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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’.
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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"`
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संबंधित प्रश्न
(a) drift speed
(b) current density
(c) electric current
(d) electric field
Why alloys like constantan and manganin are used for making standard resistors?
Define relaxation time of the free electrons drifting in a conductor. How is it related to the drift velocity of free electrons? Use this relation to deduce the expression for the electrical resistivity of the material.
Consider the following statements.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
Thomson Effect is caused _______________ .
The identical conductors maintained at same temperature are given potential difference in the ratio 1 : 2. Then the ratio of their drift velocities is ______.
Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why not?
- Consider circuit in figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity?
- Electrons give up energy at the rate of RI2 per second to the thermal energy. What time scale would one associate with energy in problem (a)? n = no of electron/volume = 1029/m3, length of circuit = 10 cm, cross-section = A = (1mm)2
Define relaxation time.
A potential difference (V) is applied across a conductor of length 'L' and cross-sectional area 'A'.
How will the drift velocity of electrons and the current density be affected if another identical conductor of the same material were connected in series with the first conductor? Justify your answers.
