Test: Drift Velocity & Resistivity of Electrons - JEE MCQ

To convert temperature to voltage we can do a precise measurement of the temperature in a room. A NTC resistor or a thermistor
It is used as a sensor that has a strong temperature dependence.

n increases with temperature and this increase more than compensates any decrease in relaxation time. Hence, for semiconductors resistivity decreases with the increase in temperature.

F=-eE .
we know that,
F= ma ,
then
a=F/m.
a=-eE/m.

A Nichrome or manganin is commonly used as the metal wires in wire-wound resistors because they provide high resistance to the electric current and operate at high temperature.

The resistance of a material at temperature T is given by 
R=R₀​[1+α(T−T₀​)]
Where R₀​= resistance at reference temperature T​₀=0^oC and α is the temperature coefficient of resistance. 
From the above equation, the unit of the temperature coefficient is per degree Celsius (/^oC). So, dimension will be [C⁻¹]

Heating a conductor makes it more difficult for electricity to flow through it. These collisions cause resistance and generate heat.Heating the conductor causes atoms to vibrate more, which in turn makes it more difficult for the electrons to flow, increasing resistance.

Resistance of a conductor is given by R = ρ l/A,
where ρ is the specific resistance, l is the length and A is the cross-sectional area of the conductor.
Now, when l = 1 and A = 1, R = ρ. So specific resistance or resistivity of a material may be defined as the resistance of a specimen of the material having unit length and unit cross-section. Hence, specific resistance is a property of a material and it will increase with the increase of temperature, but will not vary with the dimensions (length, cross section) of the conductor.
 

Current does not depend on the area of the conductor; hence it remains a constant.
Current density is inversely a constant.
Current density is inversely proportional to area (i.e.,) J∝1/A​ electric field drift speed is also inversely proportional to area (i.e.,) E∝1/A​,V_d​∝1/A​
Hence current is constant along the conductor.

Drift velocity, v=I/nAe
=2/(2x10^-6)x(5x10²⁶)x(1.6x10^-19)
=1.25x10^-2m/s

 Answer :- b

Temperature coefficient of resistance is very low

For manganin, the temp coefficient of resistance is very low, and its resistivity is quite large. Due to which the resistance of the manganin wire remains almost unchanged with change in temperature. It is due to this fact; the wire of the manganin is used for making standard resistance coil.

Drift velocity is directly proportional to potential difference.
Drift velocity is defined as the average velocity with which free electrons get drifted towards the positive end of the conductor under the influence of an external electric field.
Drift velocity is given by
v_d​= eEτ​/ m
But, E=V/l​
(if l is length of the conductor and V is constant potential difference applied across the ends of the conductor)
∴v_d​= eVτ​/ml
⇒v_d​∝V
So, when the potential difference is doubled the drift velocity will be doubled.
Note - Current flowing through a conductor is directly proportional to the drift velocity.

The resistance of a conductor depends on thickness (cross sectional area of the wire), length and temperature.
Resistivity is defined as the measure of the resisting power of a specified material to the flow of an electric current.
R=ρ(I/A)​
where R = Resistance of the conductor
ρ = Resistivity of the conductor
l = length of the conductor
A = Area of cross section
i.e., ρ=R (A​/l)

To determine the resistance of a carbon resistor based on the color bands, we need to refer to the standard resistor color code. The colors represent digits and multipliers as follows:

• Green: 5
• Red: 2
• Orange: Multiplier of 10^3 (1,000)

Given the color bands: Green, Red, Orange

The resistance value is calculated as follows:

1. First digit: Green = 5
2. Second digit: Red = 2
3. Multiplier: Orange = 10^3 (1,000)

So the resistance is:

Resistance=(52)×10^3 ohms=52,000 ohms=52 kilo-ohms

Answer: The approximate resistance of the resistor is 52 kΩ.

When we use a heating element that has
1. High specific resistance: a small quantity of wire is used to generate the required amount of heat or else the quantity of wire would be required higher in order to heat.
2. High melting point: a higher melting point is selected so that higher temperature is attained. Nickel and chromium alloys are ideal as a heating element.

Semiconductors are materials which have a conductivity between conductors (generally metals) and nonconductors or insulators (such as most ceramics). Semiconductors can be pure elements, such as silicon or germanium, or compounds such as gallium arsenide or cadmium selenide. In a process called doping, small amounts of impurities are added to pure semiconductors causing large changes in the conductivity of the material.

Relaxation time is the average time between two successive collisions between the free electrons and the atoms(kernel) of atoms .
It is denoted by τ.

Mobility of charge carriers in a conductor is defined as the magnitude of their drift velocity per unit applied electric field.
Mobility,
μ=Drift of electric field
μ=V_dE
S.I. unit of mobility is m²Vs or ms NC.

 

Constantan is an alloy of copper (55%) and nickel (45%) where Manganin is an alloy of copper (84%) manganese(12%) and nickel (4%).
When all metals show increase in resistivity with increase in temperature and semiconductors show the reverse, Constantan and Manganin show a completely different property.
Their main feature is their low thermal variation of their resistivity, which is constant over a wide range of temperatures.
Metals, including alloys, have free electrons as charge carriers. Their movement controls by defects. One of defects of usual metal is oscillations of atoms due to temperature. More temperature - more oscillations - more collisions of electrons with atoms - less mobility - more resistivity. In alloys, like constantan and Manganin, atoms are in disorder. So they have big resistivity. Their additional disorder due to temperature increase is insignificant. That is why they have no temperature dependence on resistivity.