18. The current (1) flowing through a conductor depends on : (i) number density of electrons (n) (ii) charge on
the electron (e) (iii) area of cross-section (A) of the conductor and (iv) the drift velocity (Vd) of the
electron. Obtain a relation for I.
[I = neAvd]
Answers
Answer:
Explanation:
consider a conductor having length L and A as area of cross section
let number of electrons in the conductor be N
when a potential difference of V is applied across the conductor
an electric field E sets across the conductor
E = V/L
due to the electric field electron experience a force F
F = E*e (e is the charge of electron)
F = ma
m a = E *e
a = E*e /m
the electron acclerates and collides with other electron and comes to stop...agiain acclerates and stops...this goes on and on until it travels the whole length of the conductor
v₁ = u +a t₁ ..here u is zero so the velocity of electron just before first collision is given by this eqn
v₂ = a t₂ velocity of electron just before second collision is given by this eqn
it goes on like v₃ v₄ v₅....................vₙ
therefore average velocity = drift velocity = v₁ + v₂ + v₃+.............vₙ / n
Vdrift = at1+at2 +at3............atn / n
a (t₁ +t₂ +t₃................tₙ)/n
let (t₁ +t₂ +t₃................tₙ)/n = avaerge relaxation time =τ
Vdrift = aτ
= (E e / m ) *τ
time taken by one electron to cross the conductor length L
t = distance L / Vdrift
current I = q/t
total number of electron = N
total charge = Ne
charge density n = Ne / AL(volume of conductor)
total charge = n*AL
CURRENT =( N A L e ) / ( L / Vdrift )
current = NAe Vdrift