Advertisements
Advertisements
प्रश्न
Explain how free electrons in a metal at constant temperature attain an average velocity under the action of an electric field. Hence, obtain an expression for it.
Advertisements
उत्तर
We know that free electrons are the current carriers in a metallic conductor, and these free electrons move randomly in all directions and constantly collide with the positive ions inside the metal, resulting in an average thermal velocity of zero. When an electric field is applied across the two ends of the metallic conductor, an electric field is set up across the two ends of the conductor, and now free electron moves in a particular direction due to external elution.
Expression for drift velocity: When a potential difference is applied across a conductor, an electric field is produced and free electrons are acted upon by an electric force (F = -Ee). Due to this, electrons accelerate and keep colliding with each other and acquire a constant (average) velocity, `v_d`.
∴ F = -Ee = `-(V/l)e`
∴ E = `V/l`
As `a = (-F)/m = (-eV)/(lm)`
and also `v` = u + at
∴ u = 0, t = τ(relaxation time)
`v_d = -atau`
`v_d = (-eV)/(lm)tau`
APPEARS IN
संबंधित प्रश्न
Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 × 10−7 m2 carrying a current of 1.5 A. Assume the density of conduction electrons to be 9 × 1028 m−3
Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 2·5 × 10−7 m2 carrying a current of 2·7 A. Assume the density of conduction electrons to be 9 × 1028 m−3
Consider the following statements.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
Peltier Effect is caused _______________ .
At room temperature, copper has free electron density of 8.4 × 1028 per m3. The copper conductor has a cross-section of l0−6 m2 and carries a current of 5.4 A. The electron drift velocity in copper is:
Metals are good conductor of heat than insulator because
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.
Two conductors, made of the same material have equal lengths but different cross-sectional areas A1 and A2 (A1 > A2). They are connected in parallel across a cell. Show that the drift velocities of electrons in two conductors are equal.
The drift velocity of electrons in a conductor connected to a battery is given by vd = `(−"eE" τ)/"m"`. Here, e is the charge of the electron, E is the electric field, τ is the average time between collisions and m is the mass of the electron.
Based on this, answer the following:
- How does the drift velocity change with a change in the potential difference across the conductor?
- A copper wire of length 'l' is connected to a source. If the copper wire is replaced by another copper wire of the same area of cross-section but of length '4l', how will the drift velocity change? Explain your answer.
Which expression gives the drift velocity in terms of electric field \[E\], relaxation time \[\tau\], electronic charge \[e\], and electron mass \[m\]?
