Q. (a) Define the term 'conductivity' of a metallic wire. Write its SI unit.
(b) Using the concept of free electrons in a conductor, derive the expression for the conductivity of a wire in terms of number density and relaxation time. Hence obtain the relation between current density and the applied electric field $E$.

Q. (a) If one of two identical slits producing interference in Young's experiment is covered with glass, so that the light intensity passing through it is reduced to $50$%, find the ratio of the maximum and minimum intensity of the fringe in the interference pattern.
(b) What king of fringes do you expect to observe if white light is used instead of monochromatic light?

Q. A bar magnet of magnetic moment $6J/T$ is aligned at ${60}^{\circ }$ with a uniform external magnetic field of $0.44T$. Calculate (a) the work done in turning the magnet to align its magnetic moment (i) normal to the magnetic field, (ii) opposite to the magnetic field, and (b) the torque on the magnet in the final orientation in case (ii).

Q. Four point charges $Q,q,Q$ and $q$ are placed at the corners of a square of side ${}^{\prime }{a}^{\prime }$ as shown in the figure.
Find the
(a) resultant electric force on a charge $Q$, and
(b) potential energy of this system.

Q. (a) Show using a proper diagram how unpolarised light can be linearly polarised by reflection from a transparent glass surface.
(b) The figure shows a ray of light falling normally on the face $AB$ of an equilateral glass prism having refractive index $\frac{3}{2}$, placed in water of refractive index $\frac{4}{3}$. Will this ray suffer total internal reflection on striking the face $AC$? Justify your answer.

Q. Two electric bulbs $P$ and $Q$ have their resistances in the ratio of $1:2$. They are connected in series across a battery. Find the ratio of the power dissipation in these bulbs.

Q. The teacher of Geeta's school took the students on a study trip to a power generating station, located nearly $200km$ away from the city. The teacher explained that electrical energy is transmitted over such a long distance to their city, in the form of alternating current (ac) raised to a high voltage. At the receiving end in the city, the voltage is reduced to operate the devices. As a result, the power loss is reduced. Geeta listened to teacher and asked questions about how the ac is converted to a higher or lower voltage.
(a) Name the device used to change the alternating voltage to a higher or lower value. State one cause for power dissipation in this device.
(b) Explain with an example, how power loss is reduced if the energy is transmitted over long distance as an alternating current rather than a direct current.
(c) Write two values each shown by the teachers and Geeta.

Q. A $10V$ cell of negligible internal resistance is connected in parallel across a battery of emf $200V$ and internal resistance $38\Omega$ as shown in the figure. Find the value of current in the circuit.

Q. Draw graphs showing variation of photoelectric current with applied voltage for two incident radiations of equal frequency and different intensities. Mark the graph for the radiation of higher intensity.

Q. (a )Use Gauss' law to derive the expression for the electric field $\left(\overrightarrow{E}\right)$ due to a straight uniformly charged infinite line of charge density $\lambda \left(C/m\right)$.
(b) Draw a graph to show the variation of $E$ with perpendicular distance $r$ from the line of charge.
(c) Find the work done in bringing a charge $q$ from perpendicular distance $r_1$ to $r_2(r_2>r_1)$.

Q. (a) Draw a ray diagram to show image formation when the concave mirror produces a real, inverted and magnified image of the object.
(b) Obtain the mirror formula and write the expression for the linear magnification.
(c) Explain two advantages of a reflecting telescope over a refracting telescope.

Q. (a) Three point charges $q,-4q$ and $2q$ are placed at the vertices of an equilateral triangle $ABC$ of side ${}^{\prime }{l}^{\prime }$ as shown in the figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge $q$.
(b) Find out the amount of the work done to separate the charges at infinite distance.

Q. (a) State Bohr's postulate to define stable orbits in hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?
(b) A hydrogen atom initially in the ground state absorbs a photon which excites it to the $n=4$ level. Estimate the frequency of the photon.

Q. A proton and an electron travelling along parallel paths enter a region of uniform magnetic field, perpendicular to their paths. Which of them will move in a circular path with higher frequency?

