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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A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^\circ$ in 0.2 s. The value of emf induced in the loop will be:

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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.The number of free electrons per unit volume ($\text{m}^3$) in a wire made of copper (resistivity $1.72 \times 10^{-8}\,\Omega\,\text{m}$) is $8.5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.

2.A magnet held vertically, with its north pole down, is dropped along the axis of a closed solenoid placed vertically on a table. If the observer looks down from the top,

4.A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^\circ$ in 0.2 s. The value of emf induced in the loop will be:

5.Find the ratio $\dfrac{\lambda_\alpha}{\lambda_p}$ of the de Broglie wavelength $\lambda_\alpha$ associated with an alpha particle to the de Broglie wavelength $\lambda_p$ associated with a proton if both are moving with the same velocity.

6.In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The number of free electrons per unit volume ($\text{m}^3$) in a wire made of copper (resistivity $1.72 \times 10^{-8}\,\Omega\,\text{m}$) is $8.5 \times 10^{28}$. Calculate the average number of collisions made by an electron in one second when an electric field is maintained in the wire.

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A magnet held vertically, with its north pole down, is dropped along the axis of a closed solenoid placed vertically on a table. If the observer looks down from the top,

4.
A square loop of side 0.50 m is placed in a uniform magnetic field of 0.4 T perpendicular to the plane of the loop. The loop is rotated through an angle of $60^\circ$ in 0.2 s. The value of emf induced in the loop will be:

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Find the ratio $\dfrac{\lambda_\alpha}{\lambda_p}$ of the de Broglie wavelength $\lambda_\alpha$ associated with an alpha particle to the de Broglie wavelength $\lambda_p$ associated with a proton if both are moving with the same velocity.

6.
In a region, the electric potential varies as \(V = 10 - 50x\), where \(V\) is in volts and \(x\) is in meters. The electric field in the region is