CBSE Class 12

Questions :
SECTION : A

Question 1.
In which orientation, a dipole placed in a uniform electric field is in
(i) stable,
(ii) unstable equilibrium?

Question 2.
Which part of electromagnetic spectrum has largest penetrating power?

Question 3.
A plot of magnetic flux (Φ) versus current (I) is shown in the figure  for two inductors A and B. Which of the two has larger value of self inductance.

Question 4.
Figure shows three point charges, + 2q, -q and +3q. Two charges + 2q and -q are enclosed within a surface ‘S’. What is the electric flux due to this configuration through the surface ‘S’?

Question 5.
A glass lens of refractive index 1.45 disappears  when immersed in a liquid. What is the value of refractive index of the liquid.

SECTION : B

Question 6.
What is the ratio of radii of the orbits corresponding to first excited state and ground state in a hydrogen atom?

Question 7.
A wire of resistance 8R,is bent in the form of a circle. What is the effective resistance between the ends of a diameter AB?

Question 8.
State the conditions for the phenomenon of total internal reflection to occur.

Question 9.
Explain the function of a repeater in a communication system.

Question 10.
(i) Write two characteristics of a material used for making permanent magnets.
(ii) Why is core of an electromagnet made of ferromagnetic materials?

OR

Draw magnetic field lines when a
(i) diamagnetic,
(ii) paramagnetic substance is placed in an external magnetic field. Which magnetic property distinguishes this behaviour of the field lines due to the two substances?

SECTION : C

Question 11.
Draw a circuit diagram of an illuminated photodiode in reverse bias. How is photodiode used to measure light intensity?

Question 12.
An electric lamp having coil of negligible inductance connected in series with a capacitor and an AC source is glowing with certain brightness. How does the brightness of the lamp change on reducing the
(i) capacitance, and
(ii) the frequency? Justify your answer.

Question 13.
Arrange the following electromagnetic radiations in ascending order of their frequencies :

1. Microwave
2. Radio wave
3. X-rays
4. Gamma rays

Write two uses of any one of these.

Question 14.
The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm. If focal length of the lens is 12 cm, find the refractive index of the material of the lens.

Question 15.
An electron is accelerated through a potential difference of 100 volts. What is the de-Broglie wavelength associated with it? To which part of the electromagnetic spectrum does this value of wavelength correspond?

Question 16.
A heavy nucleus X of mass number 240 and binding energy per nucleon 7.6 MeV is split into two fragments Y and Z of mass numbers 110 and 130. The binding energy of nucleons in Y and Z is 8.5 MeV per nucleon. Calculate the energy Q released per fission in MeV.

Question 17.

1. The bluish colour predominates in clear sky.
2. Violet colour is seen at the bottom of the spectrum when white light is dispersed by a prism. State reasons to explain these observations.

Question 18.
Plot a graph showing the variation of stopping potential with the frequency of incident radiation for two different photosensitive materials having work functions W₁ and W₂ (W₁ > W₂).
On what factors does the
(i) slope and
(ii) intercept of the lines depend?

Question 19.
A parallel plate capacitor is charged by a battery. After sometime the battery is disconnected and a dielectric slab with its thickness equal to the plate separation is inserted between the plates. How will
(i) the capacitance of the capacitor,
(ii) potential difference between the plates and
(iii) the energy stored in the capacitor be affected?
Justify your answer in each case.

Question 20.
Write the principle of working of a potentiometer. Describe briefly, with the help of a circuit diagram, how a potentiometer is used to determine the internal resistance of a given cell.

Question 21.

Write the expression for the magnetic moment ( m ) due to a planar square loop of side l carrying a steady current I in a vector form. In the given figure this loop is placed in a horizontal plane near a long straight conductor carrying a steady current I₁ at a distancel as shown.
Given reasons to explain that the loop will experience a net force but no torque. Write the expression for this force acting on the loop.

Question 22.
(a) Depict the equipotential surfaces for a system of two identical positive point charges placed at a distance d apart.
(b)

SECTION : E

Question 23.
For the last four months, the English teacher of Komal had erratic body movement, lack of coordination etc in her daily activities. Occasionally she had headache also. Komal suggested to get a MRI and other complete medical check up. After that she was diagnosed a brain tumour.

1. What values are displayed by Komal?
2. How can radioisotopes help a doctor to diagnose brain tumour?

Question 24.
Describe briefly, with the help of a labelled diagram, the basic elements of an A.C. generator. State its underlying principle. Show diagrammatically how an alternating emf is generated by a loop of wire rotating in a magnetic field. Write the expression for the instantaneous value of the emf induced in the rotating loop

OR

A series LCR circuit is connected to an ac source having voltage V = V_m sin cot. Derive the expression for the instantaneous current T and its phase relationship to the applied voltage. Obtain the condition for resonance to occur. Define ‘power factor’. Sate the conditions under which it is
(i) maximum and
(ii) minimum.

