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प्रश्न
The potential difference applied across a given conductor is doubled. How will this affect (i) the mobility of electrons and (ii) the current density in the conductor? Justify your answers.
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उत्तर
Mobility of electron `mu = (v_d)/E = (v_dl)/V`
as `E = V/l`
Hence, `mu prop 1/V`
If V becomes 2V, the mobility will become half. The current density is given by
`J = n ev_d`
J = `n e.(eVtau)/(ml)`
J = `(n e^2Vtau)/(ml)`
J ∝ V
When V become 2V current density will become twice.
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संबंधित प्रश्न
Define the term drift velocity.
Derive an expression for drift velocity of free electrons in a conductor in terms of relaxation time.
Consider the following statements.
(A) Free-electron density is different in different metals.
(B) Free-electron density in a metal depends on temperature.
Thomson Effect is caused _______________ .
Obtain the expression for the current flowing through a conductor having number density of the electron n, area of cross-section A in terms of the drift velocity vd .
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 ______.
- 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
Derive an expression for resistivity of a conductor in terms of the number density of charge carriers in the conductor and relaxation time.
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.
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.
