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प्रश्न
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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उत्तर
V = constant
l’ = 3l
(i) Drift speed of electrons `= V/("nel" rho)`
Where n is number of electrons
e is charge on electron
l is the length of the conductor
and ρ is the resistivity of conductor.
So, when length is tripled, drift velocity gets one-third.
(ii) Resistance of the conductor is given as
`R =rho l/A`
When length is tripled area of cross-section is reduced to `A/3`
Hence, `R = rho (l')/(A') = rho(3l)/(A/3) = 9rhol/A =9R`
Thus, new resistance will be 9 times the original.
संबंधित प्रश्न
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 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?
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 _______________ .
- 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.
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.
What is the average velocity acquired by free electrons in a conductor under the influence of an electric field called?
What is current density?
With what do electrons continuously collide in a conductor?
Why can current be established almost instantly even when drift speed is only a few millimetres per second?
