Electric field intensity (E) due to an electric dipole varies with distance (r) of the point from the centre of dipole as:

The correct relation between electric intensity E and electric potential V is 

A closed surface in vacuum encloses charges -q and +3q. Another charge -2q lies outside the surface. Total electric flux over the surface is 

The electric field at a point is

Dipole moment is a ............... quantity and its units are .............

When two capacitors charged to different potentials are connected by a conducting wire, what is not true?

A circular current loop of magnetic moment M is in arbitrary orientation in an external magnetic field.\(\overset { \rightarrow }{ B } \) The work does to rotate the loop by \(30°\)about an axis perpendicular to its plane is

Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?

In an electromagnetic wave, electric and magnetic fields are 200 V/m and 0.365 A/m. The maximum rate of energy flow is 

How much work is done in moving a 500\(\mu C\) charge between two points on an equipotential surface?

The electric field at a point is

S is the surface of a lump of magnetic material.

A metal plate is getting heated. It can be because

The kinetic energy of a photon of frequency v, rest mass.\({ m }_{ 0 }\) having mass m while moving with velocity v is

How is dielectric constant expressed in terms of capacitance of a capacitor ?

When a number of capacitors are connected in parallel between two points, the equivalent capacitance

A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at a/2 and 2 a is

A wire of length 2m moves with a speed of 5m/s perpendicular to a magnetic field of induction 0.1 Wb/m². The e.m.f. induced in the wire is

The total e.m. power of the sun is 

The torque acting on an electric dipole of moment p held at an angle \(\theta\) with an electric field E is ............

1 stat-Coulomb = ......... Coulomb

Two identical current carrying coaxial loops, carry current I in an opposite sense. A simple American loop passes through both of them once. Calling the loop as C,

Q factor of resonance is given by

Which of the following statements about electromagnetic waves is/are correct
(1) X-rays in vacuum travel faster than light waves in vacuum
(2) The energy of x-rays photon is greater than that of a light photon
(3) light can be polarised by x-rays cannot

The test charge used to measure electric field at a point should be vanishingly small.Why?

Electric field due to an electric dipole is

A magnet with moment M is given. If it is bent into a semicircular form, its new magnetic moment will be :

The mutual inductance M₁₂ of coil 1 with respect to coil 2

A flood light is covered with a filter that transmits red light. The electric field of the emerging beam is represented by a sinusoidal wave.
\({ E }_{ x }=36\quad sin\quad (1.20\times { 10 }^{ 7 }z=3.6\times { 10 }^{ 15 }t)\quad V/m\)
the average intensity of the beam is watt/\({ (metre) }^{ 2 }\) will be:

Does the charge given to a metallic sphere depend on whether it is hollow or solid? Give reason for your answer.

Force \(\overrightarrow { F } \) acting on a test charge q_o  in a uniform electric field \(\overrightarrow { E } \) is

In a cyclotron a charged particle 

Out of the following, choose the correct relation

An EM wave of intensity I falls on a surface kept in vacuum and experts radiation pressure kept in vacuum and experts radiation pressure p on it. Which of the following are true?

Two electrically charged particles, having charges of different magnitudes, when placed at a distance 'd' from each other, experience a force of attraction 'F'. These two particles are put in contact and again placed at the same distance from each other. What is the nature of new force between them? Is the magnitude of the force of interaction between them now more or less than F ?

Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region

In a cyclotron a charged particle 

A transformer is an electric device used for

The electric field intensity produced by the radiations coming from 100 W bulb at a 3m distance is E. The electric field intensity produced by the radiations coming from 50w bulb at the same distance is:  

A spherical shell of radius b with charge Q is expanded to a radius a. Find the work done by the electrical forces in the process.

When air inbetween the plates of a capacitor is replaced by mica of dielectric constant 6, its capacity

The magnetic field at a perpendicular distance of 2 cm from an infinite straight current carrying conductor is 2X10^-6 T. The current in the wire is

The relation \(\frac { { E }_{ s } }{ { E }_{ p } } =\frac { { n }_{ s } }{ { n }_{ p } } \) is applied only to

In an electromagnetic wave, the electric and magnetic fields are 100 V/m and 0.265 A/m. The maximum energy flow per second per unit area will be 

Why is electrostatic potential constant throught the volume of the conductor and has the same value (as inside) on its surface?

The value of absolute electrical permittivity of free space is

In a permanent magnet at room temperature

A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because

A linearly polarized electromagnetic wave given as \(E={ E }_{ 0 }\overset { \wedge }{ i } cos\quad (kz-wt)\) incident wall at \(z=a\) . Assuming that the material of the wall os optically inactive, the reflected wave will be given as

What is electric field intensity inside a cavity of a conductor kept in an electric field?

The dimensional formula of electric flux is 

The value of absolute electrical permittivity of free space is

A circular current loop of magnetic moment M is in arbitrary orientation in an external magnetic field.\(\overset { \rightarrow }{ B } \) The work does to rotate the loop by \(30°\)about an axis perpendicular to its plane is

Two particles X and Y having equal charges after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii \({ R }_{ 1 }\quad and\quad { R }_{ 2 }\) respectively. The ratio of the mass of X to that Y is

The output of a step-down transformer is measured to be 24V when connected to a 12 watt light blub. The value of the peak current is

The SI unit of electric field intensity is 

Which of the following is not an insulator?

A current carrying circular loop of radius R is placed in the x-y plane with centre at the origin. Half of the loop with x>0 is now bent so that it now lies in the y-z plane.

A magnetic needle suspended parallel to a magnetic field requires \(\sqrt { 3 } J\) of work to turn it through \({ 60 }^{ ° }.\) The torque needed to maintain the needle in this position will be :

For an LCR circuit, the power transferred from the driving source to the driven oscillator from the driving source tothe driven oscillator is P = I²Z cos \(\phi \).

Electric field due to a single charge is 

When an electric dipole is held at an angle in a uniform electric field, the net force F and torque \(\tau\) on the dipole are

If a copper wire carries a direct current, the magnetic field associated with the current will be

Two circular coils 1 and 2 are made from the same wire but the radius of the Ist coil twice that of the 2nd coil. What potential difference ratio should be applied across them so that the magnetic field at their centres is the same?

The power factor of an a.c. circuit is given by cos \(\phi \)=

The dimensional formula of electric flux is 

If \(\oint _{ s }^{ }{ E.ds } =0\) over a surface, then

A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at a/2 and 2 a is

A galvanometer having a coil resistance of \(100\Omega \) gives a full scale deflection, when a current of 1 mA is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A is 

Phase difference between voltage across L and C in series is

When an electric dipole is held at an angle in a uniform electric field, the net force F and torque \(\tau\) on the dipole are

What is not true?

A circular coil carrying current behaves as a

Two similar coils of radius R, are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2 I respectively. The resultant magnetic field at the centre will be :

The frequency of a.c. generated depends on

Charge on a body which carries 200 excess electrons is

Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region

In a cyclotron a charged particle 

A charged particle would continue to move with a constant velocity in a region wherein, 

In  a uniform magnetic field of induction B, a wire in the form of semicirclr of radius r rotates about the diameter of the circle with angulat frequency . The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R, then the mean power generated per period of rotation is

Force \(\overrightarrow { F } \) acting on a test charge q_o  in a uniform electric field \(\overrightarrow { E } \) is

The correct relation between electric intensity E and electric potential V is 

Ampere's circuital law can be derived from

In a cyclotron a charged particle 

The cause of induced e.m.f. is

When two capacitors charged to different potentials are connected by a conducting wire, what is not true?

Consider a region inside which there are various types of charges but the total charge is zero. At points outside the region

The magnetic field of earth can be modeled by that of a point dipole placed at the center of the earth. The dipole axis makes an angle of \(11.3°\)with the axis of the earth. At Mumbai, declination is nearly zero. Then,

Two particles each of mass m and charge q are attached to the two ends of a light rigid rod of length 2 R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is

A coil having n turns and resistance R is connected with a galvanometer of resistance 4R . This combination is moved in time t seconds from a magnetic flux \({ \phi }_{ 1 }\) Weber to \({ \phi }_{ 2 }\) Weber. The induced current in the circuit is :

Electric field intensity (E) due to an electric dipole varies with distance (r) of the point from the centre of dipole as:

If \(\oint _{ s }^{ }{ E.ds } =0\) over a surface, then

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude

A particle of mass m and charge q is accelerated through a potential difference V to a velocity \(\vec { \upsilon } \) towards south. The particle enters a region with both a magnetic field \(\vec { B } \) (pointing eastwards) and electric field \(\vec { E } \) (pointing downwards). The particle travels with a constant velocity through this region. The potential difference V through this region should be equal to

SI unit of magnetic flux is

Electric dipole moment is

A condenser is charged to double its initial potential. The energy stored in the condenser becomes x times, where x=

A long straight wire of radius a carries a steady current i. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at a/2 and 2 a is

A galvanometer of resistance \(25\Omega \) is connected to a battery of 2 volt along with a resistance in series. When the value of this resistance is \(3000\Omega ,\) a full scale deflection of 30 units is obtained in the galvanometer. In order to reduce this deflection 10 20 units, the resistance in series will be

Q factor of resonance is given by

A Concave mirror form the real image of an object which is magnified 4 times. The object is moved 3 cm away, the magnification of the image is 3 times. What is the focal length of the mirror?

A 4 cm thick layer of water covers a 6 cm thick glass slab. Acoin placed at the bottom of the slab and is being observed from the air side along the normal to the surface. Find the apprent position of the coin from

If in a plano-convex lens, radius of curvature of convex surface is 10 cm and the focal length of the lens is 30 cm. The refractive index of the material of the lens will be

Two lamps of powers \({ P }_{ 1 }\)and \({ P }_{ 2 }\) are placed on either side of apaper having an oil spot. The lamps are at 1m and 2 m respectively, On either side of the paper and the oil spot is invisible. What is the value of  \({ P }_{ 1 }/{ P }_{ 2 }\)?

Frequencies in the UHF range normally propagate by means of:

A speech signal of 3kHz is used to modulate a carrier signal of frequency 1MHz, using amplitude modulation.The frequencies of the sidebands will be

Identify the mathematical expression for amplitude modulated wave:

Audio sine waves of 3kHz frequency are used to amplitude modulate a carrier signal of 1.5 MHz. Which of the following statements are true?

Out of the following, which is not an essential element of a communication system?

