Define the term ‘amplitude modulation’. Explain any two factors which justify the need for modulating a low frequency base-band signal.
Amplitude Modulation is the process in which the amplitude of high frequency carrier wave changes in accordance with the instantaneous value of modulating signal.
Below are the factor justifying the need of modulation:
i. Modulation is also necessary to keep the dimension of receiving antenna within practical limit. Length of antenna bears inverse relation with the frequency of signal it receives. Hence, frequency is kept high to keep anteena length in practical limits.
ii. Size of antenna should be comparable to wavelength for audio frequency signal,
v =15KHz
λ = c/v = 3 x 108 / 15 x 103 = 20000m
⇒ Length of antenna should be = λ/4 = 20000/4 = 5000m, which is practically impossible.
if tranmission frequency is raised to 1 MHz, then,
λ = c/v = 3 x 108 / 106 = 300m
and length of antenna = = λ/4 = 300/4 = 75m,
which is reasonable. Thus there is need of converting information contained in original low frequency base band signal to high frequency setting transmission.
What is the force between two small charged spheres having charges of 2 x 10-7 C and 3 x 10-7 C placed 30 cm apart in air?
An infinite line charge produces a field of 9 × 104 N/C at a distance of 2 cm. Calculate the linear charge density.
A polythene piece rubbed with wool is found to have a negative charge of 3 × 10−7 C.
(a) Estimate the number of electrons transferred (from which to which?)
(b) Is there a transfer of mass from wool to polythene?
A 600 pF capacitor is charged by a 200 V supply. It is then disconnected from the supply and is connected to another uncharged 600 pF capacitor. How much electrostatic energy is lost in the process?
A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10-12 F). 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?
A regular hexagon of side 10 cm has a charge 5 µC at each of its vertices. Calculate the potential at the centre of the hexagon.
A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)
A conducting sphere of radius 10 cm has an unknown charge. If the electric field 20 cm from the centre of the sphere is 1.5 × 103 N/C and points radially inward, what is the net charge on the sphere?
A point charge of 2.0 μC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
A spherical capacitor consists of two concentric spherical conductors, held in position by suitable insulating supports (Figure). Show
that the capacitance of a spherical capacitor is given by
where r1 and r2 are the radii of outer and inner spheres, respectively.
An electric dipole with dipole moment 4 × 10−9 C m is aligned at 30° with the direction of a uniform electric field of magnitude 5 × 104N C−1. Calculate the magnitude of the torque acting on the dipole.
What conclusion can you draw from the following observations on a resistor made of alloy manganin?
Current A | Voltage V | Current A | Voltage V |
0.2 | 3.94 | 3.0 | 59.2 |
0.4 | 7.87 | 4.0 | 78.8 |
0.6 | 11.8 | 5.0 | 98.6 |
0.8 | 15.7 | 6.0 | 118.5 |
1.0 | 19.7 | 7.0 | 138.2 |
2.0 | 39.4 | 8.0 | 158.0 |
What is the shape of the wavefront in each of the following cases:
(a) Light diverging from a point source.
(b) Light emerging out of a convex lens when a point source is placed at its focus.
(c) The portion of the wavefront of light from a distant star intercepted by the Earth.
A uniform magnetic field of 3000 G is established along the positive z-direction. A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A. What is the torque on the loop in the different cases shown in Figure? What is the force on each case? Which case corresponds to stable equilibrium?
A small sphere of radius r1 and charge q1 is enclosed by a spherical shell of radius r2 and charge q2. Show that if q1 is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge q2 on the shell is.
A galvanometer coil has a resistance of 15 Ω and the metre shows full scale deflection for a current of 4 mA. How will you convert the metre into an ammeter of range 0 to 6 A?
A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.34. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.)
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.