Q. Define mobility of a charge carrier. What is its relation with relaxation time?

Q. (i) When an AC source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero.
(ii) A bulb is connected in series with a variable capacitor and an AC source as shown. What happens to the brightness of the bulb when the key is plugged in and capacitance of the capacitor is gradually reduced?

Q. (i) Distinguish between a conductor and a semi conductor on the basis of energy band diagram
(ii) The following figure shows the input waveforms (A, B) and the output waveform (Y) of a gate. Identify the gate, write its truth table and draw its logic symbol.

Q. Why can't we see clearly through fog? Name the phenomenon responsible for it.

Q.

Q. How are electromagnetic waves produced? What is the source of energy of these waves? Write mathematical expressions for electric and magnetic fields of an electromagnetic wave propagating along the z-axis. Write any two important properties of electromagnetic waves.

Q. (i) A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20 cm. Calculate the focal length of the lens used.
(ii) A converging lens is kept coaxially in contact with a diverging lens - both the lenses being of equal focal length. What is the focal length of the combination?

Q. Calculate the wavelength of radiation emitted when electron in a hydrogen atom jumps from $n=\infty$ to $n=1$.

Q. Find the electric field intensity due to a uniformly charged spherical shell at a point (i) outside the shell and (ii) inside the shell. Plot the graph of electric field with distance from the centre of the shell.

Q. A signal of $5kHz$ frequency is amplitude modulated on a carrier wave of frequency $2MHz$. What are the frequencies of the side bands produced?

Q. (a) Why unpolarised light from a source do not show a variation in intensity when viewed through a polaroid which is rotated? Show with the help of a diagram, how unpolarised light from Sun gets linearly polarised by scattering.
(b) Three identical polaroid sheets $P_1,P_2$ and $P_3$ are oriented so that the pass axis of $P_2$ and $P_3$ are inclined at angles of ${60}^o$ and ${90}^o$ respectively with the pass axis of $P_1$. A monochromatic source S of unpolarised light of intensity $I_0$ is kept in front of the polaroid sheet $P_1$ as shown in the figure. Determine the intensities of light as observed by the observer at O, when polaroid $P_3$ is rotated with respect to $P_2$ at angles $\theta ={30}^o$ and ${60}^o$.

Q. What is space wave propagation? State the factors which limit its range of propagation. Derive an expression for the maximum line of sight distance between two antennas for space wave propagation.

Q. State Amperes circuital law. Use this law to find magnetic field due to straight infinite current carrying wire. How are the magnetic field lines different from the electrostatic field lines?
OR
State the principle of a cyclotron. Show that the time period of revolution of particles in a cyclotron is independent of their speeds. Why is this property necessary for the operation of a cyclotron?

Q. (i) Derive Snells law on the basis of Huygens wave theory when light is travelling from a denser to a rarer medium.
(ii) Draw the sketches to differentiate between plane wavefront and spherical wavefront.

Q. (a) Derive an expression for path difference in Youngs double slit experiment and obtain the conditions for constructive and destructive interference at a point on the screen.
(b) The intensity at the central maxima in Youngs double slit experiment is $I_0$. Find out the intensity at a point where the path difference is $\frac{\lambda }{6},\frac{\lambda }{4}$ and $\frac{\lambda }{3}$.

Q. When is $H_{\alpha }$ line in the emission spectrum of hydrogen atom obtained? Calculate the frequency of the photon emitted during this transition.

Q. (i) Name two important processes that occur during the formation of a pn junction.
(ii) Draw the circuit diagram of a full wave rectifier along with the input and output waveforms. Briefly explain how the output voltage/current is unidirectional.

Q. A proton and an $\alpha$-particle are accelerated through the same potential difference. Which one of the two has (i) greater de-Broglie wavelength, and (ii) less kinetic energy? Justify your answer.

Q. (a) Distinguish with the help of a suitable diagram, the difference in the behaviour of a conductor and a dielectric placed in an external electric field. How does polarised dielectric modify the original external field?
(b) A capacitor of capacitance C is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?
(i) Charge stored by the capacitor.
(ii) Field strength between the plates.
(iii) Energy stored by the capacitor.
Justify your answer in each case.

Q. In a series LCR circuit connected to an a.c. source of voltage $v=v_{m}sin\omega t$, use phasor diagram to derive an expression for the current in the circuit. Hence, obtain the expression for the power dissipated in the circuit. Show that power dissipated at resonance is maximum.

Q. What is the amount of work done in moving a point charge Q around a circular arc of radius 'r' at the centre of which another point charge 'q' is located?

Q. Why is base band signal not transmitted directly? Give any two reasons.

Q. Two identical cells of emf 1.5 V each joined in parallel, supply energy to an external circuit consisting of two resistances of 7 $\Omega$ each joined in parallel. A very high resistance voltmeter reads the terminal voltage of cells to be 1.4 V. Calculate the internal resistance of each cell.

Q. A ray PQ incident on the refracting face BA is refracted in the prism BAC as shown in the figure and emerges from the other refracting face AC as RS such that AQ = AR. If the angle of prism $A={60}^o$ and refractive index of material of prism is $\sqrt{3}$ . Calculate angle $\theta$.

Q. What can be the causes of helical motion of a charged particle?

Q. State two important properties of photon which are used to write Einsteins photoelectric equation. Define (i) stopping potential and (ii) threshold frequency, using Einsteins equation and drawing necessary plot between relevant quantities.

Q. (a) Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus.
(b) How is the mean life of a given radioactive nucleus related to the decay constant?

Q. (a) Explain why, for a charge configuration, the equipotential surface through a point is normal to the electric field at that point ?
Draw a sketch of equipotential surfaces due to a single charge (-q), depicting the electric field lines due to the charge.
(b) Obtain an expression for the work done to dissociate the system of three charges placed at the vertices of an equilateral triangle of side 'a' as shown in the figure.

Q. When 5 V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons is $2.5\times {10}^{-4}$ m/s. If the electron density in the wire is $8\times {10}^{28}{m}^{-3}$, calculate the resistivity of the material of the wire.

Q. Seema's uncle was advised by his doctor to have an MRI (Magnetic Resonance Imaging) scan of his brain. Her uncle felt it to be expensive and wanted to postpone it.
When Seema learnt about this, she took the help of her family and also approached the doctor, who also offered a substantial discount. She then convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The information thus obtained greatly helped the doctor to treat him properly.
Based on the above paragraph, answer the question.