In good conductorsof electricity the type of bonding that exists is

In a \(p\)-type semiconductor the acceptor level is situated 60m eV above the valence band.The maximum wavelength of light required to produce a hole will be [use \(hc=12400 eVA\)

In the middle of the depletion layer of a review biased \(p-n \) junction,the 

An \(n-p-n\) transistor having a.c. current gain of 50 to be used to make an amplifier of power gain of 300.What will be the voltage gain of the amplifier

For transistor amplifier,the voltage gain

Taking the Bohr radius as a₀=53pm, the radius of Li⁺⁺ ion its ground state, on the basis of Boh''s model, will be about

The Bohr model for the spectre of a H-atom

Two H atoms in the ground state collide inelastically. The maximum amount by which their combined kinetic energy is reduced is

An electron (mass \(m\)) with an initial velocity \(v={ v }_{ 0 }\vec { i } ({ v }_{ 0 }>0)\quad \) is an electric field \(v={ v }_{ 0 }\vec { i } ({ v }_{ 0 }>0)\quad \) its de-Broglie wave-length at time \(t\) is given by

A and B are two metals with threshold frequencies \(1.8\times { 10 }^{ 14 }Hz\)and \(2.2\times { 10 }^{ 14 }Hz\)Two identical photons of energy 0.825 eV each are incident on them.Then photoelectrons are emitted in (take \(h=6.63\times { 10 }^{ -34 }J/s\)

Silver has a work function of 4.7eV when ultraviolet light of wavelength 100 nm is incident upon it, a potential 0f 7.7 is required to stop the photoelectrons from reaching the collector plate.How much potential will be required to stop the photoelectrons when light of wavelength 200 nm is incident upon silver? 

 The wavelength of a KeV photon is \(1.24\times { 10 }^{ -9 }m\) .What is the frequency of 1 MeV photon?

If v is frequency,\(\lambda \)is the wavelength and \(\overline { v } \)is the wave number then the energy of a photon can be represented by 

In a young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case

Consider the diffraction pattern for a small pinhole. As the size of the hole is increased

Which is not true for the image formed in a plane mirror? The image is 

Refractive index of glass w.r.t. water is 9/8. What is the speed of light in water? Given speed of light in glass is \(2\times 10^{ 8 }\quad m/s\) .

An astronomical telescope has a magnifying power of 10. In normal adjustment, distance between the objective and eye piece is 22 cm. The focal length of objective lens is

A linearly polarized electromagnetic wave given as \(E={ E }_{ 0 }\overset { \wedge }{ i } cos\quad (kz-wt)\) incident wall at \(z=a\) . Assuming that the material of the wall os optically inactive, the reflected wave will be given as

 An \(EM\) wave radiates out waves from a dipole antenna, with \(E_{ 0 }\) as the amplitude of its electric field vector. The electric field \(E_{ 0 }\) which transports significant energy from the source falls off as:

The source of electromagnetic waves can be a charge

An EM wave of intensity I falls on a surface kept in vacuum and experts radiation pressure kept in vacuum and experts radiation pressure p on it. Which of the following are true?

The velocity of light in vacuum can be changed by changing

In the relation \(\phi \) = BA cos \(\theta \), \(\theta \) is angle........

Out of the following, choose the correct relation

Phase difference between voltage across L and C in series is

The relation \(\frac { { E }_{ s } }{ { E }_{ p } } =\frac { { n }_{ s } }{ { n }_{ p } } \) is applied only to

An e.m.f. is produced in a coil, which is not connected to an external voltage source. This can be due to 

The magnetic field at a perpendicular distance of 2 cm from an infinite straight current carrying conductor is 2X10^-6 T. The current in the wire is

Ampere's circuital law can be derived from

A circular coil carrying current behaves as a

A circular current loop of magnetic moment M is in arbitrary orientation in an external magnetic field.\(\overset { \rightarrow }{ B } \) The work does to rotate the loop by \(30°\)about an axis perpendicular to its plane is

A toroid of n turns, mean radius R and cross-sectional radius carries a current I. It is placed on a horizontal table taken as x-y plane. Its magnetic moment \(\overset { \rightarrow }{ M } \)

A steady current is flowing in a cylindrical conductor. Is there any electric field within the conductor?

How can you keep a constant current inside a conductor?

What is the resistance of carbon resistor on which the colour of rings in sequence is black, brown, black and gold.

A 10Ω thick wire is stretched so that its length becomes three times. Assuming that there is no change in its density on stretching. Calculate the resistance of new wire

You are given 8 \(\Omega \) resistor. What length of wire of resistance 120 Ωm-1 should be joined in parallel with it to get a value of 6 \(\Omega \) ?

The SI unit of electric field intensity is 

Electric field intensity (E) due to an electric dipole varies with distance (r) of the point from the centre of dipole as:

Electrostatic potential V at a point, distant r from a charge q varies as

1 stat-Coulomb = ......... Coulomb

If \(\oint _{ s }^{ }{ E.ds } =0\) over a surface, then

Electric dipole moment is

Potential energy of an electric dipole held at an angle \(\theta\) in a uniform electric field is zero when \(\theta=\)

A closed surface in vacuum encloses charges -q and +3q. Another charge -2q lies outside the surface. Total electric flux over the surface is 

Which of the following is not an insulator?

The cause of charging is actual transfer of protons

How rubbing of the two bodies produces electricity?

The electric field by E = \({1000\over r}Vm^{-1}\), and is directed outwards. What is the sign of the charge on the wire? If two points A and B are situated such that \(r_A=0.2m\) and \(r_B=0.4m\), find the value of \((V_B-V_A)\).

Three charges (all q = 10 C) are placed at the edge of an equilateral triangle of side 2 m. Find the net potential energy of the system.

A capacitor of 200 pF is charged by a 300 V battery. The battery is then disconnected and the charge capacitor is connected to another uncharged capacitor 0f 100 pF. Calculate the difference between the final energy stored in the combined system and the initial energy stored in the single capacitor.  The difference between the final energy stored in combined system and initial energy stored in single capacitor is equal to loss in energy  \((=\frac { { C }_{ 1 }{ C }_{ 2 }\left( { V }_{ 1 }-{ V }_{ 2 } \right) ^{ 2 } }{ 2\left( { C }_{ 1 }+{ C }_{ 2 } \right) } )\)

Using Gauss's theorem, deduce an expression for the electric field intensity at any point due to a thin, infinitely long wire of charge/length '\(\lambda\)' C\m

A rectangular coil of n turns each of area A, carrying current I, when suspended in a uniform magnetic field B, experiences a torque
\(\tau =nI\quad BA\quad sin\theta \)
Where is \(\theta \) the angle which a normal drawn on the plane of coil makes with the direction of magnetic field. This torque tends to rotate the coil and bring it in an equilibrium position. In the stable equilibrium state, the resultant force on the coil is zero. The torque on the coil is also zero and the coil has minimum potential energy.
Read the above passage and answer the following questions:
(i) In which position, a current carrying coil suspended in uniform magnetic field experiences (a) minimum torque and (b) maximum torque?
(ii) a circular coil of 200 turns, radius 5 cm carries a current of 2.0 A. It is suspended vertically in a uniform horizontal magnetic field of 0.20 T, with the plane of the coil making an angle with \(60°\) the field lines. Calculate the magnitude of the torque that must be applied on it to prevent it from turning.
(iii) what is the basic value displayed by the above study?

Derive the expression for the energy stored in parallel plate capacitor. Hence, obtain the expression for the energy density of the electric field.
A fully charged parallel plate capacitor is connected across an uncharged identical capacitor.Show that the energy stored in the combination is less than stored initially in the single capacitor.

In Akash's classroom the fan above the teacher was running very slowly. Due to which his teacher was sweating and was restless and tired. All his classmates wanted to rectify this. They called for an electrician who came and changed the capacitor only after which the fan started running fast.
(a) What values did Akash and his classmates have?
(b) What energy is stored in the capacitor and where?

A student has to study the input and output characteristics of a n-p-n silicon transistor in the Common Emitter configuration. What kind of a circuit arrangement should she use for this purpose? Draw the typical shape of input characteristics likely to be obtained by her. What do we understand by the cut off, active and saturation states of the transistor? In which of these states does the transistor not remain when being used as a switch?

Two point charges \(+4\mu C\) and \(-6\mu C\) are separated by a distance of 20cm in air .At what point on the line joining the two charges is the electric potential zero?

Give four properties of electric charges.

If the potential difference across a capacitor is doubled, what happens to : (a) the charge on the capacitor and (b) the energy stored in the capacitor

Ordinary rubber is an insulator. But the special rubber tyres of aircraft's are made slightly conducting. Why is this necessary?

An electric dipole is held in an uniform electric field. Using suitable diagram, show at it doesn't undergo any translatory motion, and (ii) derive an expression for torque acting on it and specify its direction.

At 0^oC, the resistance of a conductor B is n times that of conductor A.  The temperature coefficients of resistance of A and B are \(\alpha_1\) and \(\alpha_2\) respectively. For the series combination of the two conductors find (a) the resistance at 0^oC (b) the temperature coefficient of resistance.

The refractive index of water is 4/3. Obtain the value of the semivertical angle of the cone within which the entire outside view would be confined for a fish under water. Draw an appropriate ray diagram

A lens forms a real image of an object. The distance of the object to the lens is 4 cm and the distance of the image from the lens is v cm. The given graph shows the variation of v with u. (i) What is the nature of the lens? (ii) Using this graph, find the focal length of this lens.

A ray of light passes through an equilateral glass prism, such that the angle of incidence is equal to the angle of emergence. If the angle of emergence is ¾ times the angle of the prism, Calculate the refractive index of the glass prism

(a) A point object is placed in front of a double convex lens (of refractive index n =n₂/n₁ with respect air) with its spherical faces of radii of curvature R₁ and R_2.. Show the path of rays due to surface to obtain the formation of the real image of the object.
Hence obtain the lens maker's formula for a thin lens.
(b) A double convex lens having both faces of the same radius of curvature has refractive index 1.55. Find out the radius of curvature of the lens required to get the focal length of 20 cm.

Light of wavelength \(5000\overset { \circ }{ A } \) falls on a plane reflecting surface. What are the wavelength and frequency of reflected light? For what angle of incidence is the reflected ray normal to the incident ray?

A parallel plate capacitor has circular plates each of radius 6.0 cm. It is charged such that the electric field in the gap between its plates rises constantly at the rate of 10¹⁰ V cm^-1 s^-1. What is the displacement current?

There is a parallel plate capacitor of capacitance \(2.0\mu F.\) The voltage between the plates of parallel plate capacitor is changing at the rate of 6.0 V s^-1 . What is the displacement current in the capacitor?

How would you establish an instantaneous displacement current of 2.0 A in the space between the two parallel plates of \(1\mu F\) capacitor?

A plane electromagnetic wave of frequency 25MHz travels in free space along the x-direction. At a particular point in space and time the electric vector is \(\overrightarrow { E } =6.3V/m\hat { j } \)Calculate \(\overrightarrow { B } \) at this point.

Calculate the peak values of electric and magnetic fields produced by the radiation coming from a 100 watt bulb at a distance of 3 m. Assume that the efficiency of the bulb is 2.5% and it is a point source?

