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.

Relaxation time refers to the time gap between two successive collisions of electrons in a conductor.

The relationship between the relaxation time and drift velocity is as given below.

$\begin{array}{l}v_{d} = \left ( e\frac{E}{m} \right )T\end{array}$

Where

v_d = drift velocity
e = charge of electron
E = field
m = mass of an electron
T = Relaxation time

So the expression for relaxation time (T) is

$\begin{array}{l}T = \left ( v_{d}\frac{m}{e} \right )E\end{array}$

Let

L be the length of the conductor
A be the area of the conductor
n is the current density

Then, the current flowing through the conductor is $\begin{array}{l}I = -neAv_{d}\end{array}$

$\begin{array}{l}I = neA\left ( e\frac{E}{m} \right )T\end{array}$

$\begin{array}{l}I = \frac{ne^{2}EA}{m}T\end{array}$

The field E can be therefore expressed as –

E = V/L

Then the current flowing through the conductor becomes $\begin{array}{l}I = \frac{ne^{2}VA}{mL}T\end{array}$

$\begin{array}{l}\frac{V}{I} = \frac{mL}{ne^{2}TA}\end{array}$

From Ohm’s law

V = IR

R = V/I

$\begin{array}{l}R = \left ( \frac{m}{ne^{2}T} \right )\frac{L}{A}\end{array}$

$\begin{array}{l}R = \rho \frac{L}{A}\end{array}$

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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.

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With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.

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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.

Related Questions

CBSE CLASS XII Related Questions

1.With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.

2.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.

2.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?