Murali

CBSE Sample Papers for Class 12 Physics Paper 3 are part of CBSE Sample Papers for Class 12 Physics. Here we have given CBSE Sample Papers for Class 12 Physics Paper 3.

CBSE Sample Papers for Class 12 Physics Paper 3

Time Allowed : 3 Hours

Max. Marks : 70

General Instructions 

• All questions are compulsory. There are 26 questions in all.
• This question paper has five sections: Section A, Section B, Section C, Section D and Section E.
• Section A contains five questions of 1 mark each. Section B contains five questions of 2 marks each. Section C contains twelve questions of 3 marks each. Section D contains one value based question of 4 marks and Section E contains three questions of 5 marks each.
• There is no overall choice. However, an internal choice has been provided in 1 question of 2 marks, 1 question of 3 marks and all the 3 questions of 5 marks weightage. You have to attempt only 1 of the choices in such questions.
• You may use the following values of physical constants wherever necessary :

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.

 Answers :

SECTION : A 

Answer 1.

Answer 2.
For constructing an astronomical telescope, the objective should have the maximum diameter. Of the three lenses given, L₁ has the maximum diameter so, use lens L₁ as an objective. The eyepiece should have the highest power for better magnification. Therefore, we use lens L₃ as an eyepiece.

Answer 3.
The given electromagnetic waves can be arranged in ascending order with respect to their frequencies as :
Radio waves < Microwaves < UV rays < X-rays

Answer 4.
The type of propagation in which radio waves are transmitted towards the sky and are reflected by the ionosphere towards the desired location on earth is called sky wave propagation.

Answer 5.
Magnetic field lines form closed loops around a current – carrying wire. The geometry of a straight solenoid is such that magnetic field lines cannot loop around circular wires without spilling over to the outside of the solenoid. The geometry of a toroid is such that magnetic field lines can loop around electric wires without spilling over to the outside. Hence, magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid.

SECTION : B

Answer 6.

The stopping potential increases with increasing frequency of radiations. Thus curves a and b have the same frequency but different intensities.

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

Answer 8.
Nuclear density is independent of mass number. Hence, both the atoms have the same nuclear density.
i.e.,  d₁ : d₂ = 1 : 1

Answer 9.

V becomes equal to E when no current flows through the circuit.

Hence, can say that when resistance increases from R = 0 to R = ∝ then V_T increases from minimum to maximum and current decreases from
maximum to minimum value.

Answer 10.
(i) Two equipotential surfaces cannot intersect with each other because when they will intersect,then at a point the electric field will have two directions, which is not possible.
(ii) Potential at P (7, 0, 0)

SECTION : C

Answer 11.

∴ The mass number of A₄ = 172 and the atomic number of A₄= 69

Answer 12.
(i) The de Broglie wavelength associated with potential V is

Answer 13.

Answer 14.
If there are N electrons and the velocity of the i^th electron at a given time is v_i where, i = (1, 2, 3,…N), then

For all the electrons in the conductor, average value of v. is zero. The average of v_t is v_d or drift velocity. This is the average velocity experienced by an electron in an external electric field. There is no fixed time after which each collision occurs. Therefore, we take the average time after which one collision takes place by an electron.
Let this time, also known as relaxation time, be t. Substituting this in equation (1)

Then, Negative sign shows that electrons drift opposite to the applied field.

Answer 15.
A bright spot is observed when a tiny circular object is placed in the path of light from a distant source in a single slit diffraction experiment because light rays flare into the shadow region of the circular object as they pass the edge of the tiny circular object. The light from all the edges of the tiny circular object are in phase with each other. Thus they form a bright spot at the centre of the shadow of the tiny circular object. The two differences between the interference patterns obtained in Young’s double slit experiment and the diffraction pattern due to a single slit are as follows: The fringes in the interference pattern obtained from diffraction are of varying width, while in case of interference, all are of the same width. The bright fringes in the interference pattern obtained from diffraction have a central maximum followed by fringes of decreasing intensity, whereas in case of interference, all the bright fringes are of equal intensity.