A mahnetic field of flux density 10 T acts normal to a coil of 50 turns having 50cm² area. Find emf induced if the coil is removed from the magnetic field in 0.1sec.

The magnetic flux through a coil is varying according to the relation \(\phi \)=(5t³+4t²+2t-5). Calculate the induced current through the coil at t=2s, if resistance of coil is 5 ohm.

Find the change in current in an inductor of 10 H in which the e.m.f. induced is 300 V in 10^-2 sec. Also, find the change in magnetic flux.

The self inductance of a coil having 200 turns is 10mH. Compute the total flux linked with the coil. Also, determine the magnetic flux through the cross section of the coil, corresponging to curent of 4mA.

Two coils have mutual inductance of 1.5 henry. If current in primary circuit is raised to 5 ampere in one millisecond after closing the circuit, what is the e.m.f. induced in  the secondary?

A current element 3 dl is at (0,0,0) along y-axis. if dl=1 cm, find the magnetic field at a distance 20 cm on the x-axis.

A wire of radius 0.8 cm carries a current of 100 A which is uniformly distributed over its cross-section. Find the magnetic field (a) at 0.2 cm from the axis of the wire (b) at the surface of the wire and (c) at a point outside the wire 0.4 cm from the surface of the wire. Neglect the permeability of the material of wire.

A solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A. What is the magnitude of the magnetic field inside the solenoid ?

A proton enters a magnetic field of flux density 2.5 T with a speed of 1.5 x 10⁷ ms^-1 at an angle of 30^o with the field. Find the force on the proton.

In the arrangement of resistors shown here, what fraction of I will pass through 5\(\Omega\) resistor?

You are given a 8 \(\Omega\) resistor. What length of constant wire of resistance 120\(\Omega\) m^-1 should be joined in parallel with it to get a value of 6\(\Omega\)?

Two identical cells of e.m.f 1.5V each joined in parallel provide supply to an external circuit consisting of two resistors of 17\(\Omega\) each joined in parallel. A very high resistance voltmeter reads the terminal voltage of the cells to be 1.4V. What is the internal resistance of each cell?

Storage battery of a car has an e.m.f of 12V. If the internal resistance of the battery is 0.4\(\Omega\) What is the maximum current that can be drawn from the battery?

Four identical cells, each of emf 2V are joined in parallel providing supply of current to external circuit consisting of two 15\(\Omega\) resistors joined in parallel. The terminal voltage of the cells as read by an ideal voltmeter is 1.6V Calculate the internal resistance of each cell.

A charged Particle q is shot towards another charged particle Q which is fixed , with a speed v. It approaches Q up to a closet distance r and then returns, If q were given a speed 2 v the n find the closet distance of approach.

Two Capacitors of capacitace 6\(\mu \)F and 12\(\mu \)F ae connnected in series with tha battery the volatage across the 6\(\mu \)F capacitor is 2 volt, Compute the total battery voltage.

There is a sphere of radius 20cm.What charge should be given to the sphere so that it acquires a surface charge density of \({ 3 }/{ \pi }{ cm }^{ -2 }\)?

A regular hexagon of side 10 cm has a charge 5\(\mu\) C at each of its vertices.calculate the potential at the hexagon.

Suppose while sitting in a parked car, you notice a jogger approaching towards you in the side view mirror of R = 2 m. If the jogger is running at a speed of 5 m s-1, how fast the image of the jogger appear to move when the jogger is
(a) 39 m,
(b) 29 m,
(c) 19 m, and
(d) 9 m away

A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

A small bulb is placed at the bottom of a tank containing water to a depth of 80cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)

Double-convex lenses are to be manufactured from a glass orefractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be 20 cm?

An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

Mohan went to the market to purchase a TV set.He got confused with so many features and functions of electronic appliances.He took the help of his friend Sohan, a science student.Sohan explained him about the communication system, digital and analog signals.This knowledge proved of great help to Mohan in purchasing a colour TV.
Read the above passage and the answer the following questions:
(i)  What do you mean by the term communication?
Which type of signals are better?
(ii) What type of nature Sohan has?
(iii)What is the minimum number of communication satellites required for global communication coverage?

In the famous conversation, Rakesh Sharma, the first Indian Astronaut in space, was asked by the Prime Minister Indira Gandhi as to how India looked from space.To which he replied,'Sare Jahan Se Achcha' (better than the whole world).
Read the above passage and answer the following questions:
(i)   Which scientific mode of communication enabled the Prime Minister to speak to the Astronaut?
(ii)   Name the scientific values displayed in this anecdote.
(iii) Which values are being reflected in the reply given by the astronaut?
(iv) Give one more example of this scientific mode of communication in everyday life situations.

Arnab was talking on his mobile to his friend for a long time. After his conversation was over, his sister Anita advised him that if his conversation was of such a long duration, it would be better to talk through a land line.
Answer the following questions :
(a) Why is it considered harmful to use a mobile phone for a long duration?
(b) Which values are reflected in the advice of his sister Anita?
(c) A message signal of frequency 10 kHz is superposed to modulate a carrier wave of frequency 1 MHz. Determine the sidebands produced.

Sweta had no proper knowledge about point-to-point communication and broadcast. So, she took help from her friend Rakhi explained him that in point-to-point communication mode, the communication takes place over a link between a single transmitter and a receiver. The example of this mode of communication is telephony. But in broadcast mode, there are a number of receivers corresponding to a single transmitter. The examples of this mode of communication are radio and television. Then Sweta was convinced with answer of Rakhi,
(a) What are the values displayed by Rakhi?b
(b) A message signal of frequency 10 kHz and peak voltage of 10 V is used to modulate a frequency of 1 MHz and peak voltage of 20 V. Determine (i) modulation index (ii) frequency of the side band produced.

When sunita, a class XII student, came to know that her parents are planning to rent out the top floor of their house to a mobile company she protested. She tried hard to convince her parents that this move would be a health hazard.
Ultimately her parents agreed :
  (i)  In what way can the setting up of transmission tower by a mobile company in a residential colony prove to be injurious to health?
 (ii)  By objecting to this move of her parents, what value did Sunita display?
(iii)  Estimate the range of e.m. waves which can be transmitted by an antenna of height 20m.(Given radius of the earth = 6400 km)

Suppose a 'n'-type wafer is created by doping Si crystal having  \(5\times10^{ 28 }\)atoms/\({ m }^{ 3 }\)with 1 ppm concentration of As.On the surface 200 ppm Boron is added to create \('p'\)region in this wafer. Considering \({ n }_{ i }=1.5\times10^{ 16 }m^{ -3 }\) (i) Calculate the densities of the charge carriers in the   \(n\& p\) regions.(ii)Comment which carriers would contribute largely for the reverse saturation current when diode is reverse biased.

Zener diode is a specially designed \(p-n\) junction diode,in which both \(p-side\) and \(n-side\) of \(p-n\)junction are heavily doped.The zener diode is designed to operate in the reverse break down voltage region continuously without being damaged ? Zener diode is used to remove the fluctuations  from the given voltage and thereby provides a voltage of constant magnitude (i.e., zener diode is used as voltage regulator).
Read the above paragraph and answer the following questions :
(i) What is the most important use of Zener diode?
(ii)What are the essential conditions for proper working of Zener diode?
(iii)What do you learn from the above study?

Manoj wanted to do social work during vacations.He visited a remote village where there was no electricity.He made up his mind to help the villagers for getting the solar panels.For this he educated the villagers about techonology and uses of solar panels.he requested the villagers to Villagers agreed and applied for the solar panels.They got the same from government at reduced price.When the solar panels started working,the villagers were happy.
Read the passage and answer the following questions:
(i)What is solar panel?
(ii) What is the basic principle of working of a solar cell?
(iii) What are the basic values you assess in Manoj?

Meeta father was driving her to the school.At the traffic signal she noticed that each traffic light was  made of many lights instead of a single bulb.When Meeta asked this question to her father's he explained the reason for this.
Answer the following questions based on above information:
(i) What were the values displayed by Meeta and her father?
(ii) What are the tiny lights in traffic signals called and how do these operate? 

(i) Differentiate between three segments of a transistor on the basis of their size and level of doping
(ii) How is a transistor biased to be in active state?
(iii) With the help of necessary circuit diagram, describe briefly how n-p-n transistor in CE configuration amplifies a small sinusoidal input voltage. Write the expression for the AC current gain.

How would you set up an instantaneous displacement current of 2.0 A within the space between the two parallel plates of \(3_{ \mu }F\) capacitance?

A parallel plate capacitor is made out of two rectangular metal plates of sides 30 cm \(\times \)15 cm and separated by a distance of 2.0 mm. The capacitor is charged in such a way that the charging current has a constant value of 100 mA. What must be the rate of change of potential of the charging source to ensure this and what will be the displacement current in the region between the capacitor plates?

Nitin and Rajeev were studying the effect of certain radiations on flower plants. Nitin exposed his plants to ultraviolet rays, found that his plants got damaged after few days.Rajeev exposed his plants to infrared rays, found that his plants had a beautiful bloom, after a few days.
Read the above passage and answer the following question:
(i) What is the difference between ultraviolet rays and infrared rays
(ii) Why were the plants exposed to ultraviolet rays damaged and the plants exposed infrared rays had a beautiful bloom?
(iii) What are the basic values you have learnt from this study

Draw a labelled diagram of Hertz's experiment. Explain how electromagnetic radiations are produced using this set-up.

Akil was playing cricket with his friends, when a ball hit friend Bharat on his leg. Bharat screamed with pain. Akhil rushed towards him and comforted him and asked him not to move his leg. He quickly took out his cell phone and called up Bharat's parents and briefed them about the incident. In 10 minutes Bharat was taken to the nearby hospital and was examined by the doctor who advised for an X-rays test which confirmed a hairline fracture.
(a) How are X-rays produced?
(b) Mention one another application of X-rays.
(c) Mention two qualities of Akhil which are reflected from above situation.

Radiation has dual nature,i.e., it possesses the properties of both; wave and particle.This prompted de-Broglie to predict dual nature of moving material particles.Thus waves are associated with moving material particles which are called matter waves. The wavelength of matter wave is given by \(\lambda =\frac { h }{ mv } \), where m is the mass, v is the speed of the particle and h is Plank's constant. Read the above paragraph and answer the following questions;
(i) How was the wave nature of the electron established?
(ii) What are the de-Broglie wavelength associated with a particle (i) at rest (ii) moving with infinite speed?
(iii) What are the basic values displayed with this study?

Mohan thought that there are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. But, can there be stable substances which absorb photons of larger wavelength and emit light of shorter wavelength? He got confused and could not find its answer. Then he requested his friend Sohan. Sohan explained him that in the first case, energy given out is less than the energy supplied. But in the second case, the material has to supply the energy as the emitted photon has to supply the energy as the emitted photon has more energy, which cannot happen for stable substances.
(a) What values do you notice in Sohan?
(b) Consider a metal exposed to light of wavelength 600 nm. The maximum energy of the electron doubles when light of wavelength 400 nm is used. Find the work function in eV.

