Board Paper of Class 12 2018 Physics - Solutions

All questions are compulsory.
This question paper is divided into 4 Sections, A, B, C and D as follows:
Section A

Question number 1 is of twelve marks. All parts of this question are compulsory.

Section B

Question numbers 2 to 12 carry 2 marks each with two questions having internal choice.

Section C

Question numbers 13 to 19 carry 3 marks each with two questions having internal choice.

Section D

Question numbers 20 to 22 are long-answer type questions and carry 5 marks each.

Each question has an internal choice.
The intended marks for questions are given in brackets [ ].
All working, including rough work, should be done on the same sheet as and adjacent to the rest of the answer.
Answers to sub parts of the same question must be given in one place only. A list of useful physical constants is given at the end of this paper.
A simple scientific calculator without a programmable memory may be used for calculations.
Useful Constants and Relations:

1.	Permeability of vacuum	(µ₀)	= 4π × 10^–7 H m^–1
2.	Rydberg’s constant	(R)	= 1·097 × 10⁷ m^–1

Question 1
(a) Choose the correct alternative (a), (b), (c) or (d) for each of the questions given below:
(i) The order of coloured rings in a carbon resistor is red, yellow, blue and silver. The resistance of the carbon resistor is:
(a) 24 × 10⁶Ω ± 5%
(b) 24 × 10⁶Ω ± 10%
(c) 34 × 10⁴Ω ± 10%
(d) 26 × 10⁴Ω ± 5%

(ii) A circular coil carrying a current I has radius R and number of turns N. If all the three, i.e. the current I, radius R and number of turns N are doubled, then, magnetic field at its centre becomes:
(a) Double
(b) Half
(c) Four times
(d) One fourth

(iii) An object is kept on the principal axis of a concave mirror of focal length 10 cm, at a distance of 15 cm from its pole. The image formed by the mirror is:
(a) Virtual and magnified
(b) Virtual and diminished
(c) Real and magnified
(d) Real and diminished

(iv) Einstein’s photoelectric equation is:
(a) E_max = hλ – φ₀

(b) $E_{\max} = \frac{h c}{λ} - φ_{0}$

(c) E_max = hν + φ₀

(d) $E_{\max} = \frac{h c}{λ} + φ_{0}$

(v) In Bohr's model of hydrogen atom, radius of the first orbit of an electron is r₀. Then, radius of the third orbit is:
(a) $\frac{r_{0}}{9}$
(b) r₀
(c) 3r₀
(d) 9r₀

(b) Answer the following questions briefly and to the point.
(i) In a potentiometer experiment, balancing length is found to be 120 cm for a cell E₁ of emf 2V. What will be the balancing length for another cell E₂ of emf 1·5V? (No other changes are made in the experiment.)
(ii) How will you convert a moving coil galvanometer into a voltmeter?
(iii) A moving charged particle q travelling along the positive x-axis enters a uniform magnetic field B. When will the force acting on q be maximum?
(iv) Why is the core of a transformer laminated?
(v) Ordinary (i.e. unpolarised) light is incident on the surface of a transparent material at the polarising angle. If it is partly reflected and partly refracted, what is the angle between the reflected and the refracted rays?
(vi) Define coherent sources of light.
(vii) Name a material which is used in making control rods in a nuclear reactor. VIEW SOLUTION

Question 2
Define current density. Write an expression which connects current density with drift speed. VIEW SOLUTION

Question 3
A long horizontal wire P carries a current of 50A. It is rigidly fixed. Another wire Q is placed directly above and parallel to P, as shown in Figure 1 below. The weight per unit length of the wire Q is 0·025 Nm^–1and it carries a current of 25A. Find the distance ‘r’ of the wire Q from the wire P so that the wire Q remains at rest.

