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प्रश्न
The number density of free electrons in a copper conductor is 8.5 × 1028 m−3. How long does an electron take to drift from one end of a wire 3.0 m long to its other end? The area of cross-section of the wire is 2.0 × 10−6 m2 and it is carrying a current of 3.0 A.
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उत्तर
Given: Number density of free electrons in a copper conductor, n = 8.5 × 1028 m−3
Length of the copper wire, l = 3.0 m
Area of cross-section of the wire, A = 2.0 × 10−6 m2
Current carried by the wire, I = 3.0 A, which is given by the relation,
Formula: I = nAeVd
Where,
e = Electric charge = 1.6 × 10−19 C
Vd = Drift velocity =`"Length of the wire (l)"/"Time taken to cover l(t)"`
I = `(nAel)/t`
t = `(nAel)/I`
= `(3 xx 8.5 xx 10^28 xx 2 xx 10^-6 xx 1.6 xx 10^-19)/3.0`
= `(81.6 xx 10^3)/3.0`
= 27.2 × 103 s
Therefore, the time it takes for an electron to drift from one end of the wire to the other is 27.2 × 103 s.
संबंधित प्रश्न
How does drift velocity of electrons in a metallic conductor vary with increase in temperature? Explain.
(a) drift speed
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(c) electric current
(d) electric field
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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.
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The drift velocity of a free electron inside a conductor is ______
- Consider circuit in figure. How much energy is absorbed by electrons from the initial state of no current (ignore thermal motion) to the state of drift velocity?
- Electrons give up energy at the rate of RI2 per second to the thermal energy. What time scale would one associate with energy in problem (a)? n = no of electron/volume = 1029/m3, length of circuit = 10 cm, cross-section = A = (1mm)2
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.
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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 symbol denotes relaxation time?
When an electric field \[E\] is applied to a conductor, what force direction does an electron of charge \[-e\] experience?
Which expression gives the acceleration of an electron in an electric field?
If \[n\] is the number of free electrons per unit volume and \[A\] is the conductor’s cross-sectional area, which expression gives the current from electron drift?
Which expression gives current density in terms of free electron density, relaxation time, and electric field?
What is the microscopic expression for conductivity?
What is the effect of collisions on the acceleration produced by an electric field?