Answer 16.
According to Gauss law,

Where, q is the point charge,
E is electric field due to the point charge,
dA is a small area on the Gaussian surface at any distance,
e₀ is the proportionally constant.
For a spherical shell at distance r from the point charge, the integral § dA is merely the sum of all differential of dA on the sphere.
Therefore,

Therefore, for a thin conducting spherical shell of radius R and charge Q, spread uniformly over its surface, the electric field at any point outside the shell is


The graph of electric field E(r) with distance r from the centre of the shell for 0 ≤ r ≤ ∝.

Answer 17.
For transmitting a signal, the antenna should have a size comparable to the wavelength of the signal (atleast λ/4 in dimension), where λ is the wavelength. If the frequency of the signal is small, then its wavelength becomes very large and it is impractical to make those large antennas for the corresponding large wavelengths. For higher frequencies, wavelength is smaller, which is the reason why high frequency carrier waves are used for transmission.

OR

The process of superimposing information containing in a low frequency signal on a high frequency signal is called modulartion

Answer 18.
Existing diagram can be redrawn as follows :

Answer 19.
(a) Energy transitions for A, B, C and D are :


(b)

For maximum wavelength, energy transition should be minimum. A undergoes minimum energy transition.
A = 2 eV
Thus, photon in A will have the maximum wavelength.

Answer 20.
(a) The phenomenon in which emf is induced in a single isolated coil due to change of flux through the coil by means of varying the current through the same coil is called self inductance. S.I. unit of inductance is henry (H).
(b) Magnetic field B inside a solenoid carrying a current i is B = μ₀ n i
Let n be the number of turns per unit length.

Answer 21.
For meter bridge :

Answer 22.

1 ampere is the value of that steady current which when maintained in each of the two very long, straight, parallel conductors of negligible cross-section and placed one metre apart in vacuum, would produce on each of these conductors a force equal to 2 x 10^-7 Newton per metre of length.

OR

Cyclotron is a machine used to accelerate charged particles or ions to high energies. It uses both electrical and magnetic fields in combination to increase the speed of the charged particles. The particles move in two semi-circular containers D₁ and D₂, called Dees. Inside the metal box, the charged particle is shielded from external electric fields. When the particle moves from one dee to another, electric field is acted on the particle. The sign of the electric field is changed alternately, in tune with the circular motion of the particle. Hence, the particle is always accelerated by the electric field. As the energy of the particle increases, the radius of the circular path increases.


The above expression is the expression for cyclotron frequency. The oscillator applies an ac voltage across the dees and this voltage must have a frequency equal to that of cyclotron frequency.

SECTION : D

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.

We hope the CBSE Sample Papers for Class 12 Physics Paper 2 help you. If you have any query regarding CBSE Sample Papers for Class 12 Physics Paper 2, drop a comment below and we will get back to you at the earliest.   

CBSE Sample Papers for Class 12 Physics Paper 1 are part of CBSE Sample Papers for Class 12 Physics. Here we have given CBSE Sample Papers for Class 12 Physics Paper 1.

CBSE Sample Papers for Class 12 Physics Paper 1

• Time Allowed : 3 Hours
  Max. Marks : 70
  General Instructions 

  • All questions are compulsory. There are 26 questions in all.
  • This question paper has five sections: Section A, Section B, Section C, Section D and Section E.
  • Section A contains five questions of 1 mark each. Section B contains five questions of 2 marks each. Section C contains twelve questions of 3 marks each. Section D contains one value based question of 4 marks and Section E contains three questions of 5 marks each.
  • There is no overall choice. However, an internal choice has been provided in 1 question of 2 marks, 1 question of 3 marks and all the 3 questions of 5 marks weightage. You have to attempt only 1 of the choices in such questions.
  • You may use the following values of physical constants wherever necessary :

  

Questions :
SECTION : A

Question 1.
Define the term self-inductance of a coil. Write its S.I. unit

Question 2.
Which basic mode of communication is used for telephonic communication?

