Board Paper of Class 12-Science 2019 Physics Delhi(Set 3) - Solutions

General Instructions:

1. All questions are compulsory. There are 27 questions in all.

2. This question paper has four sections: Section A, Section B, Section C and Section D.

3. Section A contains five questions of one mark each, Section B contains seven questions of two marks each, Section C contains twelve questions of three marks each, and Section D contains three questions of five marks each.

4. There is no overall choice. However, internal choices have been provided in two questions of one mark, two questions of two marks, four questions of three marks and three questions of five marks weightage. You have to attempt only one of the choices in such questions.

5. You may use the following values of physical constants wherever necessary.

c = 3 × 10⁸ m/s

h = 6.63 × 10^–34 Js

e = 1.6 × 10^–19 C

μ_o = 4π × 10^–7 T m A^–1

ε₀ = 8.854 × 10^–12 C² N^–1 m^–2

$fraction numerator 1 over denominator 4 pi epsilon subscript 0 end fraction$ = 9 × 10⁹ N m² C^–2

m_e = 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 × 10²³ per gram mole

Boltzmann constant = 1.38 × 10^–23 JK^–1

Question 1
Distinguish between unpolarized and linearly polarized light. VIEW SOLUTION

Question 2
Define the term "Threshold frequency", in the context of photoelectric emission.

OR

Define the term "Intensity" in the photon picture of electromagnetic radiation. VIEW SOLUTION

Question 3
How is the drift velocity in a conductor affected with the rise in temperature? VIEW SOLUTION

Question 4
In skywave mode of propagation, why is the frequency range of transmitting signals restricted to less than 30 MHz?

OR

On what factors does the range of coverage in ground wave propagation depend? VIEW SOLUTION

Question 5
Draw the pattern of electric field lines when a point charge +q is kept near an uncharged conducting plate. VIEW SOLUTION

Question 6

(a) Define the terms, (i) threshold frequency and (ii) stopping potential in photoelectric effect.
(b) Plot a graph of photocurrent versus anode potential for a radiation of frequency $ν$ and intensities I₁ and I₂ (I₁ < I₂). VIEW SOLUTION

Question 7
Why a signal transmitted from a TV tower cannot be received beyond a certain distance? Write the expression for the optimum separation between the receiving and the transmitting antenna. VIEW SOLUTION

Question 8
State Bohr's quantization condition of angular momentum. Calculate the shortest wavelength of the Bracket series and state to which part of the electromagnetic spectrum does it belong.
OR

Calculate the orbital period of the electron in the first excited state of hydrogen atom. VIEW SOLUTION

Question 9
Why is the wave theory of electromagnetic radiation not able to explain the photoelectric effect? How does the photon picture resolve this problem? VIEW SOLUTION

Question 10
Two bulbs are rated (P₁, V) and (P₂, V). If they are connected (i) in series and (ii) in parallel across a supply V, find the power dissipated in the two combinations in terms of P₁ and P₂. VIEW SOLUTION

Question 11
Obtain the expression for the ratio of the de-Broglie wavelengths associated with the electron orbiting in the second and third excited states of hydrogen atom. VIEW SOLUTION

Question 12
A charged particle q is moving in the presence of a magnetic field B which is inclined to an angle 30° with the direction of the motion of the particle. Draw the trajectory followed by the particle in the presence of the field and explain how the particle describes this path. VIEW SOLUTION

Question 13
(a) Explain briefly how Rutherford scattering of α-particle by a target nucleus can provide information on the size of the nucleus.

(b) Show that density of nucleus is independent of its mass number A. VIEW SOLUTION

Question 14
State the underlying principle of a cyclotron. Explain its working with the help of a schematic diagram. Obtain the expression for cyclotron frequency. VIEW SOLUTION

Question 15
Two infinitely long straight wire A₁ and A₂ carrying currents I and 2I flowing in the same direction are kept 'd' distance apart. Where should a third straight wire A₃ carrying current 1.5 I be placed between A₁ and A₂ so that it experiences no net force due to A₁ and A₂? Does the net force acting on A₃ depend on the current flowing through it? VIEW SOLUTION

Question 16
(a) Draw the equipotential surfaces due to an electric dipole.

(b) Derive an expression for the electric field due to a dipole of dipole moment $\vec{p}$ at a point on its perpendicular bisector. VIEW SOLUTION

Question 17

Using Kirchhoff's rules, calculate the current through the 40 Ω and 20 Ω resistors in the following circuit:

OR

What is end error in a metre bridge? How is it overcome? The resistances in the two arms of the metre bridge are R = 5 Ω and S respectively.
When the resistance S is shunted with an equal resistance, the new balance length found to be 1.5 l₁, where l₁ is the initial balancing length. Calculate the value of S.
VIEW SOLUTION

Question 18
(a) Describe briefly the functions of the three segments of n-p-n transistor.

