#### Alternate Sets

Define capacitor reactance. Write its S.I units.

Concept: Capacitors and Capacitance

What is the electric flux through a cube of side 1 cm which encloses an electric dipole?

Concept: Electric Flux

A concave lens of refractive index 1.5 is immersed in a medium of refractive index 1.65. What is the nature of the lens?

Concept: Lenses

How are side bands produced?

Concept: Modulation and Its Necessity

Graph showing the variation of current versus voltage for a material Ga As is shown in the figure. Identify the region of

(i) negative resistance

(ii) where Ohm's law is obeyed.

Concept: Ohm’s Law

A proton and an α-particle have the same de-Broglie wavelength. Determine the ratio of their accelerating potentials

Concept: de-Broglie Relation

A proton and an α-particle have the same de-Broglie wavelength Determine the ratio of their speeds.

Concept: Wave Nature of Matter

Show that the radius of the orbit in hydrogen atom varies as *n*^{2}, where *n* is the principal quantum number of the atom.

Concept: De Broglie’S Explanation of Bohr’S Second Postulate of Quantisation

Distinguish between 'intrinsic' and 'extrinsic' semiconductors

Concept: Extrinsic Semiconductor

Use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f.

Concept: Ray Optics - Mirror Formula

Find an expression for intensity of transmitted light when a polaroid sheet is rotated between two crossed polaroids. In which position of the polaroid sheet will the transmitted intensity be maximum?

Concept: Polarisation

Use Kirchhoff's rules to obtain conditions for the balance condition in a Wheatstone bridge.

Concept: Kirchhoff’s Rules

Identify the part of the electromagnetic spectrum which is suitable for radar system used in aircraft navigation.

Concept: Electromagnetic Spectrum

Name the parts of the electromagnetic spectrum which is

used to treat muscular strain.

Write in brief, how these waves can be produced.

Concept: Electromagnetic Spectrum

Name the parts of the electromagnetic spectrum which is

used as a diagnostic tool in medicine.

Write in brief, how these waves can be produced.

Concept: Electromagnetic Spectrum

A giant refracting telescope has an objective lens of focal length 15 m. If an eye piece of focal length 1.0 cm is used, what is the angular magnification of the telescope ?

Concept: Optical Instruments - The Microscope

If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens ? the diameter of the moon is 3.48 × 10^{6} m and the radius of lunar orbit is 3.8 × 10^{8}m.

Concept: Optical Instruments - The Microscope

Write Einstein's photoelectric equation and mention which important features in photoelectric effect can be explained with the help of this equation.

The maximum kinetic energy of the photoelectrons gets doubled when the wavelength of light incident on the surface changes from *λ*_{1} to *λ*_{2}. Derive the expressions for the threshold wavelength *λ*_{0} and work function for the metal surface.

Concept: Einstein’s Equation - Particle Nature of Light

In the study of Geiger-Marsdon experiment on scattering of α particles by a thin foil of gold, draw the trajectory of α-particles in the coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study.

From the relation *R* = *R*_{0} *A*^{1}^{/3}, where *R*_{0} is constant and *A* is the mass number of the nucleus, show that nuclear matter density is independent of *A*

Concept: Atomic Masses and Composition of Nucleus

Distinguish between nuclear fission and fusion. Show how in both these processes energy is released. Calculate the energy release in MeV in the deuterium-tritium fusion reaction :

`""_1^2H+_1^3H->_2^4He+n`

Using the data :

m(`""_1^2H`) = 2.014102 u

m(`""_1^3H`) = 3.016049 u

m(`""_2^4He`) = 4.002603 u

m_{n} = 1.008665 u

1u = 931.5 MeV/c^{2}

Concept: Nuclear Energy - Nuclear Fusion – Energy Generation in Stars

Draw a block diagram of a detector for AM signal and show, using necessary processes and the waveforms, how the original message signal is detected from the input AM wave.

Concept: Amplitude Modulation

A cell of emf '*E*' and internal resistance '*r*' is connected across a variable load resistor R. Draw the plots of the terminal voltage *V* versus (i) *R* and (ii) the current *I*.

It is found that when *R* = 4 Ω, the current is 1 A and when R is increased to 9 Ω, the current reduces to 0.5 A. Find the values of the emf *E* and internal resistance r.

Concept: Cells, Emf, Internal Resistance

Two capacitors of unknown capacitances C_{1} and C_{2} are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of C_{1} and C_{2}. Also calculate the charge on each capacitor in parallel combination.

Concept: Combination of Capacitors

Write the underlying principle of a moving coil galvanometer.

Concept: Moving Coil Galvanometer

A galvanometer of resistance *G* is converted into a voltmeter to measure upto *V* volts by connecting a resistance *R*_{1} in series with the coil. If a resistance *R*_{2} is connected in series with it, then it can measures upto *V*/2 volts. Find the resistance, in terms of *R*_{1} and *R*_{2}, required to be connected to convert it into a voltmeter that can read upto 2 V. Also find the resistance *G* of the galvanometer in terms of *R*_{1} and *R*_{2}

Concept: Moving Coil Galvanometer

With what considerations in view, a photodiode is fabricated? State its working with the help of a suitable diagram.

