Cells in Parallel Video Lecture | Physics Class 12 - NEET

and hello friends this video on electric
circuits part eight is brought to you by
exam fee or dot-com no more fear from
exam please make sure that you have
watched all the videos in part 7 before
going ahead with part 8 look at the
parallel combination of cells like how
studied about the series combination let
us have a look at the parallel
combination when I talk about parallel
combination as quite obvious parallel
combination would mean that all the
positive terminals of the of all the
batteries or cells will be connected
together and all the negative terminals
of the batteries will be connected
together so that is known as a parallel
combination such that the voltage or the
potential difference across each cell is
the same that means as you can see here
all the positive terminals are connected
together and all the negative terminals
are connected together schematically you
can draw it like this let us suppose
these are your cells so positive
terminals of all of them are connected
together and negative terminals of all
of them are connected together so the
potential difference across each of
these cell is the same right so let us
try to find out the equivalent
resistance in I am sorry equivalent EMF
in case of a parallel combination so
here also let for the sake of it let us
for the sake of convenience let us
assume that there are two cells e1 and
e2 with internal resistances r1 and r2
connected in parallel combination we
assume that this cell is part of a
closed circuit and the current is
flowing through them said since the
current is flowing through the cell
internal resistance will be offered to
them current okay I suppose some current
is flowing through the cell
so now let us write down the expressions
as we
in the previous slide so for the first
cell with EMF E 1 the potential
difference between these two points let
us call this point as a at this point as
B so the potential difference between
points a and B will be equal to e 1
minus I R 1 now this current I is coming
in but when it reaches this point it
gets divided into two parts like this is
I 1 emphases I 2 so I when flows through
P 1 and I 2 flows through it so here
different currents flows through them
through different sets so B will be
equal to e 1 minus I 1 R 1 similarly for
the second cell e2 V will be equal to e
2 minus I 2 I 2 notice an important
thing here here the potential difference
between these two points a and we will
remain the same therefore your left hand
side is the same but here the currents
are different for the two cells and
another relation which we can see from
the figure is I is equal to i1 plus i2
right so now what - we see from here so
from this expression we get i1 is equal
to e1 minus V divided by r1 and from the
next expression we get I 2 is equal to
e2 minus V divided by r2 right so in
this expression we will put the values
of I 1 and I 2 so I will be equal to e1
minus V by r1 plus e2 minus V by RT so
this can be written as e1 by r1 plus e2
by r2
- V into 1 by r1 plus 1 by r2 so this is
the expression for current now here also
let us imagine now let us write it in
the in the form of V so this expression
can further be written as V is equal to
I divided by 1 by r1 plus 1 by r2 plus
e1 by r1 plus e2 by r2 divided by 1 by
r1 plus 1 by r2 so this is simple
mathematics here I is equal to even by I
1 plus e2 by r2 minus v1 by r1 plus 1 by
r2 so from this I wrote it in terms of V
so I got this expression now let us
assume so let us name this equation as
equation 1 now let us assume that
instead of these two EMFs we replace
these two EMF with 1 EMF that is with
one cell instead of these two cells even
at e2 we replace them with E equivalent
so now we will assume that so now we
assume e equivalent
instead of e 1 and E 2 so how will my
circuit look like myself it will look
like somewhat like this let us say this
is point a and here I have e equivalent
whose internal resistances are
equivalent and this is point B right so
now we don't have that parallel
combination thing at all so in this case
what can we write in this case we can
write that the potential difference
between point a and B that is V is equal
to e equivalent minus I R equivalent
right so now if you compare this
equation to with the previous equation
which we found that this equation one
that is this equation then what do you
get in both the cases you get V is equal
to e equivalent which is nothing but
this bigger term minus I into R
equivalent that is I into R equivalent
which is this entire term right so let
us try to write it in this form so we
have to compare these two expressions so
from let me write the expression one
here itself that is V is equal to I
divided by 1 by r1 plus 1 by r2 plus e 1
by r 1 plus e 2 by r 2 divided by 1 by
r1 plus 1 by r2 so if you want you can
simplify it further in this way that I
is equal to I into r1 r2 divided by r1
plus r2 plus e1 r2 plus e2 r1 divided by
r1 plus R right so now if you compare
this expression with this expression
what do you get V is equal to I into R
so that are equivalent is nothing but R
equivalent is nothing but r1 r2 divided
by r1 plus r2 and what does e equivalent
e equivalent is nothing but this term
that is e equivalent is equal to e 1 r2
plus e2 are
/ r1 plus r2 so this is what you get in
case of a parallel combinations look at
the scenario where n cells are connected
in parallel so we will look at it in the
similar way as we did for the series
combination let us suppose there are n
cells which are connected in a parallel
combination across an external
resistance I EMF of each of these cells
is e and the internal resistance of each
of them as I write so here first we will
calculate the effective EMF of the
circuit so what will be the effective
EMF of the circuit it will be e here the
effective EMF of the circuit is e so how
do we get this effective EMF in the
previous slide I calculated the
equivalent EMF of the circuit which came
out to be even r2 plus e2 r1 divided by
r1 plus r2 so here if you look at this
circuit r1 is equal to r2 is equal to R
and even is equal to e2 is equal to e so
if I put these values we will get e
equivalent as 2e ad divided by 2 i which
comes out to be e so the effective EMF
of the circuit is e right and what is
the total resistance of the circuit so
the total resistance of the circuit will
be equal to the external resistance plus
the equivalent internal
and what is equivalent internal
resistance that is nothing but r1 r2
divided by r1 plus r2 so here are gonna
go to his book R so this will be R
squared divided by 2r which comes out to
be R by 2 now by mistake here I assumed
that there are two cells but there are n
number of cells right so this will be R
1 R 2 R 3 R 4 and so on that means R
multiplied n number of times right
similarly here in so here instead of R
by 2 like had there been two cells I'm
sorry I mean it was my mistake that I
told in this way but assume it this way
here I considered it for two cells even
if it is n cells then what will be
equivalent for n cells it will be n II R
divided by n R so that will also come
out to be e similarly R equivalent for n
number of resistances will not be R by 2
instead it will be R by n because the
number of resistances n right so what
will be the total resistance total
resistance will be equal to capital R
plus R by n so let us calculate the
current through the circuit so the
current through the circuit that is
current through the external resistor R
this current will be equal to the
effective EMF effective EMF divided by
total resistance so what is the
effective em EMF that is e and total
resistances R plus R by n so this will
be n e divided by n R plus small R so
this will be the current which will flow
through the external circuit now here
also we can have two cases the first
case where capital R is very very small
that is external resistance is very
small in that case what will happen
that case that current will be equal to
NP / AB so current is n times the
current due to a single cell second
scenario where external resistance is
very very greater than the internal
resistance in that case the current can
be written as n e divided by n R so this
will be equal to e divided by R that
means the current to the external
resistance is equal to the current due
to a single cell right so these are the
two important things which we
contributed from here I hope I didn't
confuse you here in this part I mean it
is very simple with the help of
equivalent and odd equivalent you can
calculate it for yourself right ok so
now that we have understood the grouping
of cells in series and parallel it is
time to solve some problems because
based on the combination of cells we
should be able to solve certain kind of
problems so what did we observe till now
let us look at up with observe thank you
please visit exam fee or comm to watch
free educational videos try 3 online
tests get the best quality study
materials study from the best tutors and
mentors and much more thank you once
again