Ohms Law derivation & limitation - Current Electricity Video Lecture - Class 12

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please make sure that you have watched
all the video still part 14 before going
ahead with this one now that we
understood each and every term of Ohm's
law
you remember Ohm's law right we started
with Ohm's law and then when we deviated
ourselves to resistance that that's
because the Ohm's law had this R so now
we studied all about resistance and
again resistance had in something called
resistivity so we studied that we
covered all that so now it's time that
we derive Ohm's law so mathematically we
will try to derive Ohm's Lana with the
help of the expressions which we had
derived earlier so before we have seen
that the drift velocity of electron
would is equal to minus e into capital e
tau divided by n where E is the charge
on an electron capital e is the electric
field tau is the average time between
each collision and M is the mass of
electron and also electric field E is
equal to potential difference per unit
length because electric field is
negative gradient of potential
difference now using these two we can
write VD is equal to e into D into tau
divided by MA we have just put the value
of electric field E here so this is the
value of drift velocity so from this we
can write V is equal to drift velocity
into M into L divided by e into tau
right now from Ohm's law we know that
now not Ohm's law from before our study
between the car in relation between
current and drift velocity we know that
I is equal to a n e into VD so this
implies that VD is equal to I divided by
a n E so now we will put this value of
VD in this expression
so my expression will become therefore
this expression will become I divided by
a and e into m n divided by
itaú so this becomes equal to ml divided
by a n e square into tau into I so now
this entire term is nothing but
resistance if you look at this term what
is it it is nothing but M divided by n v
square tau into L by a into I right so
what is this this is nothing but Rho
that is the specific resistance so this
is Rho L by a so this entire term is I
so this is equal to V is equal to R into
I therefore the Ohm's law is proved so
this is how we derive or we reach at
Ohm's law so basically this entire
lesson is based on Ohm's law so you have
to understand Ohm's now very clearly see
this entire lesson I have divided into
two parts the first part talked about
Ohm's law and things related to Ohm's
law like resistance resistivity current
drift velocity and things like that and
the second part will talk about
resistors and how do we connect
resistors and circuits and the
mathematical part involved with
resistors and in our next video we will
talk about electric circuits as a whole
where we will have combination of
resistors capacitors batteries and we
will see how do we solve those circuits
so that circuit lesson will come in the
next video
okay so as of now this was your Ohm's
law
so now we will look at the limitations
of Ohm's law so we will look at whether
Ohm's law was a complete success or
there were certain failures involved
with Ohm's law
well Ohm's law was not you
mostly true for all objects we said that
voltage and current are directly
proportional to each other but this fact
didn't prove true for everything for
example one of the example is the
behavior of diodes do you know what the
diode is diode is a device if you go to
your physics lab in your school you can
see a diode diode is basically a device
which allows the unidirectional flow of
current so when we look at the I mean I
will not go into detail of diode now we
will study about diode when we talk of
when we study about semiconductors after
we are aware of semiconductors we will
talk about diodes which will come in
almost the last chapters of your
syllabus so when we observe the behavior
of diodes we see that it does not follow
Ohm's law when you see the voltage and
current variation for example if we
consider voltage long x-axis and current
along y-axis the plot looks somewhat
like this this is how the plot looks for
a diode so it is not linear the
relationship between voltage and current
is not linear here also the current
increases with voltage but it doesn't
increase linearly so that means this was
a failure of Ohm's law
similarly the behavior of water
voltammeter there we saw that if again
we take voltage along x-axis and current
along y-axis the plot looked somewhat
like this that means the voltage
increased with current but the voltage
started increasing only after certain
amount of time that means only after
reaching a value of say V naught it
started increasing before that the
voltage at the current did not increase
with voltage I mean if you look at this
portion from this point to this point
voltage kept increasing but there was no
increase in current so this is also a
failure of Ohm's law so there are many
other scenarios where Ohm's law is not
followed so that conductors which do not
follow Ohm's
they are known as non-ohmic so
conductors which follow Ohm's law are
called ohmic and those who do not follow
Ohm's law are called non ohmic but Ohm's
law still is a very strong law which
governs several phenomena around us
however there were these limitations to
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