Question 25.
State Huygens principle. Show, with the help of a suitable diagram, how this principle is used to obtain the diffraction pattern by a single slit. Draw a plot of intensity distribution and explain clearly why the secondary maxima become weaker with increasing order (n) of the secondary maxima.

OR

Draw a ray diagram to show the working of a compound microscope. Deduce an expression for the total magnification when the final image is formed at the near point. In a compound microscope, an object is placed at a distance of 1.5 cm from the objective of focal length 1.25 cm. If the eye-piece has a focal length of 5 cm and the final image is formed at the near point, estimate the magnifying power of the microscope.

Question 26.
(a) Explain the formation of depletion layer and potential barrier in a p-n junction output.
(b) In the figure given below the input waveform is converted into the output waveform by a device ‘X’. Name the device and draw its circuit diagram.

(c) Identify the logic gate represented by the circuit as shown and write its truth table.

OR

(a) Draw the circuit diagram of a common emitter transistor as an amplifier, define current gain and voltage gain of it.
(b) Distinguish between a conductor, a semiconductor and an insulator on the basis of energy band diagrams.

Answer 1.
(i) The dipole is in stable equilibrium when electric dipole is in the direction of electric field (θ = 0°).
(ii) The dipole is in unstable equilibrium when electric dipole is in the opposite direction of electric field (θ = 180°).

Answer 2.
Gamma rays.

Answer 3.
Line A.

Answer 4.
Total charge within a surface S +2q + (-q) = +q
∴ Electric flux Φ = q/ε₀

Answer 5.
The value of refractive index of the liquid is 1.45.

SECTION : B

Answer 6.
Since r ∝ n²
For ground state, n = 1
For first state , n = 2

Answer 7.
Resistance of each semi-circular part of circle is 4R.
∴ R₁ = R₂ = 4R
Since two resistors are in parallel.
∴  Effective resistance (R_e) is

Answer 8.
(i) Light should travel from denser to rarer medium
(ii) Angle of incidence in denser medium should be greater than the critical angle for the pair of media in contact.

Answer 9.
A repeater, picks up the signal from the transmitter, amplifies and retransmits it to the receiver sometimes with a change in carrier frequency. Repeaters are used to extend the range of a communication system.

Answer 10.
(i) Two characteristics of a material used for making permanent magnets are:

1. High Coercivity
2. High Retentivity

(ii) Core of an electromagnet made of ferromagnetic materials because of high permeability and low retentivity.

OR

(i) Behaviour of magnetic field lines when a diamagnetic substance is placed in an external magnetic field.

(ii) Behaviour of magnetic field lines when a paramagnetic substance is placed in an external magnetic field.

SECTION : C

Answer 11.
Circuit diagram of an illuminated photodiode :

Explanation :
The magnitude of the photocurrent depends on the intensity of incident light (photocurrent is proportional to incident light intensity). Thus, photodiode can be used to measure light intensity.

Answer 12.

When AC source is connected, the capacitor offers capacitive reactance

The current flows in the circuit and the lamp glows.

1. On reducing the capacitance C, X_c increases. Therefore the brightness of the bulb decreases.
2. On reducing the frequency v, X_c increases. Therefore, the brightness of the bulb decrease.

Answer 13.
Radio wave <Microwaves < X-rays <Gamma rays Uses of microwaves are :

1. Microwaves are used in radar systems for aircraft navigations.
2. Microwaves are used in microwave ovens for cooking purposes.

Answer 14.
Here R₁ = 10 cm, R₂ = -15 cm,  f = 12 cm,   μ = ?
Using the lens formula,

Answer 15.
Here V = 100 volts.
The de-Broglie wavelength λ is

Answer 16.
We have
²⁴⁰X = ¹¹⁰Y + ¹³⁰Z + Energy Q
Binding energy for X = 7.6 MeV
Binding energy for two fragments Y and Z = 8.5 MeV
∴  Gain in binding energy for the nucleon = 8.5 – 7.6 = 0.9 MeV
Hence total gain in binding energy per fissioning nucleus or energy Q released per fission = 240 x 0.9 = 216 MeV

Answer 17.

