Advertisements
Advertisements
प्रश्न
Consider a wire of length 4 m and cross-sectional area 1 mm2 carrying a current of 2 A. If each cubic metre of the material contains 1029 free electrons, find the average time taken by an electron to cross the length of the wire.
उत्तर
Given:-
Current through the wire, i = 2 A
Length of the wire, l = 4 m
Area of cross section, A = 1 mm2 = 1 × 10–6 m2
Number of electrons per unit volume, n = 1029
We know:-
\[i = nA V_d e\]
\[ \Rightarrow V_d = \frac{i}{nAe}\]
\[ = \frac{2}{{10}^{29} \times {10}^{- 6} \times 1 . 6 \times {10}^{- 19}}\]
\[ \Rightarrow V_d = \frac{1}{8000} m/s,\]
where Vd is the drift speed.
Let t be the time taken by an electron to cross the length of the wire.
\[\Rightarrow t = \frac{\text{Length of the wire}}{\text{Drift speed}}\]
\[ = \frac{l}{V_d}\]
\[ \therefore t = \frac{4}{\frac{1}{8000}}\]
\[ = 32 \times {10}^3 s\]
APPEARS IN
संबंधित प्रश्न
Derive an expression for drift velocity of free electrons.
What is its relation with relaxation time?
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
When electrons drift in a metal from lower to higher potential, does it mean that all the free electrons of the metal are moving in the same direction?
A conductor of length ‘l’ is connected to a dc source of potential ‘V’. If the length of the conductor is tripled by gradually stretching it, keeping ‘V’ constant, how will (i) drift speed of electrons and (ii) resistance of the conductor be affected? Justify your answer.
Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.
When a current is established in a wire, the free electrons drift in the direction opposite to the current. Does the number of free electrons in the wire continuously decrease?
A current of 1.0 A exists in a copper wire of cross-section 1.0 mm2. Assuming one free electron per atom, calculate the drift speed of the free electrons in the wire. The density of copper is 9000 kg 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.
Seebeck Effect is caused _____________ .
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 _______________ .
The position-time relation of a particle moving along the x-axis is given by x = a - bt + ct2 where a, band c are positive numbers. The velocity-time graph of the particle is ______.
When a current I is set up in a wire of radius r, the drift velocity is vd· If the same current is set up through a wire of radius 2 r, the drift velocity will be:
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:
Define relaxation time.
Consider two conducting wires A and B of the same diameter but made of different materials joined in series across a battery. The number density of electrons in A is 1.5 times that in B. Find the ratio of the drift velocity of electrons in wire A to that in wire B.
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.