Question 3.
Why do the electrostatic field lines not form closed loops?

Question 4.
1-V graph for a metallic wire at two different temperatures, T₁ and T₂ is as shown in the figure. Which of the two temperature is lower and why?

Question 5.
Why does bluish colour predominate in a clear sky?

SECTION : B

Question 6.
Use Kirchhoff’s rules to determine the potential difference between the points A and D when no current flows in the arm BE.

Question 7.
When an electron in hydrogen atom jumps from the excited state to the ground state, how would the de-Broglie wavelength associated with the electron change? Justify your answer.

Question 8.
You are given two converging lenses of focal lengths 1.25 cm and 5 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece.

OR

A small telescope has an objective lens of focal length 150 cm and eyepiece of focal length 5 cm. What is the magnifying power of the telescope for viewing distant objects in normal adjustment? If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens?

Question 9.
Calculate the shortest wavelength in the Balmer series of hydrogen atom. In which region (infra-red, visible, ultraviolet) of hydrogen spectrum does this wavelength lie?

Question 10.
Write two factors which justify the need of modulation.

SECTION : C

Question 11.
Draw a circuit diagram of a C.E. transistor amplifier. Briefly explain its working and write the expression for
(i) current gain
(ii) voltage gain of the amplifier.

Question 12.
State clearly how an unpolarised light gets linearly polarized when passed through a Polaroid.
(i) Unpolarised light of intensity I₀ is incident on a Polaroid P₁ which is kept near another Polaroid P₂ whose pass axis is parallel to that of P₁. How will the intensities of light, I₁ and I₂, transmitted by the Polaroids P₁ and P₂ respectively, change on rotating P₁ without disturbing P₂?
(ii) Write the relation between the intensities  I₁ and I₂.

Question 13.
Define modulation index. Why is its value kept, in practice, less than one? A carrier wave of frequency 1.5 MHz and amplitude 50 V is modulated by a sinusoidal wave of frequency 10 kHz producing 50% amplitude modulation. Calculate the amplitude of the AM wave and frequencies of the side bands produced.

Question 14.
A uniform magnetic field B is set up along the positive X – axis. A particle of charge ‘q’ mass ‘m’ moving with a velocity v enters the field at the origin in X – Y plane such that it has velocity components both along and perpendicular to the magnetic field B. Trace, giving reason, the trajectory followed by the particle. Find out the expression for the distance moved by the particle along the magnetic field in one rotation.

Question 15.
Find the relation between drift velocity and relaxation time of charge carriers in a conductor. A conductor of length L is connected to a d.c. source of emf ‘E’. If the length of the conductor is tripled by stretching it, keeping ‘E’ constant, explain how its drift velocity would be affected.

Question 16.
(a) Determine the value of phase difference between the current and the voltage in the given series LCR circuit.

(b) Calculate the value of the additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity.

Question 17.
Write the expression for the generalized form of Amperes Circuital law. Discuss its significance and describe briefly how the concept of displacement current is explained through charging/ discharging of a capacitor in an electric circuit. 

Question 18.
(a) Describe briefly three experimentally observed features in the phenomenon of photoelectric effect.
(b) Discuss briefly how wave theory of light cannot explain these features.

OR

(a) Write the important properties of photons which are used to establish Einstein’s photoelectric equation.
(b) Use this equation to explain the concept
(i) threshold frequency and
(ii) stopping potential.

Question 19.
Use Huygens principle to show how a plane wavelength propagates from a denser to rarer medium. Hence verify Snell’s law of refraction.

Question 20.
Identify the gates P and Q shown in the figure . Write the truth table for the combination of the gates shown.

Name the equivalent gate representing this circuit and write its logic symbol. 

Question 21.
(a) Write three characteristic properties of nuclear force.
(b) Draw a plot of potential energy of a pair of nucleons as a function of their separation. Write two important conclusions that can be drawn from the graph.

