Current Electricity

JEE Main level, single correct, medium

16 of 380

Question 16 of 380

A. The drift velocity of electrons decreases with the increase in the temperature of conductor.
B. The drift velocity is inversely proportional to the area of cross-section of given conductor.
C. The drift velocity does not depend on the applied potential difference to the conductor.
D. The drift velocity of electron is inversely proportional to the length of the conductor.
E. The drift velocity increases with the increase in the temperature of conductor.
Choose the correct answer from the options given below:

Show answer and solution

Answer: (B) A and D only

Drift velocity =(eτm)E=\left(\dfrac{e\tau }{m}\right)E
vd=(eτm)(ΔVl){v}_{d}=\left(\dfrac{e\tau }{m}\right)\left(\dfrac{\Delta V}{l}\right)
ΔV=\Delta V= Potential difference applied across the wire As temperature increases, relaxation time decreases, hence Vd{V}_{d} decreases.
As per formula, Vd∝1l{V}_{d}\propto \dfrac{1}{l}
vd=IneA{v}_{d}=\dfrac{I}{neA}, as it is not mentioned that current is at steady state neither it is mentioned that nn is constant for given conductor. So it can't be said that vd{v}_{d} is inversely proportional to AA.
I=neAvd=VR=VρlAI=neA{v}_{d}=\dfrac{V}{R}=\dfrac{V}{\rho l}A
vd=eEτm{v}_{d}=\dfrac{eE\tau }{m}
τ\tau decrease with temperature increase.
First and fourth statements are correct.
vd=Vρlne(E=Vl){v}_{d}=\dfrac{V}{\rho lne}\left(E=\dfrac{V}{l}\right)

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