OR

Calculate force per unit length acting on the wire B due to the current flowing in the wire A. (See Figure 2 below)
VIEW SOLUTION

Question 4
(i) Explain Curie’s law for a paramagnetic substance.
(ii) A rectangular coil having 60 turns and area of 0·4m²is held at right angles to a uniform magnetic field of flux density 5 × 10^–5T. Calculate the magnetic flux passing through it.
VIEW SOLUTION

Question 5
What is motional emf ? State any two factors on which it depends. VIEW SOLUTION

Question 6
(i) What is the ratio of the speed of gamma rays to that of radio waves in vacuum?
(ii) Name an electromagnetic wave which is used in the radar system used in aircraft navigation. VIEW SOLUTION

Question 7
A biconvex lens made of glass (refractive index 1·5) has two spherical surfaces having radii 20 cm and 30 cm. Calculate its focal length. VIEW SOLUTION

Question 8
State any two differences between primary rainbow and secondary rainbow. VIEW SOLUTION

Question 9

(i) State de Broglie hypothesis.
(ii) With reference to photoelectric effect, define threshold wavelength. VIEW SOLUTION

Question 10
Calculate the minimum wavelength of the spectral line present in Balmer series of hydrogen. VIEW SOLUTION

Question 11
What is meant by pair annihilation? Write a balanced equation for the same.
OR

What is meant by the terms half-life of a radioactive substance and binding energy of a nucleus? VIEW SOLUTION

Question 12
In a communication system, what is meant by modulation? State any two types of modulation. VIEW SOLUTION

Question 13
Obtain an expression for intensity of electric field at a point in end on position, i.e. axial position of an electric dipole. VIEW SOLUTION

Question 14
Deduce an expression for equivalent capacitance C when three capacitors C₁, C₂ and C₃ are connected in parallel. VIEW SOLUTION

Question 15
𝜀₁ and 𝜀₂ are two batteries having emf of 34V and 10V respectively and internal resistance of 1Ω and 2Ω respectively. They are connected as shown in Figure 3 below. Using Kirchhoff’s’ Laws of electrical networks, calculate the currents I₁ and I₂.

OR

An electric bulb is marked 200V, 100W. Calculate electrical resistance of its filament. If five such bulbs are connected in series to a 200V supply, how much current will flow through them? VIEW SOLUTION

Question 16
For any prism, prove that:

$' n' or µ = \frac{\sin (\frac{A + δ m}{2})}{\sin (\frac{A}{2})}$

where the terms have their usual meaning.
OR

When two thin lenses are kept in contact, prove that their combined or effective focal length $\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$ is given by where the terms have their usual meaning.

VIEW SOLUTION

Question 17
(i) In Young’s double slit experiment, show graphically how intensity of light varies with distance.
(ii) In Fraunhofer diffraction, how is the angular width of the central bright fringe affected when slit separation is increased? VIEW SOLUTION

Question 18
Write one balanced equation each to show:
(i) Nuclear fission
(ii) Nuclear fusion
(iii) Emission of β⁻ (i.e. a negative beta particle) VIEW SOLUTION

Question 19
With reference to semiconductor devices, define a p-type semiconductor and a Zener diode. What is the use of a Zener diode? VIEW SOLUTION

Question 20
An alternating emf of 220V is applied to a circuit containing a resistor R having resistance of 160Ω and a capacitor ‘C’ in series. The current is found to lead the supply voltage by an angle 𝜃 = tan^–1(3/4).
(i) Calculate: (1) The capacitive reactance (2) Impedance of the circuit (3) Current flowing in the circuit
(ii) If the frequency of the applied emf is 50 Hz, what is the value of the capacitance of the capacitor ‘C’?
OR

An A.C. generator generating an emf of 𝜀 = 300 sin (100𝜋𝑡) 𝑉 is connected to a series combination of 16𝜇F capacitor, 1H inductor and 100 Ω resistor.
Calculate:
(i) Impedance of the circuit at the given frequency.
(ii) Resonant frequency f_o.
(iii) Power factor at resonant frequency f_o. VIEW SOLUTION

Question 21
Draw a labelled ray diagram of an image formed by a refracting telescope with final image formed at infinity. Derive an expression for its magnifying power with the final image at infinity.
OR

(i) Using Huygen’s wave theory, derive Snell’s law of refraction.
(ii) With the help of an experiment, state how will you identify whether a given beam of light is polarised or unpolarised. VIEW SOLUTION

Question 22
(i) The forward characteristic curve of a junction diode is shown in Figure 4 below:

Calculate the resistance of the diode at:
(1) V = 0·5 V
(2) I = 60 mA

(ii) Draw separate energy band diagrams for conductors, semi-conductors and insulators and label each of them.
OR

(i) The arrangement given below represents a logic gate:

Copy the following truth table in your answer booklet and complete it showing outputs at C and D.

A B C D

0 0

1 0

0 1

1 1

(ii) Draw a labelled diagram of a common emitter amplifier, showing waveforms of signal voltage and output voltage. VIEW SOLUTION