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.

Related Questions

CBSE CLASS XII Related Questions

1. Write any two features of nuclear forces.

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

3. Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

4.What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

5. If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

6.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.

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Write any two features of nuclear forces.

2.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

3.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

4.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

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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.