Question 22.
Calculate the potential difference and the energy stored in the capacitor C₂ in the circuit shown in the figure. Given potential at A is 90 V, C₁ = 20 µF, C₂ = 30 µF and C₃ = 15 µF.

SECTION : D

Question 23.
One morning an old lady tried bare-footed to replace the fuse wire fitted with power supply mains for her house. Suddenly she cried and collapsed on the floor. Her family members cried loudly for help. Her neighbour heard the cries and rushed to the spot wearing rubber soul shoes on. He took a wooden stick and used it to switch off the main supply.
Answer the folio wing questions :

1. What are the voltage and frequency of mains supply in India?
2. These days most of the electrical devices we use require a.c. voltage. Why?
3.  Can a transformer be used to step up d.c. voltage ?
4. Write two qualities displayed by neighbour by his action.

SECTION : E

Question 24.
(a) Define electric flux. Write its S.I. unit. “Gauss’s law in electrostatics is true for any closed surface, no matter what its shape or size is”. Justify this statement with the help of a suitable example.
(b) Use Gauss’s law to prove that electric field inside a uniformly charged spherical shell is zero.

OR

(a) Derive the expression for the energy stored in a parallel plate capacitor. Hence obtain the expression for the energy density of the electric field.
(b) A fully charged parallel plate capacitor is connected across an uncharged identical capacitor. Show that the energy stored in the combination is less than that stored initially in the single capacitor.

Question 25.
Explain, using a labelled diagram, the principle and working of a moving coil galvanometer. What is the function of
(i) uniform radial magnetic field,
(ii) soft iron core?
Define the terms :
(i) current sensitivity and
(ii) voltage sensitivity of a galvanometer. Why does increasing the current sensitivity not necessarily increase voltage sensitivity?

OR

Question 26.
(a) Consider two coherent sources S₁ and S₂ producing monochromatic waves to produce interference pattern. Let the displacement of the wave produced by S₁ be given by y₁ = a cos mt and the displacement by S₂ be y₂ = a cos (ωt + Φ). Find out the expression for the amplitude of the resultant displacement at a point and show that the intensity at that point will be I = 4a² cos² Φ/2. Hence establish the conditions for constructive and destructive interference.
(b) What is the effect on the interference fringes in Young’s double slit experiment when
(i) the width of the source slit is increased,
(ii) the monochromatic source is replaced by a source of white light.

OR

(a) A ray ‘PQ’ of light is incident on the face AB of a glass prism ABC (as shown in the figure) and emerges out of the face AC. Trace the path of the ray. Show that ∠i + ∠e = ∠A + ∠δ. Where δ and e denote the angle of deviation and angle of emergence respectively.
Plot a graph showing the variation of the angle of deviation as a function of angle of incidence. State the condition under which ∠δ is minimum.
(b) A ray of light passing through an equilateral triangular prism from air undergoes minimum deviation when angle of incidence is 3/4th of the angle of prism. Calculate the speed of light in the prism.

 Answers :
SECTION : A

Answer 1.
L = Φ / I . If I = 1 then L = Φ i.e self inductance L of a coil is numerically equal to the amount of magnetic flux (Φ) linked with the coil when unit current flows through the coil. The S.I. unit of self inductance is henry (H) or weber per ampere.

Answer 2.
The basic mode of communication used in telephony is the point-to-point communications mode, which takes place through a link between a single transmitter and receiver.

Answer 3.
Electrostatic field lines originate from positive charge and terminate at negative charge.

Answer 4.
For the given figure the slope of a V – I graph is I/V = 1/R . Here the smaller the slope larger is the resistance . As the resistance of a metal increases with the increase in temperature, so resistance at T₂ is more and T₁ is lower.

Answer :
The light is scattered by air molecules. According to Lord Rayleigh the intensity of scattered light I ∝ 1/λ⁴. As λ_blue < λ_red Therefore blue colour scattered more in sky.

SECTION : B

Answer 6.