Ram knows that red light has greater and so it is much bright, but in case of photoelectric emission it cannot produce the emission of electrons from a clean zinc surface, while even weak ultraviolet radiation can do so. He could not know specific cause of such thing. Then he went to his friend Shyam for its specific explanation. Shyam explained him that the photoemission of electron does not depend on the intensity while it depends on the frequency and thus on the energy of photon of incident light. The energy of photon of red light cannot emit photoelectrons. Similarly, the energy of photon of ultraviolet light is greater than the work function of zinc, so ultraviolet light can emit photoelectrons.
(a) What values are noticed in Shyam?
(b) The work functions of lithium and copper are 2.3eV and 4eV respectively. Which of these metals are useful for the photoelectric cell working with visible light? Explain.

A function was organised in the school auditorum. There was 500 sitting arrangement in the auditorium. When entry started, students entered in groups and so counting became a great problem. Then principle of the school ordered science students managed the situation and now all the students used to enter the hall one by one. This helped them to maintain discipline and counting became easy with the help of a scientific device used by these students.
Name the scientific device which is based on application of photoelectric effect.

A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.

A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?

A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is
(a) a convex lens of focal length 20 cm, and
(b) a concave lens of focal length 16 cm?

An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21cm. Describe the image produced by the lens. What happens if the object is moved further away from the lens?

Use the mirror equation to deduce that:
(a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f.
(b) a convex mirror always produces a virtual image independent of the location of the object.
(c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.
(d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.
[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

Zener diode is a specially designed \(p-n\) junction diode,in which both \(p-side\) and \(n-side\) of \(p-n\)junction are heavily doped.The zener diode is designed to operate in the reverse break down voltage region continuously without being damaged ? Zener diode is used to remove the fluctuations  from the given voltage and thereby provides a voltage of constant magnitude (i.e., zener diode is used as voltage regulator).
Read the above paragraph and answer the following questions :
(i) What is the most important use of Zener diode?
(ii)What are the essential conditions for proper working of Zener diode?
(iii)What do you learn from the above study?

Kritika Singh was enjoying TV programme at her home with her younger brother Surya at night. Suddenly, the light went off causing darkness all over. Surya asked her to bring candle along with matchstick to put the TV switch OFF. Kritika at once picked the mobile phone and pressed the button lighting up the surrounding. Her younger brother was surprised and asked, where the light was coming. Kritika proudly showed her mobile.
Read the above passage and answer the following questions:
(i) Which value is displayed by Kritika?
(ii) Name the material used in the formation of LED.
(iii) LED works, in which biasing?

Shorya usually enjoyed loud music. One day his music system was not producing very loud sound. Shorya gets disappointed. He discussed his problem with his big brother Kamal. Kamal advised him to connect an amplifier in series with the amplifier of the stereo system. This increased the sound of Shroya's music system considerably. Read the above passage and answer the following questions:
(i) Which value is displayed by Kamal?
(ii) Why the loudness of music system get increased on connecting amplifier?
(iii) Give the equation for current gain in the transistor as an amplifier.

Sanjay was preparing an electronic project for science exhibition. He required to light the LED using a 6 V supply. LEDs need only a very small current to make them light and they do not heat up in use. So he put a resistor in series to limit the current. Then there would be p.d. of 4 V across the resistor as there is always 2.0 V across the LED itself when it is conducting. The current should be 10 mA through both LED and the resistor. He could use the resistance by equation, R = V/I to calculate the value of R.
\(R=\frac { V }{ I } =\frac { 4V }{ 10mA } =\frac { 4V }{ 0.01A } =400V\)
Thus the protecting resistor should be around 400 \(\Omega \)
(a) What are the values exhibited by Sanjay?
(b) A semiconductor has equal electron and hole concentration of \(6\times 10^{ 8 }/m^{ 3 }\) . On doping with certain impurity, electron concentration increases to \(9\times 10^{ 12 }/m^{ 3 }\) .
(i) Identify the new semiconductor obtained after doping.
(ii) Calculate the new hole concentration.
(iii) How does the energy gap vary with doping?

Anita was thinking that C, Si and Ge have same lattice structure, but C is insulator while Si and Ge are intrinsic semiconductors. For its answer she met her friend Sunita. Sunita explained her that the four bonding electrons of C, Si and Ge lie respectively in the second, third and fourth orbit. So, energy required to take out an electron from these atoms known as ionisation energy Ig will be the least for Ge, followed by Si and the highest for the least for Ge, followed by Si and the highest for C. Hence number of free electrons for conduction in Ge and Si are significant while negligibly small for C.
(a) What are the values shown by Sunita ?
(b) If a pure silicon crystal has \(5\times { 10 }^{ 28 }atoms/{ m }^{ 3 }\). It is doped by 1ppm concentration of pentavalent arsenic.
If n₁ = 1.5 x 10¹⁶/m³, then calculate the number of electrons and holes.

The magnifying power of an astronomical telescope in the normal adjustment position is 100.The distance between the objective and eye piece is 101cm.Calculate the focal lengths of objective and eye piece.

An astronomical telescope is designed to have a magnifying power of 50 in normal adjustment.If the length pf the tube is 120cm, find the powers of objective and eye piece.

Kanchan while driving her scooty sees a woman behind driving a moped through his rear view mirror. She sees that her saree is almost touching the wheels of the vehicle. She stops her and alert that it may cause a severe accident.
Read the above passage and answer the folllowing questions:
(i) What values do you observe in Kanchan?
(ii) Name the mirror used in rear view in scooty. Draw a ray diagram for the same.

Answer the following questions.
(i) You have learnt that plane and convex mirrors produce virtual images of objects. Can they produce real images under some circumstances? Expalin.
(ii) A virtual image, we always say, cannot be caught on a screen. Yet when we see a virtual image, we are obviously bringing it on to the screen (i.e. the retina) of our eye. Is there a contradiction?
(iii) A diver under water, looks obliquely at a fisherman standing on the bank of a lake. Would the fisherman look taller or shorter to the diver than what he actually is?
(iv) Does the apparent depth of a tank of water change, if viewed obliquely? If so, does the apparent depth increase or decrease?

(i) In a double slit experiment using light of wavelength 600 nm, the angular width of the fringe formed on a distant screen is \(0.1^o\) . Find the spacing between the two slits.
(ii) Light of wavelength 5000\(\dot { A } \) 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?

Mohan went to the market to purchase a TV set.He got confused with so many features and functions of electronic appliances.He took the help of his friend Sohan, a science student.Sohan explained him about the communication system, digital and analog signals.This knowledge proved of great help to Mohan in purchasing a colour TV.
Read the above passage and the answer the following questions:
(i)  What do you mean by the term communication?
Which type of signals are better?
(ii) What type of nature Sohan has?
(iii)What is the minimum number of communication satellites required for global communication coverage?

Raj was cycling from his village to a neighbouring village.On the way, he met an old man who was walking in the direction of the same neighbouring village. Raj invited the old man to sit on his cycle and took him to the neighbouring village.The old man got down from the cycle, thanked Raj and gave him blessing.
Read the above passage and answer the following questions:
(i)  What are the values displayed by Raj?
(ii) Can you relate the given paragraph with the process of modulation?

Anuj's mother was having constant headaches. After a medical check-up, she was diagnosed with tumour. Anuj realized there was a telecommunication tower very close to their house. He enquired from the doctor if the radiation from the tower could have caused the tumour. As the doctor supported his anxiety, he lodged a complaint with the police and ultimately succeeded in getting the tower removed to a distant place away the from residential colony?
Answer the following :
(i)  What values were displayed by Anuj?
(ii) Anuj made a rough estimate about the height of the antenna to be 20 m from the ground. Calculate the maximum distance upto which radiations from the tower are likely to reach. Use the value of radius of the Earth = 6400 x 10³ m.

Sweta had no proper knowledge about point-to-point communication and broadcast. So, she took help from her friend Rakhi explained him that in point-to-point communication mode, the communication takes place over a link between a single transmitter and a receiver. The example of this mode of communication is telephony. But in broadcast mode, there are a number of receivers corresponding to a single transmitter. The examples of this mode of communication are radio and television. Then Sweta was convinced with answer of Rakhi,
(a) What are the values displayed by Rakhi?b
(b) A message signal of frequency 10 kHz and peak voltage of 10 V is used to modulate a frequency of 1 MHz and peak voltage of 20 V. Determine (i) modulation index (ii) frequency of the side band produced.

A nuclear reactor is a powerful device, wherein nuclear energy is utilised for peaceful purposes. It is based upon controlled nuclear chain reaction. The nuclear chain reaction is controlled by the use of control rods (of boron or cadmium) and moderators like heavy water, graphite, etc. The whole reactor is protected with concrete walls 2 to 2.5 metre thick, so that radiations emitted during nuclear reactions may not produce harmful effects.
Read the above passage and answer the following questions:
(i) Give any two merits of nuclear reactors.
(ii) What is radiactive waste?
(iii) Why do people often oppose the location site of a nuclear reactor? What do you suggest?

According to Bohr's theory of hydrogen atom, total energy of electron in a stationary orbit is \(E=-\frac { 13.6 }{ { n }^{ 2 } } eV,\) where n is the number of orbit. Clearly, total energy of electron in a stationary orbit is negative, which means the electron is bound to the nucleus and is not free to leave it. An n increases, value of negative energy decreases, i.e., energy is progressively larger in the outer orbits.
Read the above passage and answer the following questions :
(i) What is total energy of electron in ground state of hydrogen atom? What does it imply?
(ii) Energy required to remove an electron is smaller when atoms is in any one excited state. Comment.
(iii) How is this concept translated in day to day life?

On the basis of Bohr's theory of H-atom, total energy of electron in a stationary orbit is given by the relation
Where, n is the number of orbits. It is clear that total energy of electron in a stationary orbit is negative which implies that electron is bound to the nucleus and is not free to leave it. The value of negative energy decreases as n increases.
Read the above p[assagr and answer the following questions:
(i) What is the total energy of electron in ground state of hydrogen atom? What does it indicate?
(ii) Why does energy required to remove an electron is smaller when atom is in any one excited state?

Asha's mother read an article in the newspaper about a disaster that took place at Chernobyl. She could not understand much from the article and asked a few questions from Asha regarding the article.
Asha tried to answer her mother's questions based on what she learnt in Class XII Physics?

Distinguish between reactance and impedance. When a series combination of a coil of inductance L and a resistor of resistance R is connected across a 12 V, 50 Hz supply, a current of 0.5 A flows through the circuit. The current differs in phase from applied voltage by \(\frac { \pi }{ 3 } \) radian. Calculate the value of L and R.