1. As per Rayleigh’s law (scattering ∝ 1/λ⁴), lights of shorter wavelengths scattered more by an atmospheric particles. This results in a dominance of bluish colour in the scattered light.
2. In the visible spectrum, violet light having its shortest wavelength, has the highest refractive index. Hence, it is deviated the most.

Answer 18.

The graph is showing the variation of stopping potential (V₀) with the frequency of incident radiation (v₀) for two different photosensitive materials having work functions W₁ and W₂ (W₁ > W₂).

Answer 19.
As battery in disconnected, charge will remain

Becomes 1/K times therefore, energy stored becomes 1/K times.

Answer 20.
Working principle :
When constant current flows through a wire of uniform cross-section, then potential difference across the wire is directly proportional to the length of wire. With k₂ open, balance is obtained at length l₁ (AN₁).

Then ε = Φ (Φ = potential gradient)                                                                                     ….(1)
When key K₂ is closed, the cell sends a current (I) through the resistance box (R.B.). If V is the terminal potential difference of the cell and balance is obtained at length l₂ (AN₂).

Answer 21.

Answer 22.

(a) Equipotential surfaces of two identical positive point charges placed at a distance ‘d’ apart.

By the superposition principal for fields, we add up the work done on q₂ against the two fields.

OR

SECTION : E

Answer 23.

1. Keen observer, helpful, responsible and concerned.
2. The doctor can retrace and observe the difference between the movement of an appropriate isotope through a normal brain and a brain having tumour in it.

Answer 24.
It consists of a coil mounted on a rotor shaft. The axis of rotation of the coil is perpendicular to the direction of the magnetic field. The axis of rotation of the coil is mechanically rotated in the uniform magnetic field by some external means. The ends of the coil are connected to an external circuit by means of slip rings and brushes.

Underlying Principle :
As the coil rotates in a magnetic field B, the effective area of loop (the face perpendicular to the field) which is A cos θ, where θ is the angle between area (A) and magnetic field (B) changes continuously. Hence, magnetic flux linked with the coil keeps on changing with time and an induced emf is produced.
The instantaneous value of the emf is e = NBA ω sin ωt

OR

(i) Power factor is minimum when cos Φ = 0 = 1
i.e., when R = Z or X_L = X_c
(ii) Power factor is minimum when cosΦ = 0
i.e., when R = 0

Answer 25.
Huygens principle: Each point of wavefront is the source of a secondary disturbance and the wavelets emanating from these points spread out in all directions with the speed of the wave. The common tangent/forward envelope, to all these secondary wavelets gives the new wavefront at later time.

Application to diffraction pattern :
All the points of incoming wavefront (parallel to the plane of slit) are in phase with plane of slit. However, the contributions of the secondary wavelets from different points, at any point, on the screen. Total contribution at any point, may add up to give a maxima or minima dependent on the phase differences.

The central point is a maxima as the contribution of all secondary wavelet pairs are in phase here. Consider a next point on the screen where an angle θ = 3λ/2a. Divide the slit into three equal parts. Here the first two-thirds of the slit can be divided into two halves which have a λ/2 path difference. The contributions of these two halves cancel. Only the remaining one-third of the slit contributes to the intensity at a point between the two minima. Hence, this will be much weaker than the central maximum (where the entire slit contributes in phase). We can similarly show that there are maxima at θ = (n + 1/2) λ/a with n = 2, 3, etc. These become weaker with increasing n, since only one-fifth, one-seventh, etc. of the slit contributes in these cases.

OR

Ray diagram :

Expression for total magnification :
Magnification due to the objective

Magnification m_e, due to eyepiece, (when the final image is formed at the near point)

Answer 26.
(a) Depletion region :
Due to the concentration gradient across p-side and n-side, holes diffuse from p-side to n-side (p → n) and electrons diffuse from n-side top-side (n → p). As the electrons diffuse from n → p, a layer of positive charge (or positive space-charge region) is developed on n-side of the junction. Similarly as the holes diffuse, a layer of negative charge (or negative space-charge region) is developed on the p-side of the junction. The space – charge region on either side of the junction together is known as depletion region.
Barrier potential :
The loss of electrons from the n-region and the gain of electron by the n-region cause a difference of potential across the junction of the two regions. The polarity of this potential is such as to oppose further flow of carriers.

(b) Full-wave rectifier :

(c) AND gate :

OR

(a) Common Emitter Amplifier Current and Voltage Gain :
The ratio between collector current (change in collector current) and base current (change in base current) is equal to current gain and voltage gain is given by the product of current gain and ratio of output resistance of the collector circuit to the input resistance of base circuit.