According to Kirchhoff’s junction law at B
i₃ = i₁ + i₂
i₃ = i₁
As  i₃ = 0  (given)
Applying second law to loop AFEB, electronic network shown in the figure.

∴   i₃ x 2 + i₃ x 3 + i₂ R₁ = 1+3 + 6
∴   i₃ = i₁ = 2A

From A to D along AFD
∴  V_AD = 2 i₃ – 1 + 3 x i₃
= (4 – 1 + 6)V
= 9V

Answer 7.
In an hydrogen atom, the negatively charged electron revolves in a circular orbit around the heavy positively charged nucleus. The centripetal force required by the electron is produced by the attractive force exerted by the nucleus on it. The energy is radiated, when an electron jumps from higher to lower energy orbit and the energy is absorbed, when jumps from lower to higher energy orbit.

It is called Bohr’s frequency condition.

Answer 8.
Given, f₀ = 5 cm , f_e = 1.25 cm and m = 30
Let S be tube length (distance between the objective and the eyepiece).

Thus, the height of the image would be 31.58 m.

Answer 9.
The formula for wavelength (λ) by Balmer series is :

Answer 10.
Two factors that justify the need for modulation of low frequency signals to high frequency signals are :

• increase in range of communication base band signals suffer from attenuation and so cannot be transmitted over long distances, and
• the antenna height and aperture is inversely proportional to the radiated signal frequency, implying that higher frequencies result in smaller antennas.

SECTION : C

Answer 11.

The purpose of this circuit is to amplify a small a.c input signal, such as an audio or radio signal. A small a.c. voltage is applied to the input through a coupling capacitor. The ratio of the a.c. component of the output to the a.c. component of the input, is known as gain.

Answer 12.
Polaroid filters are made of a special material that is capable of blocking of the two planes of vibration of an electromagnetic wave. In this sense, a Polaroid serves as a device that filter out one-half of the vibrations upon transmission of the light through the filter. When unpolarised light is transmitted through a Polaroid filter, it emerge with one-half the intensity and with vibrations in a single plane; it emerges as polarized light.

Answer 13.
The modulation index p, can be defined as the ratio between the amplitude of the modulating signal and the amplitude of the carrier signal. A modulation index above 1 causes over-modulation, causing the carrier to experience 180° phase reversals. These reversals give rise to additional side and audio signal will be distorted during reception.
Given,
carrier wave frequency = 1.5 MHz, amplitude (V _m) = 50 V
sinusoidal wave frequency = 10 kHz
amplitude modulation = 50%

Thus, amplitude of the AM wave = 250 volt
Now,
f _USB = 1.5 x 1000+ 10 kHz
⇒ 1500 + 10 = 1510 kHz
f _LSB = 1.5 x 1000 -10 = 1490 kHz

Answer 14.
Field at an axial point of a circular coil.

Where N is the number of turns of the circular coil. If M =iA is the magnetic moment of the coil, then

∵ a = 0, For small loop,

Where p is electric dipole  moment.

Answer 15.
The drift velocity of electrons can be formulated as :

Answer 16.

Answer 17.
Generalized form of Ampere Circuital Law :

It signifies that the source of magnetic field is not just due to the conduction of electric current due to flow of charge but also due to the time rate of change of electric field called displacement current.

Displacement current :
During charging and discharging of a capacitor the electric field between the plates will change so there will be a change of electric flux (displacement current) between the plates.

Answer 18.
(a)
(i) The photoelectric effect will not occur when the frequency of the incident light is less than the threshold frequency. Different materials have different threshold frequencies and most elements have threshold frequencies in the ultraviolet region of the electromagnetic spectrum.
(ii) The maximum KE of a stream of photo electrons increases linearly with the frequency of the incident light above the threshold frequency.
(iii) The rate at which photo electrons are emitted from a photosensitive surface is directly proportional to the intensity of incident light when the frequency is constant.

