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**PHYSICS (Theory)**

**General Instructions**

**You may use the following values of physical constants wherever necessary : c = 3 × 10 ^{8} m/s h = 6.63 × 10^{–34} Js e = 1.6 × 10^{–19} C μ_{0} = 4π × 10^{–7} T m A^{–1} ε_{0} = 8.854 × 10^{–12} C^{2} N^{–1} m^{–2} Mass of electron = 9.1 × 10^{–31} kg Mass of neutron = 1.675 × 10^{–27} kg Mass of proton = 1.673 × 10^{–27} kg Avogadro’s number = 6.023 × 10^{23} per gram mole Boltzmann constant = 1.38 × 10^{–23} JK^{–1}**

**Q1. A point charge +Q is placed at point O as shown in the figure. Is the potential difference V _{A} – V_{B} positive, negative or zero ?**

**(1)**

**Ans**: Positive

**Q2. How does the electric flux due to a point charge enclosed by a spherical Gaussian surface get affected when its radius is increased ?**

**(1)**

**Ans: **Electric flux remains unaffected

**Q3. Write the underlying principle of a moving coil galvanometer.**

**(1)**

**Ans: **A current carrying coil, in the presence of magnetic field, experiences a torque, which produces proportionate deflection.

**[Alternatively**

(deflection) θ α (Torque)]

**Q4. Why are microwaves considered suitable for radar systems used in aircraft navigation ? **

**(1)**

Ans:Due to their short wavelengths, (they are suitable for radar system used in aircraft navigation).

**Q5. Define ‘quality factor’ of resonance in series LCR circuit. What is its SI unit ?**

**(1)**

**Ans: **Quality factor

**[Alternatively]**

Quality factor Q = , Alternatively, It gives the sharpness of the resonance circuit.] It has no unit.

**Q6. Explain the terms (i) Attenuation and (ii) Demodulation used in Communication System.**

**(2)**

Ans:

(i) The loss of strength of a signal while propagating through a medium.

**(1)**

(ii) The process of retrieval of information, from the carrier wave, at the receiver.

**(1)**

**Q7. Plot a graph showing variation of de-Broglie wavelength λ versus 1/√V, where V is accelerating potential for two particles A and B carrying same charge but of masses m _{1}, m_{2} (m_{1} > m_{2}). Which one of the two represents a particle of smaller mass and why ?**

**(2)**

Ans:

**(½ + ½)**

**(½)**

As the charge of two particles is same , therefore

Hence, particle with lower mass ( m_{2}) will have greater slop.

**(½)**

**Q8. A nucleus with mass number A = 240 and BE/A = 7.6 MeV breaks into two fragments each of A = 120 with BE/A = 8.5 MeV. Calculate the released energy.**

**OR**

**Calculate the energy in fusion reaction :**

**(2) **

Ans:Binding energy of nucleus with mass number 240,

= 240 × 7.6 MeV

**(½)**

Binding energy of two fragments

= 2 × 120 × 8.5 MeV

**(½)**

Energy released = 240 (8.5 – 7.6) MeV

= 240 × 0.9

= 216 MeV

**(½)**

**OR**

Total Binding energy of Initial System

= (2.23 + 2.23) MeV

= 4.46 MeV

**(½)**

Binding energy of Final System i.e

= 7.73 MeV

**(½)**

Hence energy released = 7.73 MeV- 4.46 MeV

= 3.27 MeV

**(1)**

**Q9. Two cells of emfs 1.5 V and 2.0 V having internal resistances 0.2 Ω and 0.3 Ω respectively are connected in parallel. Calculate the emf and internal resistance of the equivalent cell.**

**(2)**

Ans:

**(½)**

**(½)**

**(½)**

**(½)**

**Q10. State Brewster’s law.The value of Brewster angle for a transparent medium is different for light of different colours. Give reason.**

**(2)**

**Ans:** When unpolarised light is incident on the surface separating two media, the reflected light gets (completely) polarized only when the reflected light and refracted light become perpendicular to each other.

[ Alternatively

If the student draws the diagram, as shown, and writes as the polarizing angle, award this 1 mark.

If the student just writes award half mark olny.]

**(1)**

The refractive index of denser medium, with respect to rarer medium, is given by

**(½)**

Since Refractive index (μ) of a transparent medium is different for different colours, hence Brewster angle is different for different colours.