A series LCR circuit with L=0.12 H, C=480 nF, R=23 \(\Omega \) is connected to a 230 V variable frequency supply.
(a) What is the source frequency for which current amplitude is maximum? Obtain this maximum value.
(b) What is the source frequency for which average power absorbed by the circuit is maximum? Obtain the value of this maximum power.
(c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies? 
(d) What is the Q-factor of the given circuit? 

A magnetic field \(\overrightarrow { B } ={ B }_{ 0 }\sin { \left( \omega t \right) } \hat { k } \)  covers a large region where a wire AB slides smoothly over two parallel conductors separated by a distance d. The wires are in the x-y plane. The wire AB (of length d) has resistance R and the parallel wires have negligible resistance. If AB is moving with velocity v. what is the current in the circuit. What is the force needed to keep the wire moving at constant velocity?

What are conservative and non-conservative fields?

What do you mean by quality factor or Q value of resonance circuit?

In the Auger process an atom makes a transition to a lower state without emitting a photon.the excess energy is transferred to an outer electron which may be ejected by the atom.(This is called an Auger electron).Assuming the nucleus to be massive, calculate the kinetic energy of an n=4 Auger electron emitted by Chromium by absorbing the energy from a n=2 to n=1 transition.

A nuclear reactor is a powerful device, wherein nuclear energy is utilised for peaceful purposes. It is based upon controlled nuclear chain reaction. The nuclear chain reaction is controlled by the use of control rods (of boron or cadmium) and moderators like heavy water, graphite, etc. The whole reactor is protected with concrete walls 2 to 2.5 metre thick, so that radiations emitted during nuclear reactions may not produce harmful effects.
Read the above passage and answer the following questions:
(i) Give any two merits of nuclear reactors.
(ii) What is radiactive waste?
(iii) Why do people often oppose the location site of a nuclear reactor? What do you suggest?

Natural radioactivity is a spontaneous and self disruptive activity exhibited by a number of heavy elements in nature. Thus a heavy element disintegrates by itself without being forced by any external agent to do so.
According to radioactive decay law, the number of atoms disintegrated per second (i.e., rate of disintegration of radioactive atoms) at any instant is directly proportional to the number of radioactive atoms actually present in the sample at that instant, i.e., \(-\frac { dN }{ dt } \propto N \ or \ R=-\frac { dN }{ dt } =\lambda N,\) where is \(\lambda \) decay constant.
Read the above passage and answer the following questions :
(i) The count rate from a radioactive sample containing \({ 10 }^{ 16 }\)  atoms is \(4\times { 10 }^{ 16 }\)  per second. What is the value of decay constant?
(ii) Name the three types of radiactive radiations. Which one of them is most penetrating?
(iii) What does radioactive decay law imply in day to day life?
 

Marie Curie and her teacher turned husband Pierre Curie worked hard to extract radium chloride (R_aCl₂) from uranium ore. They succeeded in 192 after a long struggle. About 0.19 g of R_aCl₂ was extracted and its radioactivity was studied. They were awarded by the noble prize, which they shared it which they shared it which they shared it with Henri Becquerel.
Read the above passage and answer following questions:
(i) What are the values shown by Marie Curie and her husband?
(ii) What do you understand by radioactivity? How the half-life period is related to the disintegration constant?
(iii)How is average-life of radioactive element related to half-life?

On the basis of Bohr's theory of H-atom, total energy of electron in a stationary orbit is given by the relation
Where, n is the number of orbits. It is clear that total energy of electron in a stationary orbit is negative which implies that electron is bound to the nucleus and is not free to leave it. The value of negative energy decreases as n increases.
Read the above p[assagr and answer the following questions:
(i) What is the total energy of electron in ground state of hydrogen atom? What does it indicate?
(ii) Why does energy required to remove an electron is smaller when atom is in any one excited state?

Consider a thin target \(({ 10 }^{ -2 }\)m square, \({ 10 }^{ -3 }\)m thickness) of sodium, which produces a photocurrent of \(100\mu A\) when a light of intensity 100w/\({ m }^{ 2 }\) ( \((\lambda =660nm)\) falls on it.Find the probability that a photoelectron is produced when a photon strikes a sodium atom.[Take density of Na=0.97 kg/\({ m }^{ 3 }\)

Radiation has dual nature,i.e., it possesses the properties of both; wave and particle.This prompted de-Broglie to predict dual nature of moving material particles.Thus waves are associated with moving material particles which are called matter waves. The wavelength of matter wave is given by \(\lambda =\frac { h }{ mv } \), where m is the mass, v is the speed of the particle and h is Plank's constant. Read the above paragraph and answer the following questions;
(i) How was the wave nature of the electron established?
(ii) What are the de-Broglie wavelength associated with a particle (i) at rest (ii) moving with infinite speed?
(iii) What are the basic values displayed with this study?

"Know your face beauty through comp[lexion meter" was one of the stall on science exhibition.A student interested to know his/her face beauty was made to stand on a platform and light from a lamp was made to fall on his/her face.The reading of complexion meter indicated the face beauty of the student which might be very fair, fair,semi-fair, semidark dark etc.
(i)What is the basic concept used in the working of complexion meter?
(ii) How is the face beauty recorded by face complexation meter?
(iii) What basic values do you learn from the above study?

Neha's brother was riding the bike on the highway and she was sitting behind him. While sitting, at a place traffic signal turned red from green and her brother continued riding without noticing the signal change. Neha observed the whole situation and asked her brother to stop. Her brother felt happy on his sister's intelligence.
Read above passage and answer the following questions:
(i) Why Neha's brother became happy? What kind of value is expressed by Neha?
(ii) What are the principles that are used in maintaining traffic signals?
(iii) What is the leading physical quantity i8n the process? Write an equation for the speed of the photoelectron.

Mohan thought that there are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. But, can there be stable substances which absorb photons of larger wavelength and emit light of shorter wavelength? He got confused and could not find its answer. Then he requested his friend Sohan. Sohan explained him that in the first case, energy given out is less than the energy supplied. But in the second case, the material has to supply the energy as the emitted photon has to supply the energy as the emitted photon has more energy, which cannot happen for stable substances.
(a) What values do you notice in Sohan?
(b) Consider a metal exposed to light of wavelength 600 nm. The maximum energy of the electron doubles when light of wavelength 400 nm is used. Find the work function in eV.

Discuss relative strengths of electrical and magnetic forces.

Discuss the sensitivity of a moving coil galvanometer.

Find the expression for maximum energy of a charged particle accelerated by a cyclotron.

Explain using a labelled diagram, the principle and working of a moving coil galvanometer. What is the function of
(i) uniform radial magnetic field
(ii) soft iron core?
Also, define the terms
(iii) current sensitivity and
(iv) voltage sensitivity of a galvanometer.
Why does increasing the current sensitivity not necessarily increase voltage sensitivity?

(i) Derive an expression for torque acting on a bar magnet held at an angle \(\theta \) with the direction of magnetic field.
(ii) A bar magnet of magnetic moment 5A-\({ m }^{ 2 }\) has poles 0.20m apart. Calculate the pole strength.

(a) State Ohm's law.

(b) Define resistance. Give its SI unit.

How will you establish the electrons carry current?

Establish the relation between current and drift velocity.

Define the term resistivity and write its S.I. unit. Derive the expression for the resistivity in terms of number density of free electrons and relaxation time.

Ramaniamma was a childless window. She ran her life only by the pension for the Sr. citizens from the Government. When she switches ON one bulb in her house, all the other appliances get switched OFF. She could not even spend for an electrician. Sujatha living nearby decided to do something for her. She referred to Physics books and learned that the series combination for the household connection could be the reason. She called an electrician and had the circuit changed to parallel combination. The problem was solved and Ramaniamma was happy. She thanked Sujatha for her help to solve the problem.
Read the above passage and answer the following questions.
(i) What are the values possessed by Sujatha?
(ii) Why a parallel combination is used for household? Give two advantages.

A rectangular coil of n turns each of area A, carrying current I, when suspended in a uniform magnetic field B, experiences a torque
\(\tau =nI\quad BA\quad sin\theta \)
Where is \(\theta \) the angle which a normal drawn on the plane of coil makes with the direction of magnetic field. This torque tends to rotate the coil and bring it in an equilibrium position. In the stable equilibrium state, the resultant force on the coil is zero. The torque on the coil is also zero and the coil has minimum potential energy.
Read the above passage and answer the following questions:
(i) In which position, a current carrying coil suspended in uniform magnetic field experiences (a) minimum torque and (b) maximum torque?
(ii) a circular coil of 200 turns, radius 5 cm carries a current of 2.0 A. It is suspended vertically in a uniform horizontal magnetic field of 0.20 T, with the plane of the coil making an angle with \(60°\) the field lines. Calculate the magnitude of the torque that must be applied on it to prevent it from turning.
(iii) what is the basic value displayed by the above study?

A physics teacher tells his students in the class that in paramagnetic materials, every atom has some permanent magnetic dipole moment. In the absence of an external magnetic field, the atomic dipoles are randomly oriented so that average magnetic moment per unit volume of the material behaves as a magnet. When an external magnetic field is applied, the torque developed tries to align the atomic magnetic dipoles in the direction of the field. That is why the specimen gets magnetized weekly in the direction of the field.
Read the above passage and answer the following questions:
(i) Name any three paramagnetic materials
(ii) Name any two ferromagnetic materials. How is their behavior different from that of paramagnetic materials?
(iii) The teacher asks the students how true is the famous saying: 'Spare the rod and spoil the child', comment.

Use Gauss's theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density \(\sigma\) .
(ii) An infinitely large thin plane sheet has a uniform surface charge density \(+\sigma\). Obtain the expression for the amount of work done in bringing a point charge q from infinity to a point, distant r, in front of the charged plane sheet.

An electric dipole of dipole moment p consists of point charges +q and q separated by a distance 2a apart. , Deduce the expression for the electric field E due to the dipole at a distance x from the centre of the dipole on its axial line in terms of the dipole moment p. Hence, show that in the limit
x>> a, E \(\longrightarrow\) 2P\((4\pi{\epsilon}_{0}{x}^{3})\).
Given the electric field in the region E = 2x \(\hat{i}\), find the net electric flux through the cube and the charge enclosed by it.

(i) If two similar large plates, each of area A having surface charge densities +σ and -σ are separated by a distance.d in air, find the expression for
(a) field at points between the 'two plates and on outer 'side of the plates. Specify the direction of the field in each case.
(b) the potential difference between the plates.
(c) the capacitance of the capacitor so formed.
(ii) Two metallic spheres of radii R and 2R are charged, so that both of these have same surface charge density σ.  If they are connected to each other with a conducting wire, in which direction will the charge flow and why?

