Board Paper of Class 12-Science 2019 Physics Delhi(Set2) - 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
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 2
When unpolarized light is incident on the interface separating the rarer medium and the denser medium, Brewster angle is found to be 60°. Determine the refractive index of the denser medium. VIEW SOLUTION

Question 3
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 4
When a potential difference is applied across the ends of a conductor, how is the drift velocity of the electrons related to the relaxation time? VIEW SOLUTION

Question 5
Draw the equipotential surfaces due to an isolated point charge. VIEW SOLUTION

Question 6
Explain with the help of Einstein's photo electric equation any two observed features in photoelectric effect which cannot be explained by wave theory. VIEW SOLUTION

Question 7
A deuteron and an alpha particle having same momentum are in turn allowed to pass through a magnetic field $\vec{B}$ , acting normal to the direction of motion of the particles. Calculate the ratio of the radii of the circular paths described by them. VIEW SOLUTION

Question 8
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 9
Calculate the radius of curvature of an equi-concave lens of refractive index 1.5, when it is kept in a medium of refractive index 1.4, to have a power of −5D?
OR

An equilateral glass prism has a refractive index 1.6 in the air. Calculate the angle of minimum deviation of the prism, when kept in a medium of refractive index $4 \sqrt{2} / 5$ .
VIEW SOLUTION

Question 10
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 11
(a) Plot a graph showing variation of deBroglie wavelength (λ) associated with a charged particle of mass m, versus $\sqrt{V}$ , where V is the accelerating potential.

(b) An electron, a proton and an alpha particle have the same kinetic energy. Which one has the shortest wavelength? VIEW SOLUTION

Question 12
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 13

(a) State the underlying principle of a moving coil galvanometer.

(b) Give two reasons to explain why a galvanometer cannot as such be used to measure the value of the current in a given circuit.
(c) Define the terms : (i) voltage sensitivity and (ii) current sensitivity of a galvanometer. VIEW SOLUTION

Question 14

(a) Define mutual inductance and write its S.I. unit.

(b) A square loop of side 'a' carrying a current I₂ is kept at distance x from an infinitely long straight wire carrying a current I₁ as shown in the figure. Obtain the expression for the resultant force acting on the loop.
VIEW SOLUTION

Question 15

(a) Draw equipotential surfaces corresponding to the electric field that uniformly increases in magnitude along with the z-directions.
(b) Two charges –q and +q are located at points (0, 0, –a) and (0, 0, a). What is the electrostatic potential at the points (0, 0, ± z) and (x, y, 0)? VIEW SOLUTION

Question 16

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 17

(a) Write the relation between half life and average life of a radioactive nucleus.
(b) In a given sample two isotopes A and B are initially present in the ratio of 1 : 2. Their half lives are 60 years and 30 years respectively. How long will it take so that the sample has these isotopes in the ratio of 2 : 1? VIEW SOLUTION

Question 18
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 19

(a) Define the term 'self-inductance' of a coil. Write its S.I. unit.

(b) A rectangular loop of sides a and b carrying current I₂ is kept at distance 'a' from an infinitely long straight wire carrying a current I₁ as shown in the figure. Obtain an expression for the resultant force acting on the loop.
VIEW SOLUTION

Question 20
(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 21
(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 22

(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 23

(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 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 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

Question 26
(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 27

(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