**(½)**

**Q11. A charge is distributed uniformly over a ring of radius ‘a’. Obtain an expression for the electric intensity E at a point on the axis of the ring. Hence show that for points at large distances from the ring, it behaves like a point charge.**

**(3)**

Ans;

Net Electric Field at point P =

dE = Electric field due to a small element having charge dq

Let λ = Linear charge density

At large distance i.e. x>>a

This is the Electric field due to a point charge at distance x.

(NOTE: Award two marks for this question, if a student attempts this question but does not give the complete answer)

**Q12. Write three characteristic features in photoelectric effect which cannot be explained on the basis of wave theory of light, but can be explained only using Einstein’s equation.**

**(3)**

**Ans; **The three characteristic features which can’t be explained by wave theory are:

i. Kinetic energy of emitted electrons are found to be independent of intensity of incident light.

**(1)**

ii. Below a certain frequency (threshold) there is no photo-emission.

**(1)**

iii. Spontaneous emission of photo-electrons.

**(1)**

**Q13. (a) Write the expression for the magnetic force acting on a charged particle moving with velocity n in the presence of magnetic field B.**

**(b) A neutron, an electron and an alpha particle moving with equal velocities, enter a uniform magnetic field going into the plane of the paper as shown. Trace their paths in the field and justify your answer.**

**(3)**

**Ans**;

Justification: Direction of force experienced by the particle will be according to the Fleming’s Left hand rule / (any other alternative correct rule.)

**Q14. (i) Define mutual inductance. (ii) A pair of adjacent coils has a mutual inductance of 1.5 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux inkage with the other coil ?**

**(1)**

Ans.(i) Magnetic flux, linked with the secondary coil due to the unit current flowing in the primary coil,

[Alternatively

Induced emf associated with the secondary coil, for a unit rate of change of current in the primary coil . ]

[Also accept the Definition of Mutual Induction, as per the

Hindi translation of the question]

[i.e. the phenomenon of production of induced emf in one coil

due to change in current in neighbouring coil

(ii) Change of flux linkage

**Q15.Two parallel plate capacitors X and Y have the same area of plates and same separation between them. X has air between the plates while Y contains a dielectric medium of e _{r} = 4.**

** **

**(i) Calculate capacitance of each capacitor if equivalent capacitance of the combination is 4 μF. (ii) Calculate the potential difference between the plates of X and Y. (iii) Estimate the ratio of electrostatic energy stored in X and Y.**

**(3)**

Ans;

ii) Total charge Q = CV

= 4μF × 15 V= 60μC

(Also accept any other correct alternative method)

**Q.16Two long straight parallel conductors carry steady current I1 and I2 separated by a distance d. If the currents are flowing in the same irection, show how the magnetic field set up in one produces an attractive force on the other. Obtain the expression for this force. Hence define one ampere.**

**(3)**

Ans.

As shown in Figure, the direction of force on conductor b is attractive

[Alternatively:

[Alternatively:

at a point on wire 2, is along -

on wire 2, due to the , is along -

towards wire1. Hence the force is attractive.

Magnetic field, due to current in conductor a,

The magnitude of force on a length L of conductor b,

One ampere is that steady current which, when maintained in each of the two very long, straight, parallel conductors, placed one meter apart in vacuum, would produce on each of these conductors a force equal to newton per meter of their length.

**Q17. How are em waves produced by oscillating charges ? Draw a sketch of linearly polarized em waves propagating in the Z-direction. Indicate the directions of the oscillating electric and magnetic fields.**

**OR**

**Write Maxwell’s generalization of Ampere’s Circuital Law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is **

**where is the electric flux produced during charging of the capacitor plates**.

**(3)**

Ans.

;A charge oscillating with some frequency, produces an oscillating electric field in space, which in turn produces an oscillating magnetic field perpendicular to the electric field, this process goes on repeating , producing em waves in space perpendicular to both the fields.

Directions of and are perpendicular to each other and also perpendicular to direction of propagation of em waves.

OR

Ampere’s circuital law is given by as .

