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.
Advertisements
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
Define the term drift velocity.
Derive an expression for drift velocity of free electrons.
What is its relation with relaxation time?
Write its (‘mobility’ of charge carriers) S.I. unit
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
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.
How does drift velocity of electrons in a metallic conductor vary with increase in temperature? Explain.
On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. On what factors does resistivity of a conductor depend?
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.
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.
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:
Metals are good conductor of heat than insulator because
Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why not?
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.
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.