Sea water at frequency \(v=4\times { 10 }^{ 8 }\)Hz has permittivity \(\varepsilon \quad \approx \quad 80\quad { \varepsilon }_{ 0 }\),  permeability \(\mu ={ \mu }_{ 0 }\) and resistivity \(\rho =0.25\quad \Omega -m\) Imagine a parallel plate capacitor immersed in sea water and driven by an alternating voltage source  \(v(t)\quad =\quad { V }_{ 0 }\quad sin\quad (2\pi vt)\) . What fraction of the conduction current density is the displacement current density? 

Discuss the quantitative production of electromagnetic waves when a charge is accelerated.

What are the uses of electromagnetic waves?

A parallel plate capacitor made of circular plates each of radius R=5.0 cm has a capacitance C=96 pF. The capacitor is connected to a 220 V a.c supply with (argular) frequency of 300 rad \({ s }^{ -1 }\) .

A radio can be tuned to any station in the 6 MHz to MHz band. What is the corresponding wavelength between 6 MHz and 9 MHz?

Explain the terms interference of light and define constructive and destructive interference. Is law of conservation of energy obeyed?

Distinguish between interference and diffraction.

The mixture a pure liquid and a solution in a long vertical column (i.e., horizontal dimensions << vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical deviates from its original path. find the deviation in travelling a horizontal distance d<

(i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as \(\omega (b)={ \omega }_{ 0 }-\frac { { b }^{ 2 } }{ a } ,\) where b is the vertical distance from the pole. \({ \omega }_{ 0 }\) is a constant. using Fermat's principle i.e., the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. find the focal length

(ii) A gravitational lens may be assumed to have a varying width of the form show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius \(\beta =\sqrt { \frac { (n-1){ k }_{ 1 }\frac { u }{ v } }{ u+v } } \) 

A refracting telescope has an objective of focal length 1m  and an eye of the sun 10cm in diameter is formed at a distance of 24cm from eye piece.what angle does the sun subtend at the objective?

An LC circuit a 20 mH inductor and a \(50\mu F\) capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t=0.
(a) What is the total energy stored initially? IS it conserved during LC oscillations?
(b) What is the natural frequency of the circuit?
(c)  At what time is the energy stored 
(i) completely electrical (i.e., stored in the capacitor)?
(ii) completely magnetic (i.e., stored in the inductor).
(d) At what times is the total energy shared equally between the inductor and the capacitor?
(e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?

Consider an infinitely long wire carrying a current I (t), with \(\frac { dI }{ dt } =\lambda =constant.\) Find the current produced in the rectangular loop of wire ABCD if its resistance is R

A rod of mass m and resistance R slides smoothly over two parallel perfectly conducting wires kept sloping at an angle \(\theta \) with respect to the horizontal. The circuit is closed through a perfect conductor at the top. There is a constant magnetic field B along the vertical direction. If the rod is initially at rest, find the velocity of the rod as a function of time.

State Lenz's law and illustrate it with experiment.

What is the difference between electric field produced by stationary charges and moving charges?

A straight horizontal conducting rod of length 0.45m and mass 60g is suspended by two vertical wires at its ends.  A current of 5.0 A is set up in the rod though the wires.
(a) What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?
(b) What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) g = 9.8 ms^-2.

How are materials classified according to their behaviour in magnetic field?

Discuss the sensitivity of a moving coil galvanometer.

Find the expression for maximum energy of a charged particle accelerated by a cyclotron.

Explain using a labelled diagram, the principle and working of a moving coil galvanometer. What is the function of
(i) uniform radial magnetic field
(ii) soft iron core?
Also, define the terms
(iii) current sensitivity and
(iv) voltage sensitivity of a galvanometer.
Why does increasing the current sensitivity not necessarily increase voltage sensitivity?

The length of a half wave dipole antenna is 0.5 m. Calculate the optimum transmission frequency.

What should be the length of the dipole antenna for a carrier wave of frequency \(3\times10^{ 8 }\)Hz?

A sinusoidal voltage amplitude modulates another sinusoidal voltage of amplitude 2 kV resulting in two side bands of amplitude 200 V.Find the modulation index.

A band width of 5 MHz is available for AM transmission.If the maximum audio signal frequency used for modulating the carrier is not to exceed 5 kHz,how many stations can be broadcast within this band simultaneously without interfering with each other?

In a diode detector,output circuit consisits of \(R=1M\Omega \) and C=1 pF.Calculate the carrier frequency it can detect.

Two amplifiers are connected one after the other in series (cascaded). The first amplifier has a voltage gain of 10 and the second has a voltage gain 20. If the input signal is 0.01 volt,Calculate the output ac.signal.

In an n-type silicon, which of the following statement is true?
(a) Electrons are majority carriers and trivalent atoms are the dopants.
(b) Electrons are minority carriers and pentavalent atmos are the dopants.
(c) Holes are minority carriers and pentavalent atmos are the dopants.
(d) Holes are majority carriers and trivalent atmos are the dopants.

For the transistor action, which of the following statements are correct?
(a) Base, emitter and collector regions should have similar size and doping concentrations
(b) The base region must be very thin and lightly doped
(c) The emitter junction is forward biased and collector junction is reverse biased.
(d) Both the emitter junction as well as the collector junction are forward biased.

When an electronic field is applied across a semiconductor

(a) electrons move from lower energy level to lower energy level in the conduction band.

(b) electrons move from higher energy level to lower energy level in the conduction band.

(c) holes in the valence band move from higher energy level to lower energy level.

(d) holes in the valence band move from lower energy level to higher energy level 

To reduce the ripples in a rectifier circuit with capacitor filter

(a) \(R_{ L }\) should be increased

(b) input frequency should be decreased.

(c) input frequency should be increased.

(d) Capacitors with high capacitance should be used.

(a) Define the term decay constant and half life of a radioactive sample. Derive the relation connecting the two.

(b) How many disintegrations per second will occur in one gram of ₉₂U²³⁸, if its half-life against alpha decay is \(1.42\times { 10 }^{ 17 }s\) ?

(a)Using the Bohr's model, calculate the speed of the electron in a hydrogen atom in the n=1,2, and 3 levels (b)Calculate orbital period in each of these levels.

What is the minimum energy that must b given to a H-atom in ground state so that it can angular momentum of the system is conserved, what would be the angular momentum of such H photon?

Deine the term:

(a)(i)Work function (ii)threshold frequency and(iii)stopping potential with reference to photoelectric effect

(b)Calculate the maximum kinetic energy of electrons emitted from a photosensitive surface of work function 3.2 eV for the incident radiation of wavelength 300 nm.

The energy flux of sunlight reaching the surface of the earth is.\(1.388*{ 10 }^{ 3 }w/{ m }^{ 2 }\). How many photons (nearly) per square metre are incident on the Earth per second?Assume that the photons in the sunlight have an average wavelength of 550 nm.

Estimating the following two numbers should be interesting.The first number will tell you why radio engineers do not need to worry much about photons.The second number tells you why our eye can never count photons,even in barely detectable light.
(a) The number of photons emitted per second by an MW transmitter of 10 kW power emitting radio waves of wavelength 500 m.
(b)The number of photons entering the pupil of our eye per second corresponding to the minimum intensity of while light that we humans can perceive (\(\sim \)\({ (10 }^{ -10 }Wm^{ -2 })\) .Take the area of the pupil to be white light to be about 0.4 cm²and the average frequency of white light to be about 6 x 10¹⁴ Hz.

Answer the following question.
(a)Quarks inside protons and neutrons are thought to carry fractional charges \(\left( +\frac { 2 }{ 3 } e,-\frac { 1 }{ 3 } e \right) .\) Why do they not show up in Millikan's oil drop experiment?
(b) What is so special about the combination elm?Why do we not simply talk of e and \(m\) specially?
(c) Why  should gases be insulators at ordinary pressure and start conducting at very low pressure.
(d)Every metal has a definite work function,Why do photoelectrons not come out all with same energy if incident radiations is monochromatic?Why is there an energy distribution of photoelectrons?
(e) The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations :\(E=hv,p=\frac { h }{ \lambda } \)
​​​​​​​But while the value of  \(\lambda \) is physically significant , the value of \(v\) (and therefore the value of the phase speed \(v\lambda \) ) has no physical significance.Why?

A double convex lens made of glass of refractive index 1.5 has both radii of curvature of magnitude 20 cm. An object 2 cm high is placed at 10 cm from the lems. Find the position, nature and size of the image.

In the normal adjustment of an astronomical telescope, the distance between the objective lens and the eye lens is 10 sm. The magnifying power of the telescope is 4. Calculate the focal lengths of objective and eye lens.

A breaker is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the beaker is measured by a microscope to be 9.4 cm. What is the refractive index of water ? If  water is If water is replaced by a liquid of refractive index 1.63 upto the same height, by what distance would the microscope have to be moved to focus on the needle again ?

Explain how corpuscular theory predicts the speed of light in a medium, say water, is greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment?

Suppose that the electric field part of an electromagnetic wave in vacuum is 
\(\overrightarrow { E } =\left\{ \left( 3.1N/C \right) \cos { \left[ \left( 1.8㎭/m \right) y+\left( 5.4\times { 10 }^{ 6 }㎭-{ s }^{ -1 }t \right) \right] } \right\} \hat { i } \)
(a) What is the direction of propagation?
(b) What is the wavelength \(\lambda \)?
(c) What is the frequency \(v\) ?
(d) What is the amplitude of the magnetic field part of the wave?
(e) Write an expression for the magnetic field part of the wave.

About 5% of the power of a 100 W light bulb is converted to visible radiation. What is the average intensity of visible radiation.
(a) At a distance of 1 m from the bulb
(b) At a distance of 10 m?
Assume that the radiation is emitted isotropically and neglect reflection.

Monica's mother was heating food on a gas stove. Her friend Ruchi came and saw her mother heating food on the gas stove. Ruchi told Monica's mother, "Why don't you buy a microwave oven"? Monica's mother replied at once that she doesn't like to use microwave oven. Monica and Ruchi made it clear that microwave is not harmful for cooking food. This is an easy and safe process. Monica's mother got convinced and ordered for a microwave oven. Monica's mother then arranged a small party for her friends and told them the advantages of a microwave oven.
What value was displayed by Monica and her friend?
What value was displayed by Monica to her friends?

The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is B₀ = 510 nT. What is the amplitude of the electric field part of the wave?

The galvanometer in the circuit shown here has a resistance of 20\(\Omega\)The terminals X and Y are connected to a cell of e.m.f. 1.5V and internal resistance 10\(\Omega\) Calculate the current flowing in the galvanometer:
(i) When the switch S is in position.
(ii) When the switch S is in position B.

A battery of e.m.f. 10V and internal resistance \(3\Omega \) is connected to a resistor. If the current in the circuit is 0.5A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

Kirchhoff's junction rule is a reflection of 

(a) conservation of current density vector.

(b) conservation of charge

(c) the fact that the momentum with which a charged particle approaches a junction is unchanged as the charged particle leaves the junction.