But for a circuit containing capacitor, during its charging / discharging the current within the plates of the capacitor varies, (producing displacement current Therefore, the above equation, as generalized by Maxwell, is given as

During the process of charging of capacitor, electric flux between the plates of capacitor changes with time, which produces the current within the plates of capacitor. This current, being proportional to , we have

**Q18. (a) Explain any two factors which justify the need of modulating a low frequency signal.**

**(b) Write two advantages of frequency modulation over amplitude modulation.**

**(3)**

Ans; a) A low frequency signal is modulated for the following purposes:

(i) It reduces the wavelength of transmitted signal, and the minimum height of antenna for effective communication is .Therefore

height of antenna becomes practically achievable.

(ii) Power radiated into the space by an antenna is inversely proportional to λ^{2} . Therefore, the power radiated into the space increases and signal can travel larger distance.

(Give full credit of this part for any other correct answer)

b)

(i) High efficiency

(ii) Less noise

(iii) Maximum use of transmitted power (any two)

**Q19. (i) Write the functions of three segments of a transistor. (ii) Draw the circuit diagram for studying the input and output characteristics of n-p-n transistor in common emitter configuration. Using the circuit, explain how input, output characteristics are obtained.**

**(3)**

**Ans;** (i) Emitter : Supplies the large number of majority charge carriers for the flow of current through the transistor.

Base : Controls the movement of charge carriers coming from emitter region

Collector: Collects a major portion of the majority carriers supplied by the emitter.

**(NOTE: Also accept the following explanation of these parts of the transistor as asked in Hindi translation)**

Emitter: Heavily doped and of moderate size.

Base: Central region, thin and lightly doped.

Collector: Moderately doped and large sized.

(ii)

Input characteristics are obtained by recording the values of base curren t , for different values of at constant

Output characteristics are obtained by recording the values of for different values of at constant

[Alternatively

Also accept input/output characteristic curves for this part of the question.]

**Q20. (a) Calculate the distance of an object of height h from a concave mirror of radius of curvature 20 cm, so as to obtain a real image of magnification 2. Find the location of image also. (b) Using mirror formula, explain why does a convex mirror always produce a virtual image**

**(3)**

Ans; a) Given R = -20 cm, and magnification m= -2

Focal length of the mirror

Magnification (m) =

Using mirror formula

b)

Using sign convention, for convex mirror, we have

From the formula

∵ f is positive and u is negative,

is always positive, hence image is always virtual.

**Q21. (i) State Bohr’s quantization condition for defining stationary orbits. How does de Broglie hypothesis explain the stationary orbits ? (ii) Find the relation between the three wavelengths λ _{1}, λ_{2} and λ_{3} from the energy level diagram shown below.**

**(3)**

Ans; (i) Only those orbits are stable for which the angular momentum, of revolving electron, is an integral multiple of

[Alternatively

i.e. angular momentum of orbiting electron is quantised.]

According to de Broglie hypothesis

Linear momentum

And for circular orbit L =r_{n}p where ‘r_{n} ’ is the radius of quantized orbits.

Circumference of permitted orbits are integral multiples of the wavelength λ

**Q23. Draw a schematic ray diagram of reflecting telescope showing how rays coming from a distant object are received at the eye-piece. Write its two important advantages over a refracting telescope.**

**(3)**

**Ans;**

(i) Large gathering power

(ii) Large magnifying power

(iii) No chromatic aberration

(iv) Spherical aberration is also removed

(v) Easy mechanical support

(vi) Large resolving power

(Any Two)

**Q23. Meeta’s father was driving her to the school. At the traffic signal she noticed that each traffic light was made of many tiny lights instead of a single bulb. When Meeta asked this question to her father, he explained the reason for this.Answer the following questions based on above information : (i) What were the values displayed by Meeta and her father ? (ii) What answer did Meeta’s father give ? (iii) What are the tiny lights in traffic signals called and how do these operate ?**

**(4)**

**Ans.**(i) Values displayed by Meeta:

Inquisitive/ Keen Observer/ Scientific temperament/ (Any other value.)

Values displayed by Father:

Encouraging/ Supportive /(Any other value)

(ii) Meeta’s father explained that the traffic light is made up of tiny bulbs

called light emitting diodes (LED)

(Also accept other relevant answers)

(iii)Light emitting diode

These diodes (LED’s) operate under forward bias, due to which the majority charge carriers are sent from these majority zones to minority zones. Hence recombination occur near the junction boundary, which eleases energy in the form of photons of light.