(b) Draw the circuit arrangement for studying the output characteristics of n-p-n transistor in CE configuration. Explain how the output characteristics is obtained.
OR

Draw the circuit diagram of a full wave rectifier and explain its working. Also, give the input and output waveforms. VIEW SOLUTION

Question 19
Define the term wavefront. Using Huygen's wave theory, verify the law of reflection.
OR

Define the term, "refractive index" of a medium. Verify Snell's law of refraction when a plane wavefront is propagating from a denser to a rarer medium.
VIEW SOLUTION

Question 20

(a) Identify the part of the electromagnetic spectrum used in (i) radar and (ii) eye surgery. Write their frequency range.

(b) Prove that the average energy density of the oscillating electric field is equal to that of the oscillating magnetic field.
VIEW SOLUTION

Question 21

Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position.
A giant refracting telescope at an observatory has an objective lens of focal length 15 m and an eyepiece of focal length 1.0 cm. If this telescope is used to view the Moon, find the diameter of the image of the Moon formed by the objective lens. The diameter of the Moon is 3.48 × 10⁶ m, and the radius of lunar orbit is 3.8 × 10⁸ m. VIEW SOLUTION

Question 22
(a) If A and B represent the maximum and minimum amplitudes of an amplitude modulated wave, write the expression for the modulation index in terms of A and B.

(b) A message signal of frequency 20 kHz and peak voltage 10 V is used to modulate a carrier of frequency 2 MHz and peak voltage of 15 V. Calculate the modulation index. Why the modulation index is generally kept less than one? VIEW SOLUTION

Question 23

(a) State Gauss's law for magnetism. Explain its significance.

(b) Write the four important properties of the magnetic field lines due to a bar magnet.

OR
Write three points of differences between para-, dia- and ferro- magnetic materials, giving one example for each. VIEW SOLUTION

Question 24
(a) Three photodiodes D₁, D₂ and D₃ are made of semiconductors having band gaps of 2.5 eV, 2 eV and 3 eV respectively. Which of them will not be able to detect light of wavelength 600 nm?

(b) Why photodiodes are required to operate in reverse bias? Explain. VIEW SOLUTION

Question 25
(a) Describe briefly the process of transferring the charge between the two plates of a parallel plate capacitor when connected to a battery. Derive an expression for the energy stored in a capacitor.

(b) A parallel plate capacitor is charged by a battery to a potential difference V. It is disconnected from battery and then connected to another uncharged capacitor of the same capacitance. Calculate the ratio of the energy stored in the combination to the initial energy on the single capacitor.

OR

(a) Derive an expression for the electric field at any point on the equatorial line of an electric dipole.

(b) Two identical point charges, q each, are kept 2m apart in air. A third point charge Q of unknown magnitude and sign is placed on the line joining the charges such that the system remains in equilibrium. Find the position and nature of Q. VIEW SOLUTION

Question 26

(a) In a series LCR circuit connected across an ac source of variable frequency, obtain the expression for its impedance and draw a plot showing its variation with frequency of the ac source.

(b) What is the phase difference between the voltages across inductor and the capacitor at resonance in the LCR circuit?

(c) When an inductor is connected to a 200 V dc voltage, a current at 1A flows through it. When the same inductor is connected to a 200 V, 50 Hz ac source, only 0.5 A current flows. Explain, why? Also, calculate the self inductance of the inductor.

OR

(a) Draw the diagram of a device which is used to decrease high ac voltage into a low ac voltage and state its working principle. Write four sources of energy loss in this device.

(b) A small town with a demand of 1200 kW of electric power at 220 V is situated 20 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is 0.5 Ω per km. The town gets the power from the line through a 4000-220 V step-down transformer at a sub-station in the town. Estimate the line power loss in the form of heat.
VIEW SOLUTION

Question 27
(a) Describe any two characteristic features which distinguish between interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young's double slit experiment.

(b) In the diffraction due to a single slit experiment, the aperture of the slit is 3 mm. If monochromatic light of wavelength 620 nm is incident normally on the slit, calculate the separation between the first order minima and the 3^rd order maxima on one side of the screen. The distance between the slit and the screen is 1.5 m.

OR

(a) Under what conditions is the phenomenon of total internal reflection of light observed? Obtain the relation between the critical angle of incidence and the refractive index of the medium.

(b) Three lenses of focal length +10 cm, –10 cm and +30 cm are arranged coaxially as in the figure given below. Find the position of the final image formed by the combination.

VIEW SOLUTION