(b)

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Questions :
SECTION : A

Question 1.
If the angle between the pass axis of polarizer and the analyser is 45°, write the ratio of the ‘ intensities of original light and the transmitted light after passing through the analyser.

Question 2.
You are given following three lenses. Which two lenses will you use as an eyepiece and as an objective to construct an astronomical telescope?

Question 3.
Write the following electromagnetic waves in ascending order with respect to their frequencies: X-rays, microwaves, UV rays and radio waves.

Question 4.
What is sky wave propagation?

Question 5.
Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid. Why?

SECTION : B

Question 6.
The figure shows a plot of three curves a, b, c, showing the variation of photocurrent v/s collector plate potential for three different intensities I₁ I₂ and I₃ having frequencies v₁ v₂ and v₃ respectively incident on a photosensitive surface. Point out the two curve for which the incident radiations have same frequency but different intensities.

Question 7.
What type of wavefront will emerge from a
(i) point source, and
(ii) distant light source?

Question 8.
Two nuclei have mass numbers in the ratio 1 : 2. What is the ratio of their nuclear densities?

Question 9.
A cell of emf ‘E’ and internal resistance ‘V’ is connected across a variable resistor ‘R’ Plot a graph showing the variation of terminal potential ‘V’ with resistance R. Predict from the graph the condition under which ‘V’ becomes equal to ‘E’.

Question 10.
(i) Can two equipotential surfaces intersect with each other? Give reasons.
(ii) Two charges -q and +q are located at points A (0,0, -a) and B (0,0, +a) respectively. How much work is done in moving a test charge from point P (7, 0, 0) to Q (-3, 0, 0)?

SECTION : C

Question 11.
A radioactive nucleus ‘A’ undergoes a series of decays according to the following scheme :

The mass number and atomic number of A are 180 and 72 respectively. What are these numbers for A_{4 ?}

Question 12.
An electron and a proton are accelerated through the same potential. Which one the two has
(i) greater value of de Broglie wavelength associated with it and
(ii) less momentum? Justify your answer.

Question 13.
By what percentage will the transmission ranges of TV tower be affected when the height of the tower is increased by 21 %?

Question 14.
Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.

Question 15.
In a single slit diffraction experiment, when tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why? State two points of difference between the interference pattern obtained in Young’s double slit experiment and the diffraction pattern due to a single slit.

Question 16.
A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s law, derive an expression for an electric field at a point outside the shell. Draw a graph of electric field E(r) with distance r from the centre of the shell for 0 ≤ r ≤ ∝.

Question 17.
Why are high frequency carrier waves used for transmission?

OR

What is meant by term modulation’? Draw a block diagram of a simple modulator for obtaining an AM signal.

Question 18.
Three identical capacitors C₁, C₂ and C₃ of capacitance 6 μF each are connected to a 12 V battery as shown :

Find
(i) charge on each capacitor
(ii) equivalent capacitance of the network
(iii) energy stored in the network of capacitors

Question 19.
(a) The energy levels of an atom are as shown below. Which of them will result in the transition of a photon of wavelength 275 nm?

(b) Which transition corresponds to emission of radiation of maximum wavelength?

Question 20.
(a) Define self inductance. Write its S.I. units.
(b) Derive an expression for self inductance of a long solenoid of length l, cross-sectional area A having N number of turns.

Question 21.
The figure shows experimental set up of a meter bridge. When the two unknown resistances X and Y are inserted, the null point D is obtained 40 cm from the end A. When a resistance of 10Ω is connected in series with X, the null point shifts by 10 cm.Find the position of the null point when the 10Ω resistance is instead connected in series with resistance ‘Y’. Determine the values of the resistances X and Y.

Question 22.
Derive the expression for force per unit length between two long straight parallel current carrying conductors. Hence define one ampere.

OR

Explain the principle and working of a cyclotron with the help of a schematic diagram. Write the expression for cyclotron frequency.

SECTION : D

Questin 23.
Shivani was interested to gift something to her mother on her birthday. But she could not decide what to give her mother.She asked her brother. Her brother advised to gift a microwave oven to the mother. But their father said it is a wastage of money. They convinced him for a microwave and ultimately her father was agreed for microwave.

1. hat qualities Shivani and her brother possess?
2. State how a microwave oven works?

SECTION : E

Question 24.
(i) Draw a circuit diagram to study the input and output characteristics of an n-p-n transistor in its common emitter configuration. Draw the typical input and output characteristics.
(ii) Explain, with the help of a circuit diagram, the working of n-p-n transistor as a common emitter amplifier.

