Determine the magnetic moment of magnet.**

**(ii) What is work done by an external force is moving it from its most stable to most unstable position.**

**Ans.**Given θ = 30

^{o}, = 0.016Nm.

B = 800 x 10

^{-4}T

(i) = M sinθ

⇒ / B sinθ = 0.016/800 x 10

^{-4}x 1/2 = 16/40 =0.4Am^{2}
(ii) W

= 2MB

= 2e = 0.032J

_{θ=0→θ=180}= MB(cosθ_{1}– cosθ_{2})= 2MB

= 2e = 0.032J

**SECTION-D**

**28. (a) Derive an expression for energy stored per unit volume in parallel plate Capacitor.**

**(b) A 10 µF Capacitor is charged by a 30 v d.c. Supply and then connected t across an uncharged 50 µF Capacitor. Calculate the final potential difference across the combination and loss of energy in the process?**

**Ans.**

(a)

A capacitor of capacitance is charged with an external source.

The graphical Variation of charge with applied potential is shown. The work done to charge upto Maximum value Q

_{O}is given by
Area of OABi.e W = 1/2 OB x AB = V

_{o}Q_{o}
= V

_{o}CV_{o}
W = CV

_{o}^{2}= U
As ⇒ u = V

_{0}^{2}Put V_{0 }= E_{0}x d
U =

Energy stored per unit volume =

(b) C

_{1}= 10μF C_{2}= 50μF
V

_{1}= 30V V_{2}= 0
V

_{Com}= ? ΔU = ?
As V

_{Common}= = 5 Volt
ΔU = Loss in energy =

=

= 3.75 x 10

^{-5}J**29. State gauss theorem. Use gauss theorem to obtain the expression for electric field due to linearly charged wire. Sketch the graphical variation of electric field with distance r from wire.**

**Ans.**

**Statement :-**It states that the net flux linked with any closed surface will be 1/∈

_{0 }times the charge enclosed i.e Φ = q/∈

_{0}

**Derivation :-**

According to gauss law

Φ = q/∈

_{0 }- - - - - - - - - (i)**30. Explain briefly, with the help of a labeled diagram the basic principle of working of a.c. generator. In an a.c. generator coil of N turns and area A is rotated at rotation per second in a uniform magnetic field B. Write the expression of the emf produced.**

**Ans.**Principle: when a coil is rotated in a uniform magnetic field with a uniform angular velocity w flux linked with coil changes and emf is induced.

Induced emf e = e

_{0}sinwf
e = NBA w sinwf

Let θ be angle b/w and at anytime ‘t’ = wf , θ = wt

As , let N = Number of turns in the coil

Φ = . for ne turn

= N (.) = NAB cosθ

Induced emf .e = (NABcosθ)

= NAB(sinwt) w

e = NAWBsinwt

e = e

_{0}sinwt
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