(b) Classical wave theory cannot explain :
(i) The existence of threshold frequency because it predicts that electrons would absorb enough energy to escape and there would not be any threshold frequency.
(ii) The almost immediate emission of photo electrons as, according to this theory, electrons require a period of time before sufficient energy is absorbed by it to escape from the metal; however such a thing does not happen practically; and
(iii) The independence of KE of photo electrons on intensity and dependence on frequency because it cannot explain why maximum KE is dependent on frequency and independent of intensity.

OR

(i) The important property of photons that is useful in establishing Einstein’s photoelectric equation is their ability to hold on to the electrons of an atom by their forces of attraction.
(ii) Einstein’s photoelectric equation states that :

Answer 19.
Medium 1

Answer 20.
Logic gate P is AND gate and logic Q is NOT gate.

The combination is NAND

Answer 21.
(a)
(i) Nuclear forces are short range forces.
(ii) Nuclear forces are primarily attractive and extremely strong.
(iii) Nuclear forces are charge independent

(b) Nuclear forces is of attractive nature when separation between the nuclei is greater than 1 fm and of repulsive nature when separation is less than 1 fm.

Answer 22.

SECTION : D

Answer 23.

1. The voltage and frequency of mains supply in India are 220 V and 50 Hz respectively.
2. Most electrical devices require a.c. voltage because a.c. is available by default through the mains supply and also because d.c., is actually a one-way current, is available only through batteries.
3. No, a transformer cannot be used to set-up d.c. voltage because a transformer works on the magnetic effect of current and d.c. voltage does not produces any magnetic field.
4. The two qualities displayed by neighbour are :
   (a) preventing himself from being the earthing conductor by putting on his shoes and
   (b) switching off the mains connection to prevent the old lady from acting as an earthing conductor

SECTION : E

Answer 24.
(a) The electric flux through an area is defined as the electric field multiplied by the area of the surface projected on a plane, perpendicular to the field. Its S.I. unit is volt-metres (Vm) or Newton metres square per coulomb (Nm² C^-1 ). The given statement is justified because while measuring the flux, the surface area is more important than its volume or its size.
(b) To prove that the electric field inside a uniformly charged spherical shell is zero, we place a single positive point charge ‘q’ at the centre of an imaginary spherical surface with radius R. The field lines of this point radiate outside equally in all directions. The magnitude E of the electric field at every point on the surface is given by

OR

(a) When charging parallel plate capacitor, whose plate area is A and distance between the plate is d. When charge on capacitor is q, potential difference increase 0 to V. Hence average

(b) Let the capacitance of the charged capacitor C₁ by and the voltage be ∆V₁

Answer 25.
The basic principle of a moving coil galvanometer is that when a current carrying coil is placed in a magnetic field, it experiences a torque.

When the current I is passed through the coil, the torque experienced is given by
τ = NIAB sinθ
Where
N = no. of turns of the coil,
A =  area of the coil
B = magnetic field and
θ = angle between normal of coil and magnetic field
(i) The uniform radial magnetic field allows the coil to rotate and
(ii) The soft iron core makes the magnetic field linked with the coil to be radial.
The current sensitivity is defien as the deflection produced in the galvanometer, while passing a current of 1 ampere (1amp).
Thus,

The voltage sensitivity is defined as the deflection produced in the galvanometer when a potential difference of IV is applied to the coil.
Thus,

Where, R is the resistance.
Increasing the current sensitivity does not necessarily increase the voltage sensitivity as there is an increase in the resistance as well.

OR

The direction of dB is perpendicular to the plane formed by dl and r. It has an x-component dB_x. When the components perpendicular to the x-axis are summed over, they cancel out and we obtain null result. Thus only the x-component survives.

If the coil has N turns, then each turn will contribute equally to B. Then


Where μ₀ in the permeability of free space. Ampere’s circuital law in electromagnetism is analogous to Gauss’ law in electrostatics.

Answer 26.
(a) Let S be a narrow slit illuminated by a monochromatic source of light, and Sj and S₂ two similar parallel slits very close together and equidistant from S.

