Advertisements
Advertisements
प्रश्न
Explain the term ‘drift velocity’ of electrons in conductor. Hence obtain the expression for the current through a conductor in terms of ‘drift velocity’.
Advertisements
उत्तर
‘Drift velocity’ of electrons in a conductor - Metals contain a large number of free electrons. These electrons are in continuous random motion. Due to the random motion, the free electrons collide with positive metal ions with high frequency and undergo change in direction at each collision. So the average velocity for the electrons in a conductor is zero.
Now, when this conductor is connected to a source of emf, an electric field is established in the conductor, such that E = `"V"/"L"`
Where V= potential difference across the conductor and
L = length of the conductor.
The electric field exerts an electrostatic force ‘-Ee’ on each free electron in the conductor. The acceleration of each electron is given by
`vec"a" = ("e"vec"E")/"m"`
Where e = electric charge on electron and
m = mass of electron
The negative sign indicates that the force and hence the acceleration is in a direction opposite to the direction of the electric field. Due to this acceleration, the electrons attain a velocity in addition to thermal velocity in the direction opposite to that of electric field.
The average velocity of all the free electrons in the conductor is called the drift velocity of free electrons of the conductor.
`vec"v"_"d" = - ("e"vec"E")/"m" tau` ....... (1)
Thus, the expression for the drift velocity is
Electric field, `"E" = - "V"/"L"` .....(2)
where `tau` = relaxation time between two successive collision.
Let n = number density of electrons in the conductor.
No. of free electrons in the conductor = nAL
Total charge on the conductor, q = nALe
Time taken by this charge to cover the length L of the conductor, `"t" = "L"/"V"_"d"`
current `"I" = "q"/"t"`
`= ("nALe")/"L" xx "v"_"d"`
`= "nAev"_"d"`
Using eq (1) and (2) , we get that
`"I" = "nAe" xx (-("e"vec"E")/"m" tau)`
`= "nAe" xx (- ("e"(-"V"))/("mL") tau)`
`= (("n" "e"^"2A")/("mL")tau)"V"`
APPEARS IN
संबंधित प्रश्न
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?
Why alloys like constantan and manganin are used for making standard resistors?
A conductor of length ‘l’ is connected to a dc source of potential ‘V’. If the length of the conductor is tripled by gradually stretching it, keeping ‘V’ constant, how will (i) drift speed of electrons and (ii) resistance of the conductor be affected? Justify your answer.
Electrons are emitted by a hot filament and are accelerated by an electric field, as shown in the figure. The two stops at the left ensure that the electron beam has a uniform cross-section.
Consider the following statements.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
Peltier Effect is caused _______________ .
Obtain the expression for the current flowing through a conductor having number density of the electron n, area of cross-section A in terms of the drift velocity vd .
Amount of charge in coulomb required to deposit one gram equivalent of substance by electrolysis is:-
An electric bulb.is rated 220 v and 100 watt power consumed by it when operated on 'no volt is:-
Two conductors, made of the same material have equal lengths but different cross-sectional areas A1 and A2 (A1 > A2). They are connected in parallel across a cell. Show that the drift velocities of electrons in two conductors are equal.
The drift velocity of electrons in a conductor connected to a battery is given by vd = `(−"eE" τ)/"m"`. Here, e is the charge of the electron, E is the electric field, τ is the average time between collisions and m is the mass of the electron.
Based on this, answer the following:
- How does the drift velocity change with a change in the potential difference across the conductor?
- A copper wire of length 'l' is connected to a source. If the copper wire is replaced by another copper wire of the same area of cross-section but of length '4l', how will the drift velocity change? Explain your answer.
