The current of a conductor flowing through a conductor in terms of the drift speed of electrons is (the symbols have their usual meanings)

Question

The current of a conductor flowing through a conductor in terms of the drift speed of electrons is (the symbols have their usual meanings) (A) I = √n Ae vd (B) I = A √n e vd (C) I = (n e/A vd) (D) I = n e A vd

Tardigrade Admin · Accepted Answer

Relation between current and drift velocity : Consider a conductor of length

l

and area of cross – section

A

having

n

electrons per unit length, as shown in the figure.
The volume of the conductor =

A l

∴

Total number of electrons in the conductor
= Volume

\times

electron density =

A l n

If

e

is the charge of an electron, then
total charge contained in the conductor,

Q = e n A l

Let a potential difference V is applied across the conductor. The resulting electric field in the conductor is given by

E = \frac{V}{l}

Under the influence of this field E, free electrons begin to drift in a direction opposite to that of the field. Time taken by electrons to cross – over the conductor is

t = \frac{l}{v _{d}}

where,

v_{d}

is the drift velocity of electrons.
Therefore, the current through the conductor is given by

I = \frac{Q}{t} = \frac{e n A l}{I / v _{d}}

or

I = n e A v_{d}

\Rightarrow I α v_{d}

[∵ n, e, A

are all constant]
Hence, Current density is proportional to drift velocity.

Q. The current of a conductor flowing through a conductor in terms of the drift speed of electrons is (the symbols have their usual meanings)

$I = n A e v_{d}$

$I = A n e v_{d}$

$I = \frac{n e}{A v _{d}}$

$I = n e A v_{d}$

Q. The current of a conductor flowing through a conductor in terms of the drift speed of electrons is (the symbols have their usual meanings)

I=nAe​vd​

I=Ane​vd​

I=Avd​ne​

I=neAvd​

$I = n A e v_{d}$

$I = A n e v_{d}$

$I = \frac{n e}{A v _{d}}$

$I = n e A v_{d}$