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Question : 26
Total: 26
(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 circuitA B 1 m 10 Ω AO ( = l )
(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
Solution:
(i) Definition of drift velocity
(ii) Derivation of expression of resistivity
Factors affecting resistivity
(iii) Reason of using constantan and manganin
(i) Average velocity acquired by the electrons in the conductor in the presence of external electric field.
[Alternatively:
v d =
τ
(ii)v d =
We haveE = −
V l
v d =
Current flowing I = n e A v d
I = n e A v d
=
=
=
Also,R = ρ
Comparing (i) and (ii),
ρ =
Resistivity of the material of a conductor depends on the relaxation time, i.e., temperature and the number density of electrons.
(iii) Because constantan and manganin show very weak dependence of resistivity on temperature.
OR
(i) Working principle of potentiometer
(ii) Calculation of potential gradient and balance length
(i) When constant current flows through a conductor of uniform area of cross section, the potential difference, across a lengthl
[ V ∝ l
(ii) Current flowing in the potentiometer wire
i =
=
=
A
∴
V A B =
× 10 V =
= 0.8 volt
Hence potential gradient
K =
=
= 0.8
Current flowing in the circuit containing experimental cell,
=
= 1 A
Hence, potential difference across lengthAO
= 0.3 × 1 V = 0.3 V
⇒ 0.3 = K × l A O
= 0.8 × I AO
⇒ l A O =
m = 0.375 m
= 37.5 cm
(ii) Derivation of expression of resistivity
Factors affecting resistivity
(iii) Reason of using constantan and manganin
(i) Average velocity acquired by the electrons in the conductor in the presence of external electric field.
[Alternatively:
(ii)
We have
Also,
Comparing (i) and (ii),
Resistivity of the material of a conductor depends on the relaxation time, i.e., temperature and the number density of electrons.
(iii) Because constantan and manganin show very weak dependence of resistivity on temperature.
OR
(i) Working principle of potentiometer
(ii) Calculation of potential gradient and balance length
(i) When constant current flows through a conductor of uniform area of cross section, the potential difference, across a length
(ii) Current flowing in the potentiometer wire
Hence potential gradient
Current flowing in the circuit containing experimental cell,
Hence, potential difference across length
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