Current & Drift velocity - Current Electricity Video Lecture - Class 12

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electricity part 10 is brought to you by
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please make sure that you have watched
all the videos to the part 9 before
going ahead with part 10 I will see how
is current related to electrons drift
velocity because as the electrons drift
that constitutes that electric current
right so we will see with the help of
mathematical expression how current is
related to electrons drift velocity so
here also let us consider the same
conductor of length L and let us suppose
that the area of this conductor is a and
we say that the number of electrons per
unit volume in this conductor is n that
is n is the number density of electrons
so number of electrons per unit volume
is n therefore what will be the total
number of electrons so total number of
electrons will be equal to number
density into the volume of the conductor
so that will be number density into
volume is nothing but area into length
of the conductor so this will be the
total number of electrons in the
conductor so what will be the charge on
total number of electrons charged on
total number of electrons will be equal
to e into n al right so this is
basically the total charge that is
present inside this conductor right and
what is the potential difference and we
say that the let us suppose that the
potential difference between the ends of
the conductor is V right so what will be
the electric field electric field will
be nothing but potential difference per
unit length that is V divided by L now
let us suppose now when we apply the
electric field electrons start drifting
right as soon as the electric field is
applied
electrons start drifting so how much
time will it take for an electron to
cross the conductor so the electron will
move from this point till at this point
so what is the time taken by the
electron time taken by an electron to
cross the conductor that will be equal
to the distance covered divided by
velocity time taken is anyway is always
equal to distance divided by velocity so
what does the distance cover distant
covered is nothing but it is the length
of the conductor so this will be equal
to L divided by velocity with which the
electron is moving is nothing but the
drift velocity right therefore what will
be the current current is nothing but
charge per unit time so what is this
charge charge is nothing but total
charge per unit time so total charge in
this conductor is nothing but e in a in
per unit time what is time time is
nothing but n divided by VD so this N
and L will get cancelled so we get e in
a into VD therefore the current in the
conductor I is equal to e and-a into VD
so we get so remember this expression
and from this expression we find that
current is directly proportional to the
drift velocity so as the drift velocity
increases the current also increases now
you must be wondering if drift velocity
is a very small velocity because in the
last slide I told you that drift
velocity is a velocity which is of very
small magnitude because the electron
basically gains a very small velocity
then how is it that current traveled so
fast if electrons are moving so very
slowly with such a small velocity then
how is that in traveling so fast so from
this expression you can see that drift
velocity is one of
the factors which determine the current
but it is not the only factor the other
factors also include the number density
of electrons right so now what happens
is even though the drift velocity is
very small that is the velocity with
which an electron is drifting that is
very small but the number of electrons
which are present within the conductor
that is very huge so what happens is
each person let us suppose you have to
carry hundred bricks to the tenth floor
of a building now if you are the only
person to carry those hundred bricks to
the tenth floor you will take some
amount of thing now let us suppose that
there are 100 people to carry those
hundred bricks to the 8th floor of the
building then what will happen
all of them will pick even if each
person picks one break even then very
easily and very quickly you can pick all
the hundred bricks to the 8th floor
that's because the word got distributed
amongst so many people so similar is the
case yet even though the drift velocity
of one electron is very small but there
are a huge number of electrons the
number density is very high so since
there are so many electrons so the small
small drift velocity of each of those
electrons went to be considered together
becomes a very high current
so therefore the current is very large
so please make a note of this point
general drift velocity is small but
number of electrons is large therefore
current is also large right so now I
hope that the concept of drift velocity
is clear to you so I hope now you
understood how basically a current flows
within a conductor who carries the
current how the carriers carry the
current and thank you please visit
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