Short Answer TypeObtain the relation between the decay constant and half-life of a radioactive sample.
The half-life of a certain radioactive material against 
decay is 100 days. After how much time, will the undecayed fraction of the material be 6.25%?
(a) Define the term 'intensity of radiation' in terms of photon picture of light.
(b) Two monochromatic beams, one red and the other blue, have the same intensity.
In which case:
(i) the number of photons per unit area per second is larger,
(ii) the maximum kinetic energy of the photoelectrons is more? Justify your answer.
Long Answer TypeDuring a thunderstorm the 'live' wire of the transmission line fell down on the ground from the poles in the street. A group of boys, who passed through, noticed it and some of them wanted to place the wire by the side. As they were approaching the wire and trying to lift the cable, Anuj noticed it and immediately pushed them away, thus preventing them from touching the live wire. During pushing some of them got hurt. Anuj took them to a doctor to get them medical aid.
Based on the above paragraph, answer the following questions:
(a) Write the two values which Anuj displayed during the incident.
(b) Why is it that a bird can sit on a suspended 'live' wire without any harm whereas touching it on the ground can give a fatal shock?
(c) The electric power from a power plant is set up to a very high voltage before transmitting it to distant consumers. Explain, why.a) State Kirchhoff's rules and explain on what basis they are justified.
(b) Two cells of emfs E1 and E2 and internal resistances r1 and r2 are connected in parallel.
Derive the expression for the
(i) Emf and
(ii) internal resistance of a single equivalent cell which can replace this combination.
OR
(a) 'The outward electric flux due to charge +Q is independent of the shape and size of the surface which encloses is.' Give two reasons to justify this statement.
(b) Two identical circular loops '1' and '2' of radius R each have linear charge densities -
and +
C/m respectively. The loops are placed coaxially with their centre distance apart. Find the magnitude and direction of the net electric field at the centre of loop '1'.
Two infinitely long straight parallel wires, '1' and '2', carrying steady currents I1 and I2 in the same direction are separated by a distance d. Obtain the expression for the magnetic field due to the wire '1' acting on wire '2'. Hence find out, with the help of a suitable diagram, the magnitude and direction of this force per unit length on wire '2' due to wire '1'. How does the nature of this force changes if the currents are in opposite direction? Use this expression to define the S.I. unit of current.
Draw a necessary arrangement for winding of primary and secondary coils in a step-up transformer. State its underlying principle and derive the relation between the primary and secondary voltages in terms of number of primary and secondary turns. Mention the two basic assumptions used in obtaining the above relation.
State any two causes of energy loss in actual transformers.
Underlying principle of a step-up transformer: A transformer which increases the ac voltage is known as a step up transformer.
Working of step-up transformer is based on the principle of mutual inductance and it converts the alternating low voltage to alternating high voltage. The number of turns in the secondary coil is greater than the number of turns in the primary coil.
i.e., NS > NP
Working: When an A.C source is connected to the ends of the primary coil, the current changes continuously in the primary coil. Hence, the magnetic flux which is linked with the secondary coil changes continuously. So, the emf which is developed across the secondary coil is same as that in the primary coil. The emf is induced in the coil as per Faraday’s law.
Let, EP be the alternating emf applied to primary coil and np be the number of turns in it.
Consider 
as the electric flux associated with it.
Then, 
Assumption: We assume that there is no leakage of flux so that, the flux linked with each turn of primary coil is same as flux linked with secondary coil.
Two sources of energy loss in the transformer:
Joule Heating – Energy is lost in resistance of primary and secondary windings in the form of heat.
H = I2Rt
Flux leakage - Energy is lost due to coupling of primary and secondary coils not being perfect, i.e., whole of magnetic flux generated in primary coil is not linked with the secondary coil.
iii)
Conservation of law of energy is not violated in step-up transformer. When output voltage increases, the output current automatically decreases. Thus, there is no loss of energy.
(a) Use Huygens' principle to show the propagation of a plane wavefront from a denser medium to a rarer medium. Hence find the ratio of the speeds of wavefront in the two media.
(b) (i) Why does an unpolarized light incident on a polaroid get linearly polarized ?
(ii) Derive the expression of Brewster's law when unpolarized light passing from a rarer to a denser medium gets polarized on reflection at the interface.
A biconvex lens with its two faces of equal radius of curvature R is made of a transparent medium of refractive index 
1. It is kept in contact with a medium of refractive index 2 as shown in the figure.
a) Find the equivalent focal length of the combination.
b) Obtain the condition when this combination acts as a diverging lens.
c) Draw the ray diagram for the case 
when the object is kept far away from the lens. Point out the nature of the image formed by the system.
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