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प्रश्न
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.
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उत्तर
In a series circuit current flowing through the entire circuit is exactly the same, hence
`I = n_A A_e(v_d)_A`
= `n_B A_e(v_d)_B`
`((v_d)_A)/((v_d)_B) = n_B/n_A = n_B/(1.5n_B) = 1/1.5`
= `10/15 = 2/3`
`(v_d)_A : (v_d)_B = 2 : 3`
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संबंधित प्रश्न
Define the term drift velocity.
Derive an expression for drift velocity of free electrons.
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.
Electrons are emitted by a hot filament and are accelerated by an electric field, as shown in the figure. The two stops at the left ensure that the electron beam has a uniform cross-section.
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 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 \[m\]?
Which expression gives current density in terms of free electron density, relaxation time, and electric field?
What is the microscopic expression for conductivity?
Why can current be established almost instantly even when drift speed is only a few millimetres per second?
