Q25 of 26 Page 1

A 2 μF capacitor, 100 W resistor and 8 H inductor is connected in series with an AC source.

(i) What should be the frequency of the source such that current drawn in the circuit is maximum? What is this frequency called?


(ii) If the peak value of e.m.f. of the source is 200 V, find the maximum current.


(iii) Draw a graph showing variation of amplitude of circuit current with changing frequency of applied voltage in a series LRC circuit for two different values of resistance R1 and R2 (R1 > R2).


(iv) Define the term ‘Sharpness of Resonance’. Under what condition, does a circuit. become more selective?


OR


(i) With the help of a neat and labelled diagram, explain the principle and working of a moving coil galvanometer.


(ii) What is the function of uniform radial field and how is it produced?


(iii) Define current sensitivity of a galvanometer. How is current sensitivity increased?


Given:


Capacitor, C=2μF


Resistance,


Inductance, L=8 H


Calculation:


The circuit must be at resonance to draw maximum current from a series LCR circuit.


The condition for resonance is,


XL=XC


The frequency is given by,



(ii) Given:


EMF, E=200V


Resistance,


Calculation:


The maximum current is given by,



(iii)



(iv) The ratio of the voltage developed across the inductance at resonance to the voltage developed across the resistance is known as the sharpness of resonance. It can also define as the ratio of the resonance angular frequency to the band width of the circuit.


or


The condition for selectiveness of the circuit is given as follows:


The resonance becomes sharper the maximum current is more. For smaller range of the frequencies the circuit is close to resonance.


OR


(i) The torque acting on the coil is given by,



Where,


θ=between plane and coil



When the coil is parallel to the magnetic field


Thus, torque is given by,



Let’s assume that C is the torsional rigidity of the wire and θ is the twist of suspension strip. The restoring torque is given by,



For equilibrium position,



Thus, deflection of the coil is directly proportional to the current flowing through the coil.


(ii) The radial magnetic field produces torque as,



This causes the deflection is directly proportional to the current. This results in making the radial magnetic field as scale linear. The radial magnetic field from the pole piece of permanent magnet are produced by placing cylindrical and soft iron core between them. This soft iron core helps to decrease energy losses due to eddy current.


(iii) The current sensitivity is defined as the deflection of the coil per ampere.


Current sensitivity is given by,



Thus, the sensitivity of the galvanometer is directly proportional to the number of the turns in the coil.


More from this chapter

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22

(i) Define self-inductance. Write its SI units.

(ii) A long solenoid with 15 turns per cm has a small loop of area 2.0 cm2 placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?


 23

Gautam went for a vacation to the village where his grandmother lived. His grandmother took him to watch ‘nautanki’ one evening. They noticed a black box connected to the mike lying nearby. Gautam’s grandmother did not know what that box was. When she asked this question to Gautam, he explained to her that it was an amplifier.

(i) Which values were displayed by the grandmother? How can inculcation of these values in students be promoted?


(ii) What is the function of an amplifier?


(iii) Which basic electronic device is used in the amplifier?


 24

(i) State the essential conditions for diffraction of light.

(ii) Explain diffraction of light due to a narrow single slit and the formation of pattern of fringes on the screen.


(iii) Find the relation for width of central maximum in terms of wavelength ‘l’, width of slit ‘a’, and separation between slit and screen ‘D’.


(iv) If the width of the slit is made double the original width, how does it affect the size and intensity of the central band?


OR


(i) Draw a labelled schematic ray diagram of astronomical telescope in normal adjustment.


(ii) Which two aberrations do objectives of refracting telescope suffer from? How are these overcome in reflecting telescope?


(iii) How does the resolving power of a telescope change on increasing the aperture of the objective lens? Justify your answer.


 26

(i) In the circuit diagram given below, AB is a uniform wire of resistance 15 Ω and length 1 m. It is connected to a cell E1 of emf 2V and negligible internal resistance and a resistance R. The balance point with another cell E2 of emf 75 mV is found at 30 cm from end A. Calculate the value of R.


(ii) Why is potentiometer preferred over a voltmeter for comparison of emf. of cells?


(iii) Draw a circuit diagram to determine internal resistance of a cell in the laboratory.


OR


(i) Plot a graph showing variation of voltage vs the current drawn from the cell.


How can one get information from this plot about the emf of the cell and its internal resistance?


(ii) Two cells of emf’s E1 and E2 and internal resistance r1 and r2 are connected in parallel. Obtain the expression for the emf and internal resistance of a single equivalent cell that can replace this combination?