Q24 of 26 Page 1

A. Draw a labeled diagram of AC generator. Derive the expression for the instantaneous value of the emf induced in the coil.


B. A circular coil of cross-sectional area and 20 turns is rotated about the vertical diameter with angular speed of in uniform magnetic field of magnitude Calculate the maximum value of the current in the coil.


OR


A. Draw a labeled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of number of turns and currents in the two coils.


B. A power transmission line feeds input power at 2200 V to a step-down transformer with its primary windings having 3000 turns. Find the number of turns in the secondary to get the power output at 220 V.

A)


The schematic diagram of an AC generator is shown in the above figure. This is an electrical machine which converts mechanical energy into useful electrical energy. AC generator consists of a coil mounted on a rotor shaft. The rotational axis of the coil is kept at 900 to the direction of the magnetic field. The coil (called armature) is mechanically rotated in the uniform magnetic field which can be produced by permanent magnets or electromagnets. The rotation of the coil causes the magnetic flux through it to change, so as per Faraday’s law of electromagnetic induction, an emf is induced in the coil. To connect the coil to the external circuit its ends are connected by slip rings and brushes.


When the coil is rotated with a constant angular speed ω, the angle between the magnetic field vector B and the area vector A of the coil at any instant t is,



Assuming when the coil was at rest, the angle between B and A was zero. As a result, the effective area of the coil exposed to the magnetic field lines changes with time, and thus, the flux at any time t is



By Faraday’s law of electromagnetic induction,



Thus,


e =N B A ω sin ωt


Considering the peak voltage E0 = B A ω,


e = e0 sin ωt


If the coil is of N turns the formula becomes,


e = N B A ω sin ωt


And the peak voltage becomes e0 = N B A ω


B) using the above formula,


e = N B A ω sin ωt


Where given data is,


B = 3.0 × 10-2 T


A = 200 × 10-4 m2


ω = 50 rad/s


N = 20 turns, so,


e0 = N B A ω


E0 = 3.0 × 10-2 × 200 × 10-4 × 50 × 20 = 600000 × 10-6


E0 = 0.6 V


Let the resistance of the coil be R, so the peak current in the coil will be,



OR


A) the diagram of a step-up transformer is given below



Transformer uses the principle of mutual induction. A transformer consists of two sets of coils, insulated from each other. They are wound on a soft-iron core, either one on top of the other as shown in the diagram 1 or on separate limbs of the core as shown in the diagram 2. One of the coils called the primary coil has NP turns. The other coil is called the secondary coil; it has NS turns.


For a step-up transformer, NP < NS


Let the associated flux be , then induced voltage in secondary coil will be



And the back emf generated in the primary coil is,



But we know that, ep = vp, so,



So,



Also, in an ideal transformer there is no loss of power so,


iP vP = iS vS


So,



B) using the above relation on the given data is,


vP = 2200 V,


NP = 3000 turns,


vs = 220 V


we get,



Hence,


NS = 300 turns.


More from this chapter

All 26 →
22

Describe the working principle of a moving coil galvanometer. Why is it necessary to use (i) a radial magnetic field and (ii) a cylindrical soft iron core in a galvanometer? Write the expression for current sensitivity of the galvanometer.

Can a galvanometer as such be used for measuring the current? Explain.


OR


A. Define the term ‘self-inductance’ and write its S.I. unit.


B. Obtain the expression for the mutual inductance of two long co-axial solenoids and would one over the other, each of length L and radii and and and number of turns per unit length, when a current I is set up in the outer solenoid

23

Mrs. Rashmi Singh broke her reading glasses. When she went to the shopkeeper to order new specs, he suggested that she should get spectacles with plastic lenses instead of glass lenses. On getting the new spectacles, she found that the new ones were thicker than the earlier ones. She asked this question to the shopkeeper but he could not offer satisfactory explanation for this. At home, Mrs. Singh raised the same question to her daughter Anuja who explained why plastic lenses were thicker.

A. Write two qualities displayed each by Anuja and her mother.


B. How do you explain this fact using lens maker’s formula?

 25

A. Distinguish between unpolarized light and linearly polarized light. How does one get linearly polarised light with the help of a polaroid?

B. A narrow beam of unpolarized light of intensity is incident on a polaroid The light transmitted by it is then incident on a second polaroid with its pass axis making angle of 60o relative to the pass axis of Find the intensity of the light transmitted by .


OR


A. Explain two features to distinguish between the interference pattern in young’s double slit experiment with the diffraction pattern obtained due to a single slit.


B. A monochromatic light of wavelength 500 mm is incident normally on a single slit of width 0.2 mm to produce a diffraction pattern. Find the angular width of the central maximum obtained on the screen.


Estimate the number of fringes obtained in Young’s double slit experiment with fringe width 0.5 mm, which can be accommodated within the region of total angular spread of the central maximum due to single slit. (the wavelength of the light is given in mm but all the calculations are done using it as nm)

 26

(i) Derive an expression for drift velocity of electrons in a conductor. Hence deduce Ohm’s law.

(ii) A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts. Which of the following quantities remain constant in the wire?


A. drift speed


B. current density


C. electric current


D. electric field


Justify your answer.


OR


(i) State the two Kirchhoff’s laws. Explain briefly how these rules are justified.



(ii) The current is drawn from a cell of emf E and internal resistance r connected to the network of resistors each of resistance r as shown in the figure. Obtain the expression for (i) the current draw from the cell and (ii) the power consumed in the network.