Displacement of the wave produced by S₁ is given by
y₁ = a cos ωt and
the displacement of the Wave produced by S₂ is given by
y₂ = a cos (ωt + Φ)
The resultant displacement is given by
y = y₁ + y₂ = a cos(ωt + Φ) + a cos (ωt + Φ)
⇒ y = 2a cos Φ/2 cos (ωt + Φ/2)
The amplitude of the resultant displacement is 2a cos Φ/2. The intensity of light is directly proportional to the square of amplitude of the wave.
The resultant intensity in given by
I = 4a cos² Φ/2

(b)  (i) As the width of the slits is increased, the fringe width decreases. It is because,

(ii) The different colours of white light will produce different interference patterns but the central bright fringes due to all colours are at the same positions. Therefore, the central bright fringe is white in colour. Since the wavelength of the blue light is smallest, the fringe close to the either side of the central white fringe is blue and farthest is red.
OR

(a) Let the incident ray meet refracting face AB of the prism at point P. Ray PQ is the refracted ray inside the prism and δ₁ and r₁, are the angle of the deviation and refraction at interface AB. At interface AC the ray goes out of the prism. Let e be the angle of emergence. The angle of deviation at point Q is δ₂ as shown in figure. Using geometry, we see that at point P,



So angle of deviation produced by a prism depends upon the angle of incidence, refracting angle of prism, and the material of the prism.

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.1 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.1.

• Ratio and Proportion Class 6 Ex 12.2
• Ratio and Proportion Class 6 Ex 12.3

NCERT Solutions for Class 6 Maths Chapter 12 Ratio and Proportion Ex 12.1

Question 1.
There are 20 girls and 15 boys in a class.
(a) What is the ratio of a number of girls to the number of boys?
(b) What is the ratio of a number of girls to the total number of students in the class?
Solution :
(a) Ratio of number of girls to the number of boys

(b) Total number of students in the class = 20 + 15 = 35
∴ Ratio of number of girls to the total number of students in the class

Question 2.
Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of:
(a) Number of students liking football to a number of students liking tennis.
(b) Number of students liking cricket to the total number of students.
Solution :
(a) Number of students liking tennis = 30-(6+ 12) = 30 – 18 = 12
∴ Ratio of number of students liking football to number of students liking tennis

(b) Number of students liking cricket to total number of students

Question 3.
See the figure and find the ratio of:
(a) Number of triangles to the number of circles inside the rectangle.

(b) Number of squares to all the figures inside the rectangle.
(c) Number of circles to all the figures inside the rectangle.
Solution :
(a) Number of triangle inside the rectangle = 3 . , Number of circles inside the rectangle = 2 Ratio of number of triangles to the number of circles inside the rectangle = \(\frac{ 3 }{ 2 }\) =3:2.
(b) Number of squares inside the rectangle = 2 Number of all the figures inside the rectangle = 7
∴ Ratio of number of squares to all the figures 2
inside the rectangle = \(\frac{ 2 }{ 7 }\) =2:7.
(c) Ratio of number of circles to all the figures inside the rectangle = \(\frac{ 2 }{ 7 }\) =2:1.

Question 4.
Distance travelled by Hamid and Akhtar in an hour are 9 km and 12 km. Find the ratio of speed of Hamid to the speed of Akhtar.
Solution :
Ratio of speed of Hamid to the speed of

Question 5.
Fill in the following blanks:

Solution :

Question 6.
Find the ratio of the following :
(a) 81 to 108
(b) 98 to 63
(c) 33 km to 121 km
(d) 30 minutes to 45 minutes.
Solution :

Question 7.
Find the ratio of the following :
(a) 30 minutes to 1.5 hours
(b) 40 cm to 1.5 m
(c) 55 paise to ₹ 1
(d) 500 ml to 2 litres.
Solution :
(a) 1.5 hours = 1.5 × 60 minutes = 90 minutes