OR

How is a zener diode fabricated so as to make it a special purpose diode? Draw I-V characteristics of zener diode and explain the significance of breakdown voltage. Explain briefly, with the help of a circuit diagram, how a p-n junction diode works as a half wave rectifier

Question 25.
Trace the rays of light showing the formation of an image due to a point object placed on the axis of a spherical surface separating the two media of refractive indices n₁ and n₂. Establish the relation between the distances of the object, the image and the radius of curvature from the central point of the spherical surface. Hence derive the expression of the lens makers formula.

OR

Draw the labelled ray diagram for the formation of image by a compound microscope. Derive the expression for the total magnification of a compound microscope. Explain why both the objective and the eyepiece of a compound microscope must have short focal lengths.

Question 26.
(a) Derive an expression for the average power consumed in a series LCR circuit connected to a.c. source in which the phase difference between the voltage and the current in the circuit is Φ.
(b) Define the quality factor in an a.c. circuit. Why should the quality factor have high value in receiving circuits? Name the factors on which it depends.

OR

(i) Derive the relationship between the peak and the rms value of current in an a.c. circuit.
(ii) Describe briefly, with the help of labelled diagram, working of a step-up transformer. A step-up transformer converts a low voltage into high voltage. Does it not violate the principle of conservation of energy? Explain.

Answer 7.
(i) For a point source, wavefront will be spherical,
(ii) For a distant light source, the wavefronts will be plane.

Answer 23.

1. (a) Caring, love, affection and respect towards her parents.
   (b) General awareness about scientific gadgets and their utilities.
2. In microwave oven the frequency of microwaves is selected to match the resonant frequency of water molecules so that energy from the waves is transferred efficiently to the kinetic energy of molecules. In this way temperature of any food item containing water increases.

SECTION : E

Answer 24.
(i)

Input characteristics :

Output characteristics :

(ii) The input (base-emitter) circuit is forward and the output (collector-emitter) circuit is reversed biased. When no a.c. signal is applied, the potential difference Vcc between the collector and emitter is given by    V_cc = V_ce +I_c R_L
When an a.c. signal is fed to the input circuit, the forward bias increase during  the positive half cycle of the input. This result in increase in I_c and decrease inV_cc. Thus during the positive half cycle of the input, the collector becomes less positive.

During the negative half cycle of the input, the forward bias is decreased resulting in decrease in I_E and hence I_c. Thus V_cc would increase making the collector more positive. Hence in a common-emitter amplifier, the output voltage is 180° out of phase with the input voltage.

• Input signal voltage V_in = I_BR_in
• Output signal voltage V_out = I_CR_L
  
• Voltage gain (A_v) of the amplifier is

OR

Zener diode is fabricated such that both the p-type and the n-type are highly doped. This makes the depletion region thin. When an electric field is applied, a high electric field appears across the thin depletion region. When the electric field becomes very high, it knocks off electrons from the host atoms to create a large number of electrons. This results in a large value of current inside the circuit.

Zener has a sharp breakdown voltage and this property of zener is used for voltage regulation.

An a.c. current has a positive half cycle and a negative half cycle. A p-n junction allows current to pass only in one direction and that is when it is forward biased. When a positive half-cycle occurs, the p-side has a lower potential. Therefore, the diode is now forward biased and therefore, conducts and this positive cycle is available for the load. When a negative half cycle occurs, the «-side has a higher potential than the p-side. Hence, the diode is now reverse biased and thus, does not conduct. As a result, this negative half cycle does not conduct. Therefore, it does not appear at the load and is cut-off. We obtain a waveform, which has only positive half cycles and therefore it is called halfwave rectifier.

Answer 25.
In the given figure, image is I and object is denoted as O. The centre of curvature is X. The rays are incident from a medium of refractive index n₁ to another of refractive index n₂ We consider NM to-be perpendicular to the principal axis.

For a thin lens , BI₁  = DI₁
Adding  (ii) and (iii) , we obtain

Answer 26.
(a) The rate of dissipation of energy in an electrical circuit is called the ‘power’. It is equal to the product of the emf and the current. The power of an alternating-current depends upon the phase difference between the emf and the current. The instantaneous values of the emf and the current in an a.c. circuit are given by

(b) Quality Factor :
It is defined as the ratio of the voltage drop across inductor or capacitor to the applied voltage.

The quality factor has high value in receiving circuits in order to get a sharp gain for the desired channel frequency. The quality factor depends on the following values :

• Inductance
• Resistance
• Capacitance

OR

(a) The instantaneous power dissipated in the resistor is


No, a step-up transformer steps up the voltage while steps down the current. So input and output power remains same, provided there is no loss. Hence, there is no violation of principle of conservation of energy.