(d) the fact that there is no accumulation of charges at a junction.

(a) Define electric current. What is its S.I. unit? Is it a scalar or a vector quantity? What is the direction of electric current?
(b) How many electrons flowing per second should flow to produce a current of 1A?

(a) State Ohm's law.

(b) Define resistance. Give its SI unit.

How rubbing of the two bodies produces electricity?

Define electric field at a point.An electron moves a distance of 6.0cm when accelerated from rest by an electric field of strength \(2\times {{10}^{4}} N{{C}^{-1}}\).Calculate the times of travel.

(i) Explain, using suitable diagram,  the  difference in the behaviour of a 
(a) conductor
(b) dielectric in the presence of external electric field. Define the terms polarisation of a dielectric and write its relation with susceptibility.
(ii) 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 another charge +2Q is placed outside the shell at a distance x from the centre as shown in figure. Find
(a) the force on the charge at the centre of the shell and at point A,
(b) the electric flux through the shell.

The electric field at a point on the axial line at a distance of 10 cm from the center of an electric dipole is 3.75\(\times\) N/C.Calculate the length of an electric dipole.

(i) Three equal charges, each equal to q are placed at the three corners of square of side \(\alpha \) .Find the electric field at the fourth corner.
(ii) Find the electric field at the point P in figure given below.

A uniform magnetic field of 1.5 T exists in a cylindrical region of radius 10.0 cm, its direction is parallel to the axis along east to west.  A wire carrying current of 7.0 A in the north to south direction passes through this region.  What is the magnitude and direction of the force on the wire if,
(a) the wire intersects the axis,
(b) the wire is turned from N-S to northeast-southwest direction,
(c) the wire in the N-S direction is lowered from the axis by a distance of 6.0 cm?

A circular coil of 20 turns and radius 10 cm is placed in a uniform magnetic field of 0.10 T normal to the plane of the coil.  If the current in the coil is 5.0 A, what is the 
(a) total torque on the coil,
(b) total force on the coil,  
(c) average force on each electron in the coil due to the magnetic field?
(The coil is made of copper wire of cross-sectional area 10^-5 m², and the free electron density in copper is given to be about 10²⁹ m^-3)

A long straight horizontal cable carries a current of 2.5A in the direction 10^o south of west to 10^o north of east. The magnetic meridian of the place happens to be 10^o west of the geographic meridian, The earth's magnetic field at the location is 0.33G, and the angle of dip is zero. Locate the line of neutral points(Ignore the thickness of the cable).

A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12cm. The coil is in a vertical plane making an angle of 45^o with the magnetic meridian. When the current in the coil is 0.35A, the needle points west to east

(a)Determine the horizontal component of the earth's magnetic field at the location.

(b)The current in the coil is reserved and the coil is rotated about its vertical axis by an angle of 90^o in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the place to be zero.

A closely wound solenoid of 2000 turns and area of cross-section 1.6X10^-4m² carrying a current of 4.0A is suspended through its centre allowing it to turn in a horizontal plane.

(a)What is the magnetic moment associated with the solenoid?

(b)What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5X10^-2T is set up at an angle of 30^o with the axis of the solenoid?

(a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of a side a as shown inthe figure given below.

(b) Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with constant velocity, V=10ms^-1. Calculate the induced emf in the loop at the instant when x=0.2m. Take a=0.1 m and assume that the loop has a large resistance.

A series LCR circuit with \(R=20\Omega \) , L=1.5H and \(C=35\mu F\) is connected to a variable frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

A coil of inductance 0.50H and resistance \(100\Omega \) is connected to a 240V, 50 Hz ac supply. 

(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

A \(100\mu F\) capacitor in series with a \(40\Omega \) is connected to a 110 V, 60 Hz supply.

(a) What is the maximum current in the circuit?

(b) What is the time lag between the current maximum and the voltage maximum?

Explain why the coils of the resistance box are wound over themselves.

Figure shows a potentiometer with a cell of 2.0V and internal resistance of 0.40\(\Omega\) maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02V (for very moderate currents upto a few mA) gives a balance point at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell a very high resistance 600k\(\Omega\) is put in series with it Which is shorted cell is then replaced by a cell of unknown emf E and the balance point found similarly, turns out to be at 82.3 cm length of the wire.

(a) What is the value E?
(b) What purpose does the high resistance o 600k\(\Omega\) have?
(c) Is the balance point affected by this high resistance?
(d) Is the balance point affected by the internal resistance of 600k\(\Omega\) have?
(e) Would the method work in the above situation if the driver cell of the potentiometer had an emf of 1.0V instead of 2.V?
(f) Would the circuit work well for determining an etremely small emf say of the order of a few mV (such as the typical emf of a thermo-couple)? If not how will you modiy the circuit?

A dc supply of 120V  is connected to a large resistance X. A voltmeter of resistance 10k\(\Omega\)placed in series in the circuit reads 4V. What is the value of X? What so you think is the purpose in using a voltmeter instead of an ammeter to determine the large resistance X?

(a) Three resistors \(1\Omega ,2\Omega \ and\ 3\Omega \) are combined in series. What is the total resistance of the combination?
(b) If the combination is connected to a battery of emf 12 V and negligible internal resistance, obtain the potential drop across each resistor.

(a) Six lead-acid type of secondary cells each of emf 2.0 V and internal resistance are joined in series to provide a supply to a resistance of \(8.5\Omega \) . What are the currents drawn from the supply, and its terminal voltage? (b) A secondary cell after long use has an emf 1.9 V and a large internal resistance of \(380\Omega \). What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?

Answer the following questions:
(a) A steady current flows in a metallic conductor of non-uniform cross-section. Say which of these quantities is constant along the conductor current density, electric field, drift speed?
(b) Is Ohm's law universally applicable for all conducting elements? If not, give examples of elements which do not obey Ohm's law.
(c) A low voltage supply from which one needs high currents must have very low internal resistance. Why?
(d) A high tension (HT) supply of say 6kV must have a very large internal resistance. Why?

The electrostatic force on a small sphere of charge 0.4 \(\mu\)C due to another small sphere of charge -0.8 \(\mu\)C in air is 0.2 N.
(a) What is the distance between the two spheres?
(b) What is the force on the second sphere due to the first?

Check that the ratio ke²/Gm_em_p is dimensionless. Look up a table of physical constants and determine the value of this ratio. What does the ratio signify?

A parallel plate capacitor with air between the plates has a capacitance of 8pF(1pF=10F) ^-12F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?

Three capacitors each of capacitance 9 pF are connected in series.
(a) What is the total capacitance of the combination?
(b) What is the potential difference across each capacitor, if the combination is connected to a 120 volt supply?

A 12pF capacitor is connected to a 50V battery. How much electrostatic energy is stored in the capacitor?

Explain the "green house effect" of earth's atmosphere.

On what factors does the maximum range of ground wave propagation depend? How can the maximum range on ground wave propagation be increased?

Distinguish between 'Analog and Digital signals'.

a) Identify the boxes, 'P' and 'Q' in the block diagram of a receiver shown in the figure:

(b) Write the functions of the blocks 'P' and 'Q'.

The energy gap of silicon is 1.14 eV. Find the maximum wavelength at which silicon starts energy absorption.

How does the conductivity and resistivity change with rise of temperature in case of intrinsic semiconductors?

Why does the width of depletion layer of a \(p-n\) junction increase in reverse biasing?

Write the truth for the circuit shown in figure below. Name the gate that the circuit resembles.

There are two semiconductor materials A and B which are made by doping germanium crystal with indium and arsenic respectively. As shown in the figure, the junction of two is biased with a battery. Will the junction be forward bias and reverse bias?

The electron in the hydrogen atom passes from the n=4 energy level to the n=1 level.What is the maximum number of photons that can be emitted? and minimum number?

If elements with principal quantum number n > 4 did not exist in nature, what would be the possible number of elements?

How many electrons, protons, and neutrons are there in a nucleus of atomic number 11 and mass number 24?

Give the order of magnitude of nuclear mass density and average atomic mass density. Compare these densities with the typical mass density of solids, liquids, and gases (at ordinary temperature and pressure).

Why is \(_{ 92 }{ { U }^{ 238 } }\) not suitable for chain reaction?

The work function for a certain metal is 4.2eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm? Use, \(h=6.6\times { 10 }^{ -34 }Js\)

Ultraviolet light is incident on two photosensitive materials having work function.\({ \phi }_{ 1 }and{ \phi }_{ 2 }\) In which case will the K.E. of the emitted electrons be greater? Why? 

If the wavelength of an electromagnetic radiation is doubled, what will happen to (i) the energy of photons and (ii) the momentum of a photon?

Why is the wave nature of matter not more apparent to our daily observations?

A particle with rest mass is \({ m }_{ 0 }\) moving with velocity c. What is the de-Broglie wavelength associated with it?

A convex lens of local length 25 cm is placed coaxially in contact with a concave lens of focal length 20 cm. Determine the power of the combination. Will the system be converging or diverging in nature ?

Name the phenomenon which proves transerve wave nature of light.Gives two uses of the devices whose functioning is based on this phenomenon.

(i) Draw a ray diagram for a convex mirror showing the image formation of an object placed anywhere in front of the mirror.
(ii) Use this ray diagram to obtain the expression for its linear magnification.

What is the relation between critical angle and refractive  index of a material?
(ii) Does critical angle depend on the colour of light?

In a single slit diffraction experiment, a monochromatic source of light of wavelength \(\lambda\) illuminates a narrow slit of width a. Show giving appropriate reasoning, that the half angular width of the central maximum in the observed pattern is (nearly) equal to \(\lambda\)/a.

Show that the radiation pressure exerted by an EM wave of intensity I on a surface kept in vacuum is I/c.

What happens to the intensity of light from a bulb if the distance from the bulb is doubled? As a laser beam travels across the length of a room, its intensity essentially remains constant. What geometrical characteristic of LASER beam is responsible for the constant intensity which is missing in the case of light from the bulb?

The electromagnetic waves are the radiations of the large range of wavelength. what are their velocities
(i) In vacuum and
(ii) In a medium?

(i) An electromagnetic wave is travelling in a medium with a velocity v=\(\upsilon \overset { \wedge }{ i } \) . Draw a sketch showing the propagation of the electromagnetic wave indicating the direction of the oscillating electric and magnetic fields.
(ii) How are the magnitudes of the electric and magnetic fields related to velocity of the electromagnetic wave?

A capacitor made of two parallel plates each of the plate A and separationd, is being chrged by an external AC source. Show that the displacement current inside the capacitor is capacitor.

A solenoid with an iron core and a bulb are connected to a.d.c source. How does the brightness of bulb change when iron core is removed from the solenoid ?

What are phase lines and neutral line in respect of a generator?

A solenoid with an iron core and a bulb are connected to a d.c. source. How does the brightness of the bulb change when iron core is removed from the solenoid?

