Q26 of 26 Page 1

(i) Define the term drift velocity.

(ii) On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. On what factors does resistivity of a conductor depend?


(iii) Why alloys like constantan and manganin are used for making standard resistors?


OR


(i) State the principle of working of a potentiometer.


(ii) In the following potentiometer circuit AB is a uniform wire of length 1 m and resistance 10 Ω. Calculate the potential gradient along the wire and balance length AO ( = l).



(i)


The velocity with which the charge particle move or drift towards the positive terminal of the conductor, when under the influence of the electric field.


(ii)


The formula for the drift velocity can be written as



And the current that flows in the conductor is



where


is the drift velocity, e is the charge, E is the electric field, m is the mass of the charge/electron, t is the time difference after electrons collide or the relaxation time, A is the area of the conductor, n is the number of charge.


Now finding the resistance, R which can be written as



Placing the value of current, I as and V as



Now as we know that both resistivity and resistance is related by



In the above formula the value of , then the resistance can be written as



Hence, the resistivity is



The resistivity of the conductor depends on


1. Resistivity is inversely proportional to the number of free electrons in the conductor volume.


2. Resistivity depends inversely on the time of electron relaxation after collision.


(iii)


Alloys like constantan and manganin are used for making standard resistors because of high resistivity and low temperature coefficient.


OR


(i)


The potential difference between two current carrying points with a wire having uniform area and substance, the potentiometer reading is directly proportional to the length of the wire.


(ii)


Given


A potentiometer circuit diagram Fig 26.2 is given as



The length of the potentiometer circuit is 1m, the balance length of the potentiometer is AO = l, the main resistance is , the resistance on the circuit wire AB is .


Formula Used


To find the length AO, we use the formula of potential difference which states the ratio of Voltage upon Resistance.



where


is the potential difference, is the resistance on the wire AB, V is the voltage supplied.


The potential difference across the wire with is




The potential difference across AO with is




Therefore, the length of the wire AO is



More from this chapter

All 26 →
22

Draw a schematic ray diagram of reflecting telescope showing how rays coming from a distant object are received at the eye-piece. Write its two important advantages over a refracting telescope.

 23

Meeta’s father was driving her to the school. At the traffic signal she noticed that each traffic light was made of many tiny lights instead of a single bulb. When Meeta asked this question to her father, 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 answer did Meeta’s father give?


(iii) What are the tiny lights in traffic signals called and how do these operate?


 24

(i) An a.c. source of voltage V = V0 sin ωt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expressions for impedance of the circuit and phase angle between voltage and current. Find the condition when current will be in phase with the voltage. What is the circuit in this condition called?

(ii) In a series LR circuit XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL = XC is put in series, the power factor becomes P2. Calculate P1/P2.


OR


(i) Write the function of a transformer. State its principle of working with the help of a diagram. Mention various energy losses in this device.


(ii) The primary coil of an ideal step up transformer has 100 turns and transformation ratio is also 100. The input voltage and power are respectively 220 V and 1100 W. Calculate


(a) Number of turns in secondary


(b) Current in primary


(c) Voltage across secondary


(d) Current in secondary


(e) power in secondary


 25

(i) In Young’s double slit experiment, deduce the condition for (a) constructive, and (b) destructive interference at a point on the screen. Draw a graph showing variation of intensity in the interference pattern against position ‘x’ on the screen.

(ii) Compare the interference pattern observed in Young’s double slit experiment with single slit diffraction pattern, pointing out three distinguishing features.


OR


(i) Plot a graph to show variation of the angle of deviation as a function of angle of incidence for light passing through a prism. Derive an expression for refractive index of the prism in terms of angle of minimum deviation and angle of prism.


(ii) What is dispersion of light? What is its cause?


(iii) A ray of light incident normally on one face of a right isosceles prism is totally reflected as shown in fig. What must be the minimum value of refractive index of glass? Give relevant calculations.