**Q24. (i) An a.c. source of voltage V = V _{0} sin wt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expressions for impedance of the circuit and phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called ? (ii) In a series LR circuit X_{L} = R and power factor of the circuit is P_{1}. When capacitor with capacitance C such that X_{L }= X_{C} is put in series, the power factor becomes P_{2}. Calculate P_{1}/P_{2}.**

**OR**

**(i) Write the function of a transformer. State its principle of working with the help of a diagram. Mention various energy losses in this device. (ii) The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 220 V and 1100 W. Calculate (a) number of turns in secondary (b) current in primary (c) voltage across secondary (d) current in secondary**

**(e) power in secondary**

**(5)**

**Ans:**

From Figure

From Figure

Condition for current and voltage are in phase :

Circuit is called Resonant circuit.

(ii) Power factor

Power factor when capacitor C of Reactance is put in

series in the circuit

(i) Conversion of ac of low voltage into ac of high voltage & vice versa

Mutual induction: When alternating voltage is applied to primary windings, emf is induced in the secondary windings.

(Any one of the above diagram)

Energy losses:

a. Leakage of magnetic flux

b. Eddy currents

c. Hysterisis loss

d. Copper loss

(Any two)

(ii)

*N*_{p}= 100

Transformation ratio= 100

a) Number of turns in secondary coil

*N*_{s}= 100 x 100 = 10000

b) Input Power = Input voltage x current in primary

1100 = 220 xl_{p}

= 5A

e) Power in secondary = Power in Primary

=1100 W

**Q25. (i) In Young’s double slit experiment, deduce the condition for (a) constructive, and (b) destructive interference at a point on the screen. Draw a graph showing variation of intensity in the interference pattern against position ‘x’ on the screen. (ii) Compare the interference pattern observed in Young’s double slit experiment with single slit diffraction pattern, pointing out three distinguishing features.**

**OR**

**(i) Plot a graph to show variation of the angle of deviation as a function of angle of incidence for light passing through a prism. Derive an expression for refractive index of the prism in terms of angle of minimum deviation and angle of prism. (ii) What is dispersion of light ? What is its cause ? (iii) A ray of light incident normally on one face of a right isosceles prism is totally reflected as shown in fig. What must be the minimum value of refractive index of glass ? Give relevant calculations.**

**(5)**

**Ans.**

(i)

From figure

Path difference

For x, d << D

For constructive interference

For destructive interference

n = 0, 1, 2 .....

(ii)

(a) The Interference pattern has number of equally spaced bright and dark bands, while in the diffraction pattern the width of the centralm maximum is twice the width of other maxima.

(b) In Interference all bright fringes are of equal intensity, whereas in the diffraction pattern the intensity falls as order of maxima increases.

(c) In Interference pattern, maxima occurs at an angle , where a is the slit width, whereas in diffraction pattern, at the same angle λ/a', first minimum occurs. (Here ‘a’ is the size of the slit)

(Any other distinguishing feature)

From figure which implies r_{1}=r_{2}

(ii) The phenomenon of splitting of white light into its constituent

colours.

Cause: Refractive index of the material is different for different colours According to the equation, where A is the angle of prism, different colours will deviate through different amount.

For total internal reflection,

Hence, the minimum value of refractive index must be

**Q26.(i) Define the term drift velocity. (ii) On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. On what factors does resistivity of a conductor depend ? (iii) Why alloys like constantan and manganin are used for making standard resistors ? OR (i) State the principle of working of a potentiometer. (ii) In the following potentiometer circuit AB is a uniform wire of length 1 m and resistance 10 W. Calculate the potential gradient along the wire and balance length AO ( = l).**

**(5)**

Ans. i) Average velocity acquired by the electrons in the conductor in the presence of external electric field.

[Alternatively:

We have E = where V is potential difference across the length of

the conductor

Also, R = -----------(ii)

Comparing (i) and (ii)

Resistivity of the material of a conductor depends on the relaxation time, i.e., temperature and the number density of electrons.

iii) Because constantan and manganin show very weak dependence of resistivity on temperature

**OR**

i) When constant current flows through a conductor of uniform area of cross section, the potential difference, across a length l of the wire, is directly proportional to that length of the wire.

(Provided current and area are constant]

ii) Current flowing in the potentiometer wire

∴ Potential difference across the two ends of the wire

Hence potential gradient

Current flowing in the circuit containing experimental cell,

Hence, potential difference across length AO of the wire

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