Electric dipole moment is

1

(a)

scalar

(b)

neither scalar vector

(c)

a vector directed from -q to +q

(d)

a vector directed from +q to -q

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

1

(a)

2

(b)

4

(c)

1

(d)

1/2

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

1

(a)

1/2

(b)

1/4

(c)

4

(d)

1

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

1

(a)

\(4514\Omega \)

(b)

\(5413\Omega \)

(c)

\(2000\Omega \)

(d)

\(6000\Omega .\)

Q factor of resonance is given by

1

(a)

\(\frac { 1 }{ R } \sqrt { \frac { L }{ C } } \)

(b)

\(\frac { 1 }{ R } \sqrt { \frac { C }{ L } } \)

(c)

\(\frac { 1 }{ L } \sqrt { \frac { R }{ C } } \)

(d)

\(\frac { 1 }{ C } \sqrt { \frac { L }{ R } } \)

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

1

(a)

\(\overset { \rightarrow }{ E } \)

(b)

\(\overset { \rightarrow }{ B } \)

(c)

\(\overset { \rightarrow }{ B } \times \overset { \rightarrow }{ E } \)

(d)

\(\overset { \rightarrow }{ E } \times \overset { \rightarrow }{ B } \)

Which of the following cannot be polarized?

1

(a)

X-rays

(b)

radio waves

(c)

sound waves

(d)

light waves

The de-Broglie wavelength of electron in ground state of hydrogen atom is:[The radius of the first orbit of hyfrogen atom is 0.53 \(\overset { \circ }{ A } \)

1

(a)

0.52\(\overset { \circ }{ A } \)

(b)

1.06\(\overset { \circ }{ A } \)

(c)

1.67\(\overset { \circ }{ A } \)

(d)

3.33\(\overset { \circ }{ A } \)

Given the value of Rydberg constant is \({ 10 }^{ 7 }{ m }^{ -1 }.\) The wave number of the last line of Balmer series in hydrogen spectrum will be

1

(a)

\(0.5\times { 10 }^{ 7 }{ m }^{ -1 }\)

(b)

\(0.25\times { 10 }^{ 7 }{ m }^{ -1 }\)

(c)

\(2.5\times { 10 }^{ 7 }{ m }^{ -1 }\)

(d)

\(0.025\times { 10 }^{ 4 }{ m }^{ -1 }\)

Name the principle which is mathematical equivalent of coulomb's law and superposition principle.

1

(a)

Gauss's theorem of electrostatics.

Explain, why should the current be not passed through potentiometer wire for long time?

1

(a)

If the current in potentiometer wire is passed for long time, the potentiometer wire will get heated. Its resistance will change. Due to it, the potential gradient per unit length of the wire will also change.

A voltmeter, an ammeter and a resistance are connected in series with a lead accumulator. The voltmeter gives some deflection but the deflection of ammeter is zero. comment

1

(a)

Voltmeter resistance being very high, when connected in series, it makes the effective resistance of the very high. Due to it, the current in the circuit becomes extremely small.
Since ammeter measures the current, hence the deflection of ammeter is almost zero. As voltmeter measures potential difference between the two points, it will show the reading due to voltage of the lead accumulator.

Define 1 henry.

1

(a)

One henry is the self-inductance of that coil in which 1V emf is produced when the rate of change of current in that coil is 1 \(A{ s }^{ -1 }.\)

Mention the law, that which asserts that the electric field lines cannot form close loops?

1

(a)

Gauss’s law

A glass of refractive index 1.45 disappears when immersed in a liquid. what is the value of refractive index of the liquid 

1

(a)

The refractive index of the liquid is also 1.45

Draw the transfer characteristic curve of a base biased transistor in CE configuration. Explain 'clearly how the active region of the V₀ versus V _i  curve in a transistor is used as an amplifier.

1

(a)

In the active region, a (small) increase of V_i results in a (large, almost linear) increase in l_c, This results in an increase in the voltage drop across R_c.

Two waves A and B of frequencies 2 MHz to 3 MHz, respectively are beamed in the same direction for communication via sky wave. Which one of these is likely to travel longer distance in the ionosphere before suffering total internal reflection?

1

(a)

We know that refractive index \(\mu\) of a medium is related with wavelength of wave according to relation
\(\mu =A+\frac { B }{ { \lambda }^{ 2 } } +\frac { C }{ { \lambda }^{ 4 } } =\frac { \sin { i } }{ \sin { r } } \ and \ \lambda =\frac { c }{ v } \)
Therefore, the value of refractive index \(\mu\) of a medium increases with the decrease in wavelength or increase in frequency of wave travelling through medium. For higher frequency wave, angle of refraction r is less, i.e., bending of wave is less in medium. Due to it, the condition for total internal reflection is attained after travelling longer distance by higher frequency wave. Hence 3 MHz wave will travel longer distance in the ionosphere before suffering total internal reflection.