Distinguish between alternating current and direct current by giving two points.

Define reactance X and impedance Z. Can these be negative? If yes, when and what does it imply?

What is magnetic flux density? Define its units and give its dimensions.

What is the magnetic effect of current ? Describe the nature of the magnetic field related with the current in circular coil.

A wire of length l metre carries a current I ampere along the Y-axis. A magnetic field, \(\overset { \rightarrow }{ B } ={ B }_{ o }\left( \hat { i } +\hat { j } +\hat { k } \right) \)tesla exists in space. Find the magnitude of the force on the wire.

What is an ammeter ? How is it used in an electric circuit ? How it differ from a voltmeter ?

Identify the materials, which can be classified as paramagnetic and diamagnetic : Al, Bi, Cu, Na. 

Write the mathematical relation between mobility and drift velocity between mobility and drift velocity of charge carriers in a conductor. Name the mobile charge carriers responsible for conduction of electric current in (a) an electrolyte (b) an ionised gas.

Currents of the order of 0.1 A through the human body are fatal. What causes the death: heating of the body due to electric current or something else?

While making a standard resistance, the coil is made of manganin. The coil is double folded and is wound over a non-conducting frame. Why? 

Two students A and B were asked to pick a resistor of \(15 \ k\Omega\) from a collection of carbon resistors. A picked a resistor with bands of colours: brown, green, orange while B choose a resistor with bands black, green, red. Who picked the correct resistor? Explain.

A voltage of 200 V is applied across a colour-coded carbon resistor with first, second and third ring of blue, black and yellow colours. What is the current flowing through the resistor?

Two point charges of +2 \(\mu C\) and +6 \(\mu C\) repel each other with a force of 12N. If each is given an additional charge of -4\(\mu C\) , what will be the new force?

what does (q1 + q2) = 0 Signify ?

Can you say that SI unit of \(\epsilon_o\) is farad per metre?

A bird perches on a bare high power line and nothing happens to the bird. A man standing on the ground touches the same line and gets a fatal shock why?

Two metal plates of a parallel plate capacitor are at distance d apart. A metal sheet of thickness d / 2 of the same area is introduced between the plates, what is the ratio of capacitances in these cases.

Which of the following frequencies will be suitable for beyond the horizon communication using sky waves.

Frequencies in the UHF range normally propagate by means of:

A message signal of frequency \({ \omega }_{ m }\) is superposed on a carrier wave of frequency \({ \omega }_{ c }\) to get an amplitude modulated wave (AM). The frequency of the AM wave will be

A male voice after modulation transmission sounds like that of a female to the receiver.The problem is due to

An audio signal of 15kHz frequency cannot be transmitted over long distances without modulation because

The conduction band in a solid is partially filled at 0 k.The solid sample is

A p-type semiconductor is obtained by doping silicon with

In a \(p\)-type semiconductor the acceptor level is situated 60m eV above the valence band.The maximum wavelength of light required to produce a hole will be [use \(hc=12400 eVA\)

Which type of semiconductor is obtained by mixing arsenic with silicon?

The dominant mechanisms for motion of charge carriers in forward and reverse biased silicon \(p-n\)junction are 

Taking the Bohr radius as a₀=53pm, the radius of Li⁺⁺ ion its ground state, on the basis of Boh''s model, will be about

For the ground state, the electron in the H-atom has an angular momentum =h, according to the simple Bohr model.Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions.In actuality, this is not true,

Two H atoms in the ground state collide inelastically kinetic energy is reduced is

The Bohr model for the spectre of a H-atom

Consider a beam of electrons (each electron with energy \({ E }_{ 0 }\)) incident on metal surface kept in an evacuated chamber.Then

An electron is moving with an initial velocity \(\frac { h }{ mv } ={ v }_{ 0 }\overset { \wedge }{ L } \) and is in a magnetic field \(\vec { B= } \quad { B }_{ 0 }\vec { j } \) Then its de-Broglie wavelength

Photons absorbed in matter are converted to heat.A source emitting n photon/sec frequency v is used to convert 1 kg of ice at \({ 0 }^{ 0 }c \) . Then the time t taken for the conversation.

The maximum velocity of an electron emitted by light of wavelength \(\lambda \)incident on the surface of a metal of wor4k function \(\phi \) is[h =Plank's constant,c= speed of light and m=mass of electron]

Consider sunlight incident on a slit of width \({ 10 }^{ 4 }\)A. The image seen through the slit shall darkness as observed through the polaroid

In a young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case

For light diverging from a point source

What is range of vision?

A person looking at a mesh of crossed wires is able to see the vertical wires more distinctly than the horizontal wires.Why? How can it be corrected?

One requires 11 \(eV\) of energy to dissociate a carbon monoxide molecule into carbon and oxygen atom. The minimum frequency of the appropriate electromagnetic radiation to achieve the dissociation lines in

Light with an energy flux of \(​​20\quad W/cm^{ 2 }\) falls on a non-reflecting surface at normal incidence. If the surface has an area of \(30 cm^{ 2 }\), the total momentum delivered (for complete absorption) during \(30\) minutes is:

An EM wave of intensity I falls on a surface kept in vacuum and experts radiation pressure kept in vacuum and experts radiation pressure p on it. Which of the following are true?

A plane electromagnetic wave travels in vacuum along the z-direction. what can you say about the direction of an electric and magnetic field vectors

An electromagnetic wave consists of oscillating electric and magnetic field. what is the phase relationship between these fields?

In the relation \(\phi \) = BA cos \(\theta \), \(\theta \) is angle........

Which one is not an application of eddy currents?

Phase difference between voltage across L and C in series is

The frequency of a.c. generated depends on

The form factor of an a.c. generated is given by

The magnetic field at a perpendicular distance of 2 cm from an infinite straight current carrying conductor is 2X10^-6 T. The current in the wire is

A positive charge is moving towards an observer. The direction of magnetic induction lines is 

If a copper wire carries a direct current, the magnetic field associated with the current will be

A thin ring of radius R metre has charge q coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of f revolutions/s. The value of magnetic field induction in Wb/m² at the centre of the ring is 

Ampere's circuital law can be derived from

Is electric current a vector or scalar quantity? Explain.

A steady current is flowing in a cylindrical conductor. Is there any electric field within the conductor?

If the temperature of a good conductor increases, how does the relaxing time of electrons in the conductor change?

What are the materials generally used for making standard resistances? Give their compositions.

The specific resistance of copper, silver and constantan are (1.78 x 10^-6 Ω-cm, 10^-6 Ω-cm and 48 x 10^-6 Ω-cm, respectively. Which is the best conductor and why?

At a particular point, electric field depends upon

Electric field intensity (E) due to an electric dipole varies with distance (r) of the point from the centre of dipole as:

At a given distance from the centre of electic dipole, field intensity on axial line is k times the field intensity on equatorial line, where K=

What is meant by quantization of charge?

What do you mean by additivity of electric charge?

Which of the following frequencies will be suitable for beyond the horizon communication using sky waves.

Frequencies in the UHF range normally propagate by means of:

Three waves A, B and C of frequencies 1600 kHz, 5 MHz and 60 MHz, respectively are to be transmitted from one place to another. Which of the following is the most appropriate mode of communication:

A 100m long antenna is mounted on a 500 m tall building. The complex can become a transmission tower for waves with \(\lambda \).

A 1 kW signal is transmitted using a communication channel which provides attenuation at the rate of -2dB per km. If the communication channel has a total length of 5km, the power of the signal received is \([gain\quad in\quad dB=10\log { \left( \frac { { P }_{ 0 } }{ { P }_{ i } } \right) } ]\)

The conduction band in a solid is partially filled at 0 k.The solid sample is

In good conductorsof electricity the type of bonding that exists is

In intrinsic semiconductor at room temperature,the number of electrons and holes are

In an n-type semiconductor,the Fermi level lies 0.3 e V below the conduction band at 300 k.If the temperature is increased to 330 k ,where does the new position of the Fermi level lie?

Taking the Bohr radius as a₀=53pm, the radius of Li⁺⁺ ion its ground state, on the basis of Boh''s model, will be about

For the ground state, the electron in the H-atom has an angular momentum =h, according to the simple Bohr model.Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions.In actuality, this is not true,

O₂ molecule consists of two oxygen atoms.In the molecule, nuclear force between the nuclei of the two atoms

The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly

An electron is moving with an initial velocity \(\frac { h }{ mv } ={ v }_{ 0 }\overset { \wedge }{ L } \) and is in a magnetic field \(\vec { B= } \quad { B }_{ 0 }\vec { j } \) Then its de-Broglie wavelength

An electron (mass m) with an initial velocity \(v={ v }_{ 0 }\vec { i } \) is in an electric field \(E={ E }_{ 0 }\vec { j } E={ E }_{ 0 }\vec { j } \)  . If \(\lambda =\frac { h }{ m{ v }_{ 0 } } \) its de-Broglie wavelength at time t is given by

Relativistic corrections become necessary when the expression for the kinetic energy \(\frac { 1 }{ 2 } m{ v }^{ 2 }\) becomes comparable with \(m{ c }^{ 2 }\) where m is the mass of the particle.At what de-Broglie wavelength will relativistic corrections become important for an electron?

Consider sunlight incident on a slit of width \({ 10 }^{ 4 }\)A. The image seen through the slit shall darkness as observed through the polaroid

In a young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case

The ratio of the speed of an object to the speed of its real image of magnification m in the case of a convex mirror is

In a concave mirror, an object is placed at a distance \({ d }_{ 1 }\) from the focus and the real image is formed at a distance \({ d }_{ 2 }\) from the focus. then the focal length of the nirror is:

Which is not true for the image formed in a plane mirror? The image is 

One requires 11 \(eV\) of energy to dissociate a carbon monoxide molecule into carbon and oxygen atom. The minimum frequency of the appropriate electromagnetic radiation to achieve the dissociation lines in

A linearly polarized electromagnetic wave given as \(E={ E }_{ 0 }\overset { \wedge }{ i } cos\quad (kz-wt)\) incident wall at \(z=a\) . Assuming that the material of the wall os optically inactive, the reflected wave will be given as

If \(\overset { \rightarrow }{ E } \) and \(\overset { \rightarrow }{ B } \) represent electric and magnetic field vectors of the electromagnetic wave the direction of propagation of electromagnetic wave is along

The ratio of contributions made by the electric field and magnetic field components to the intensity of an EM wave is

The radiation force on the roof is 

In the relation \(\phi \) = BA cos \(\theta \), \(\theta \) is angle........

The cause of induced e.m.f. is

Which one is not an application of eddy currents?

A wire of length 2m moves with a speed of 5m/s perpendicular to a magnetic field of induction 0.1 Wb/m². The e.m.f. induced in the wire is

Which of the following does not have the dimension of time?