Q. (a) Define a wavefront. Using Huygen's principle, verify the laws of reflection at a plane surface.
(b) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction bond? Explain.
(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the obstacle. Explain why.

Q. (a) Explain the processes of nuclear fission and nuclear fusion by using the plot of binding energy per nucleon (BE/A) versus the mass number $A$.
(b) A radioactive isotope has a half-life of $10$ years. How long will it take for the activity to reduce to $3.125$%?

Q. A carrier wave of peak voltage $15V$ is used to transmit a message signal. Find the peak voltage of the modulating signal in order to have a modulation index of $60$%.

Q. (a) A student wants to use two $p-n$ junction diodes to convert alternating current into direct current. Draw the labelled circuit diagram she would use and explain how it works.
(b) Give the truth table and circuit symbol for NAND gate.

Q. (a) An iron ring of relative permeability ${\mu }_r$ has windings of insulated copper wire of $n$ turns per metre. When the current in the windings is $I$, find the expression for the magnetic field in the ring.
(b) The susceptibility of a magnetic material is $0.9853$. Identify the type of magnetic material. Draw the modification of the field pattern on keeping a piece of this material in a uniform magnetic field.

Q. If light of wavelength $412.5nm$ is incident on each of the metals given below, which ones will show photoelectric emission and why?

Metal	Work Function (eV)
$Na$	$1.92$
$K$	$2.15$
$Ca$	$3.20$
$Mo$	$4.17$

Q. (a) Why are infra-red waves often called heat waves? Explain.
(b) What do you understand by the statement, "Electromagnetic waves transport momentum"?

Q. Which mode of propagation is used by short wave broadcast services?

Q. (a) Give three reasons why modulation of a message signal necessary for long distance transmission.
(b) Show graphically an audio signal, a carrier wave and an amplitude modulated wave.

Q. Four nuclei of an element undergo fusion to form a heavier nucleus, with release of energy. Which of the two - the parent or the daughter nucleus - would have higher binding energy per nucleon?

Q. Draw the typical input and output characteristic of an $n-p-n$ transistor in $CE$ configuration. Show how these characteristics can be used to determine (a) the input resistance $\left(r_i\right)$, and (b) current amplification factor $\left(\beta \right)$.

Q. In a potentiometer arrangement for determining the emf of a cell, the balance point of the cell in open circuit is $350cm$. When a resistance of $9\Omega$ is used in the external circuit of the cell, the balance point shifts to $300cm$. Determine the internal resistance of the cell.

Q. A device $X$ is connected across an ac source of voltage $V=V_0\sin \omega t$. The current through $X$ is given as $I=I_0\sin (\omega t+\frac{\pi }{2})$.
(a) Identify the device $X$ and write the expression for its reactance.
(b) Draw graphs showing variation of voltage and current with time over one cycle of ac, for $X$.
(c) How does the reactance of the device $X$ vary with frequency of the ac? Show this variation graphically.
(d) Draw the phasor diagram for the device $X$.

Q. (a) Define electric flux. Is it a scalar or a vector quantity?
A point charge $q$ is at a distance of $d/2$ directly above the centre of a square of side $d$, as shown in the figure. Use Gauss' law to obtain the expression for the electric flux through the square.
(b) If the point charge is now moved to a distance ${}^{\prime }{d}^{\prime }$ from the centre of the square and the side of the square is doubled, explain how the electric flux will be affected.

Q. Name the electromagnetic radiations used for (a) water purification, and (b) eye surgery.

Q. (a) State the principle of an ac generator and explain its working with the help of a labelled diagram. Obtain the expression for the emf induced in a coil having $N$ turns each of cross-sectional area $A$, rotating with a constant angular speed ${}^{\prime }{\omega }^{\prime }$ in a magnetic field $\overrightarrow{B}$, directed perpendicular to the axis of rotation.
(b) An aeroplane is flying horizontally from west to east with a velocity of $900km/hour$. Calculate the potential difference developed between the ends of its wings having a span of $20m$. The horizontal component of the Earth's magnetic field is $5\times {10}^{-4}T$ and the angle of dip is ${30}^{\circ }$.