For transistor amplifier,the voltage gain

1

(a)

remains constant for all frequencies

(b)

is high at high and low frequencies and constant in the middle frequency range

(c)

is low at high and low frequencies and constant at mid frequencies

(d)

None of the above

The resolving power of telescope whose lens has a diameter of 1.22 m for a wavelength of 5000 A is

1

(a)

2 x 10⁵

(b)

2 x 10⁶

(c)

2 x 10²

(d)

2 x 10⁴

1. Can we give as much charge to a capacitor as we wish?

   1

   (a)

   No, the maximum charge that can be given to a capacitor is determined by the capacity of the condenser.

2. The variation of potential difference V with length l in case of two potentiometer P and Q is as shown. Which one of these two will you prefer for comparing emfs of two primary cells?

    

   1

   (a)

Derive an expression for the potential energy of an electric dipole of dipole moment \(\vec { p } \) in an electric field \(\vec { E } \).

2

(a)

Obtain, with the help of necessary diagram, the expression for the magnetic field in the interior of a toroid carrying current.

2

(a)

How does a charge q oscillating at certain frequency produce electromagnetic waves?
Sketch a schematic diagram depicting electric and magnetic fields for an electromagnetic wave propagating along the Z-direction.

2

(a)

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.

2

(a)

1. Obtain the expression for the mutual inductance of a pair of coaxial circular coils of radii r and R(R>r) place dwith their centres coinciding.

   2

   (a)

2. Why is FM signal less suspectable to noise than an AM signal?

   2

   (a)

1. The network PQRS, shown in the circuit diagram, has the batteries of 4 V and 5 V and negligible internal resistance. A milliammeter of 20 Ω resistance is connected between P and R. Calculate the reading in the Millimetre.
   

   2

   (a)

2. 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.

   2

   (a)

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

3

(a)

Consider the plane S formed by the dipole axis and the axis of earth. Let P be point on the magnetic equator and in S. Let Q be the point of intersection of the geographical and magnetic equators. Obtain the declination and dip angles at P and Q.

3

(a)

What is wattless current? Show mathematically that an ideal inductor does not consume any power in an a.c. circuit.

3

(a)

With what consideration in view, a photodiode is fabricated? State its working with a help of a suitable diagram.
Even through the current in the forward bias is known to be more than in the reverse bias, yet the photodiode works in reverse bias. What is the reason?

3

(a)

Write three important factors which justify the need of modulating a message signal. Show diagrammatically how an amplitude modulated wave is obtained when a modulating signal is superimposed on a carrier wave.

3

(a)

(i) If f = 0.5 m for a glass lens, what is the power of the lens?
(ii) The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm. Its focal length is 12 cm. What is the refractive index of glass?
(iii) A convex lens has 20 cm focal length in air. What is focal length in water? (Refractive index of air-water = 1.33, refractive index for air-glass = 1.5.)

3

(a)

1. An electric field in an electromagnetic wave is given by  \(E=200sin\frac { 2\pi }{ \lambda } (ct-x)N{ C }^{ -1}.\) Find the energy contained in a cylinder of cross section \(20 \ { cm }^{ 2 }\) length 40 cm along the x-axis 

   3

   (a)

2. (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.

   3

   (a)

1. Describe the principle and construction of a moving coil galvanometer.  Prove that the current flowing in the coil is directly proportional to its deflection.  What is the importance of the radial field?

   5

   (a)

2. Before the neutrino hypothesis, the beta decay process was thought to be the transition \(n\rightarrow p+\overset { - }{ e } \)

   If this was true, show that if the neutron was at rest, the proton and electron would emerge with fixed energies and calculate them. Experimentally, the electron energy was found to have a large range.

   5

   (a)

1. A resistor of 12\(\Omega \), a capacitor of reactance 14 ohm and a pure inductor of inductance 0.1H are joined in series and placed across 200V, 50Hz a.c. supply. Calculate
   (i) current in the circuit
   (ii) phase angle between current and voltage. Take  \(\pi\) = 3

   5

   (a)

2. Monochromatic light of frequency \(6.0\times { 10 }^{ 14 }Hz\) is produced by a laser.The power emitted is \(2.0\times { 10 }^{ -3 }W\).
   (a) What is the energy of a photon in the light beam?
   (b) How many photons per second, on the average, are emitted by the source?
   Given \(h=6.63\times { 10 }^{ -34 }Js\)

   5

   (a)

1. What should be the distance between the object in Exercise and the magnifying glass if the virtual image of each square in the figure is to have an area of 6.25 mm². Would you be able to see the squares distinctly with your eyes very close to the magnifier?
   [Note: Exercises will help you clearly understand the difference between magnification in absolute size and the angular magnification (or magnifying power) of an instrument.]

   5

   (a)

2. Electric field intensity at point 'B' due to a point charge 'Q' kept at point 'A' is 24NC^-1 and the electric potential at point 'B' due to same charge is 12JC^-1.Calculate the distance AB and also the magnitude of charge Q.

   5

   (a)