Even though the current in the forward bias is known to be more than in the reverse bias, yet the photodiode works in reverse bias. What is the reason?

Concept: Special Purpose P-n Junction Diodes

Draw a circuit diagram of a transistor amplifier in CE configuration.

Concept: Junction Transistor - Transistor as an Amplifier (Ce-configuration)

Define the terms : Input resistance How are these determined using typical input and output characteristics?

Concept: Junction Transistor - Transistor as an Amplifier (Ce-configuration)

Define the terms :Current amplification factor. How are these determined using typical input and output characteristics?

Concept: Junction Transistor - Transistor: Structure and Action

In a double slit experiment using the light of wavelength 600 nm, the angular width of the fringe formed on a distant screen is 0.1°. Find the spacing between the two slits.?

Concept: Interference of Light Waves and Young’S Experiment

Light of wavelength 5000 Å propagating in air gets partly reflected from the surface of water. How will the wavelengths and frequencies of the reflected and refracted light be affected?

Concept: Refraction

An inductor *L* of inductance *X _{L}* is connected in series with a bulb B and an ac source. How would brightness of the bulb change when (i) number of turn in the inductor is reduced, (ii) an iron rod is inserted in the inductor and (iii) a capacitor of reactance

*X*=

_{C}*X*is inserted in series in the circuit? Justify your answer in each case.

_{L}Concept: Reactance and Impedance

A group of students while coming from the school noticed a box marked "Danger H.T. 2200 V" at a substation in the main street. They did not understand the utility of a such a high voltage, while they argued, the supply was only 220 V. They asked their teacher this question the next day. The teacher thought it to be an important question and therefore explained to the whole class.

Answer the following questions:

(i) What device is used to bring the high voltage down to low voltage of a.c. current and what is the principle of its working ?

(ii) Is it possible to use this device for bringing down the high dc voltage to the low voltage? Explain

(iii) Write the values displayed by the students and the teacher.

Concept: Transformers

State Ampere’s circuital law

Concept: Ampere’s Circuital Law

Use this law to obtain the expression for the magnetic field inside an air cored toroid of average radius '*r*', having '*n*' turns per unit length and carrying a steady current *I*.

Concept: Solenoid and the Toroid - the Solenoid

An observer to the left of a solenoid of N turns each of cross section area 'A' observes that a steady current I in it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of magnetic moment *m* = NIA.

Concept: Solenoid and the Toroid - the Solenoid

Define mutual inductance and write its S.I. units

Concept: Inductance - Mutual Inductance

Derive an expression for the mutual inductance of two long co-axial solenoids of same length wound one over the other,

Concept: Solenoid and the Toroid - the Solenoid

In an experiment, two coils c_{1} and c_{2} are placed close to each other. Find out the expression for the emf induced in the coil c_{1} due to a change in the current through the coil c_{2}.

Concept: Inductance - Mutual Inductance

Using Huygens's construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a monochromatic beam of light is incident normally.

Concept: Huygens Principle

Show that the angular width of the first diffraction fringe is half that of the central fringe.

Concept: Interference of Light Waves and Young’S Experiment

Explain why the maxima at `theta=(n+1/2)lambda/a` become weaker and weaker with increasing *n*

Concept: Fraunhofer Diffraction Due to a Single Slit

A point object 'O' is kept in a medium of refractive index *n*_{1} in front of a convex spherical surface of radius of curvature *R* which separates the second medium of refractive index *n*_{2} from the first one, as shown in the figure

Draw the ray diagram showing the image formation and deduce the relationship between the object distance and the image distance in terms of *n*_{1}, *n*_{2} and *R*.

When the image formed above acts as a virtual object for a concave spherical surface separatig the medium *n*_{2} from *n*_{1} (*n*_{2} > *n*_{1}), draw this ray diagram and write the similar (similar to (a)) relation. Hence obtain the expression for the lens maker's formula.

Concept: Lensmaker's Formula

An electric dipole of dipole moment`vecp` consists of point charges +*q *and −*q* separated by a distance 2*a* apart. Deduce the expression for the electric field `vecE` due to the dipole at a distance *x* from the centre of the dipole on its axial line in terms of the dipole moment `vecp`. Hence show that in the limit x>> a, `vecE->2vecp"/"(4piepsilon_0x^3)`

Concept: Electric Dipole

Given the electric field in the region `vecE=2xhati`, find the net electric flux through the cube and the charge enclosed by it.

Concept: Electric Flux

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.

Concept: Dielectrics and Polarisation

Define the terms polarization of a dielectric and write its relation with susceptibility.

Concept: Dielectrics and Polarisation

A thin metallic spherical shell of radius *R *carries a charge *Q* on its surface. A point charge`Q/2` is placed at its centre C and an other charge +2*Q* is placed outside the shell at a distance *x* from the centre as shown in the figure. Find (i) the force on the charge at the centre of shell and at the point A, (ii) the electric flux through the shell.

Concept: Uniformly Charged Infinite Plane Sheet and Uniformly Charged Thin Spherical Shell (Field Inside and Outside)