Question 8.
In a year, Seema earns- ₹ 1,50.000 and saves ₹ 50,000. Find the ratio of:
(a) Money that Seema earns to the money she saves.
(b) Money that she saves to the money that she spends.
Solution :
(a) Ratio of money that Seema earns to the money she saves

(b) Money that she spends
= ₹ 1,50,000 – ₹ 50,000 = ₹ 1,00,000
∴ Ratio of money she saves to the money she spends

Question 9.
There are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students.
Solution :
Ratio of the number of teachers to the number of students

Question 10.
In a college, out of4320 students, 2300 are girls. Find the ratio of:
(a) Number of girls to the total number of students.
(b) Number of boys to the number of girls.
(c) Number of boys to the total number of students.
Solution :
(a) Ratio of number of girls to the total number of students

(b) Number of boys = 4320 – 2300 = 2020
∴ Ratio of number of boys to the number of girl

(c) Ratio of number of boys to the total number of students

Question 11.
Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of:
(a) Number of students who opted basketball to the number of students who opted table tennis.
(b) Number of students who opted cricket to the number of students opting basketball.
(c) Number of students who opted basketball to the total number of students.
Solution :
(a) Number of students opting table tennis = 1800 – (750 + 800) = 1800 -1550 = 250
∴ Ratio of number of students opting basketball to number of students opting table tennis

(b) Ratio of number of students opting cricket to the number of students opting basketball

(c) Ratio of number of students opting basketball to the total number of students

Question 12.
Cost of a dozen pens is ₹ 180 and cost of 8 ball pens is ₹ 56. Find the ratio of cost of a pen to the cost of a ball pen.
Solution :
1 dozen =12 items
∴ Cost of 12 pens = ₹ 180
∴ Cost of 1 pen = ₹ \(\frac{ 180 }{ 12 }\) = ₹ 15
∴ Cost of 8 ball pens = ₹ 56
∴ Cost of 1 ball pen = ₹ \(\frac{ 56 }{ 8 }\) = ₹ 7
∴ Ratio of cost of a pen to the cost of a ball 15 pen = \(\frac{ 15 }{ 7 }\) =15:7.

Question 13.
Consider the statement: Ratio of breadth and length of a hall 2: 5. Complete the following table that shows some possible breadths and lengths of the hall.

Solution :

Hence, the completed table is as follows:

Question 14.
Divide 20 pens between Sheela and Sangeeta in the ratio 3: 2.
Solution :
Total number of pens = 20 Ratio = 3:2
Sum of the parts = 3 + 2 = 5
∴ Sheel’s shae = \(\frac{ 3 }{ 5 }\) × 20 = 12 and, Samgeeta’s share = \(\frac{ 2 }{ 5 }\) × 20 = 8

Question 15.
Mother wants to divide ₹ 36 between her daughters Shreya and Bhoomika in the ratio of their ages. If the age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get?
Solution :
Total money = ₹ 36
The ratio of the ages of Shreya and Bhoomika



Hence, Shreya will get ₹ 20 and Bhoomika will get ₹ 16.

Question 16.
Present age of the father is 42 years and that of his son is 14 years. Find the ratio of :
(a) Present age of father to the present age of the son.
(b) Age of the father to the age of son, when the son was 12 years old.
(c) Age of father after 10 years to the age of son after 10 years.
(d) Age of father to the age of son when father was 30 years old.
Solution :
(a) Ratio of the present age of father to the present age of the son

(b) Son was 12 years old 14 – 12 = 2 years before
Age of the father 2 years before = 42 – 2 = 40 years
∴ Ratio of the age of the father to the age of the son. when son was 12 years old

(c) Age of father after 10 years = 42 + 10 = 52 years
Age of son after 10 years = 14 + 10 = 24 years
∴ Ratio of age of father after 10 years to the age of son after 10 years

(d) Father was 30 years old 42 – 30 = 12 years before
Age of son 12 years before = 14 – 12 = 2 years
∴ Ratio of the age of father to the age of son when father was 30 years old

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