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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Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

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Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

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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. Write any two features of nuclear forces.

2.The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

3.Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

4.Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

5.Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

6.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° in 0.2 s. The value of emf induced in the loop will be:

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Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Write any two features of nuclear forces.

2.
The figure shows three point charges kept at the vertices of triangle ABC. The net electric field, due to this system of charges, at the midpoint M of base BC will be:

3.
Photoemission of electrons occurs from a metal (\( \phi_0 = 1.96 \, \text{eV} \)) when light of frequency \( 6.4 \times 10^{14} \, \text{Hz} \) is incident on it. Calculate: Energy of a photon in the incident light, The maximum kinetic energy of the emitted electrons, and The stopping potential.

4.
Two small identical metallic balls having charges \( q \) and \( -2q \) are kept far at a separation \( r \). They are brought in contact and then separated at distance \( \frac{r}{2} \). Compared to the initial force \( F \), they will now:

5.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

6.
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° in 0.2 s. The value of emf induced in the loop will be: