Advertisements
Advertisements
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.
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
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 1.8 A. Assume the density of conduction electrons to be 9 × 1028 m−3.
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 _______________ .
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 drift velocity of a free electron inside a conductor is ______
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.
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.
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.
