Cells in Series Video Lecture - NEET

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before going ahead with path sir we had
to study about a cell I mean as far as
their structure and property is
concerned so we started about three
important properties of a set the first
one is the EMF of a cell second one is
the internal resistance of a cell and
the third one is the terminal potential
difference of a cell and I hope that you
are able to understand each of them
properly so the next topic we will see
how low in group cells in the circuit I
mean what are the different possible
ways of arranging cells in a circuit
like how to studied in case of resistors
and capacitors we can put resistors in
series we can put them in parallel
similarly we can put the capacitors in
series as well as in parallel so in the
same way we will see what are the
possible ways of arranging cells in a
circuit so for sense also we have two
combination
the first one is the series combination
and the second one is the parallel
combination so that they are same as we
had discussed in case of resistors and
capacitors so now we will discuss each
of these combination for cells in detail
so first we will start with cells in
series so what do I mean when I say that
cells arranged in series so what do we
mean by cells connected or grouped in
series well here also the combination
would be similar to what it was in case
of resistors and capacitors but at let
us have a look it will look somewhat
like this if I have multiple cells and
if they are arranged in such a way that
the positive terminal of one is
connected to the negative terminal of
the other and then again the negative
terminal is
connected to the positive terminal and
so on then it is known as say that they
are connected in series let us draw it
using the symbol or circuit symbol if
the cells are connected like this they
are safe to be in series if you see here
negative of the first cell is connected
to the positive of the second cell
negative of the second cell is connected
to the positive of the third cell
negative of the third cell is connected
to the positive of the floatzel and so
on so then we see that the cells are
connected in a series combination so
what I mean let us suppose if in a
circuit we have some 10 cells connected
in a series so what would be the
effective EMF of that circuit like for
example here in this circuit also let us
say I say that each of these five cells
are of some EMF E 1 e 2 e 3 E 4 and E 5
so what would be the equivalent or the
effective EMF of the circuit due to
these five cells connected in series so
let us try to calculate that so in order
to calculate that with LG ohm just to
sense for now okay so let us suppose
this cell hat is an EMF of e 1 the
second one has an EMF of e 2 let us say
this is point a this point is point B at
this point is point C we say that the
potential at these three points a B and
C ad VA VB and VC right so the potential
at each of these points are different
right so now for the first cell for the
first cell with EMF E 1 so let us write
the expression or the equation for
potential difference between these two
points if I consider the cell v1
we can calculate the potential
difference between the two electrodes
right now if you look at this you can
see that it is an open circuit right
assume that it is not an open circuit
assume that it is a closed circuit right
you assume it like this that there is
some resistor and it is a closed circuit
you assume it okay
so had there been a resistor or an
external circuit or that there will be
some flow of current as soon as some
current is flowing there some resistance
will be offered by this cell itself so
let us call that internal resistances r1
for the first cell and r2 for the second
set okay so for the first cell the
expression for potential difference that
is V ay minus VB the potential
difference between these two points will
be equal to the potential difference
between the two electrodes right so the
potential difference will be equal to
the EMF EMF E 1 is the potential
difference between these two electrodes
when it is an open circuit that is when
there is no current flowing through the
cell so this will be even minus the
voltage drop across the internal
resistance that is an R 1 similarly for
e 2 the potential difference between B
and C that means it will be VB minus VC
will be equal to e 2 minus I R 2 so this
is my first equation and this is my
second equation now if you add the two
equations what do you get it is VA minus
VB plus VB minus VC so this will be your
left hand side this is equal to e1 minus
I R 1 plus e 2 minus I R 2 so this
becomes V a
- VC is equal to e1 + e2 minus I R 1
plus R 2 so this is what we get by
adding these two equations now let us
assume that e equivalent let us assume
that instead of these two cells you have
just one cell let us assume that if
there is there are not two cells instead
of that there is only one cell between
the point a and C so we are basically
replacing these two cells with one cell
whose EMF is e equivalent and internal
resistances are equivalent then what
will happen in that case so we are
assuming e equivalent instead of e 1 and
E 2 so we can write the expression for
this cell as well so for this VA minus
VC will be equal to e equivalent minus I
R equivalent right this is the for
expression now if you compare equation
for bit equation 3 what do you see
the left-hand side is equal VA minus VC
here also VA minus VC so that means the
right-hand side should also be equal now
if you compare the right-hand side you
can see that e equivalent is nothing but
e 1 plus e 2 and R equivalent is nothing
but R 1 plus RT therefore what do we
conclude we conclude that for cells
arranged in series equivalent EMF is
equal to sum of the individual EMS and
equivalent internal resistance is equal
to sum of the individual internal
resistances right so I hope I made it
clear ok so now let us look at a
scenario where
cells are connected in series let's
suppose because in the previous slide I
derive the expression for two cents okay
so now let us say that there are n cells
which are connected in series let us
suppose it is connected in an external
circuit where there is a resistance
capital R now each of this cell has
internal resistance R and EMF as e so in
this case what will happen what will be
the total resistance of the circuit
total resistance of the circuit will be
external resistance plus the equivalent
internal resistance now what will be the
equivalent internal resistance it will
be sum of all the resistances since
there are n cells that means this will
be n into R so this is the total
resistance of the circuit what is the
effective EMF of the cells in the
circuit effective EMF will be the sum of
the EMF of all the cells connected in
series so that will be n times the EMF
of each cell that is n e therefore this
is a closed circuit right so current
will flow through this external
resistance R let us say this current is
I therefore the current flowing across
external resistance R that is I will be
equal to the effective EMF effective EMF
divided by the total resistance so
effective EMF is n e divided by the
total resistance R + n because current
is what current is nothing but the
voltage divided by resistance according
to Ohm's law right so this will be your
current now this current if you
Paquette the external resistance as well
as the internal resistance plays an
important role in the current which
flows through the circuit so there are
two scenarios which can arise first is
current through the resistance when
capital R is very very greater than n
that means when the external resistance
is very high as compared to the internal
resistance in that case what will happen
to current in that case I can ignore an
R as compared to R so I can write it as
R so that it becomes n times e by r what
is e by RT by r is nothing but the
current due to a single cell current
across our current across the external
resistance due to a single cell so the
current becomes n times the current due
to a single cell across the external
resistance
the second scenario when R is very when
the external resistance is very small in
that case current will become n e
divided by n R so this will be equal to
e divided by R in that case the current
through the circuit will be equal to the
current due to a single cell right so
these are the two observations which we
can derive from this expression right so
this shows that how how does it effect
how does the arrangement of cells in
series affect the current that flows in
a circuit right so when we arrange cells
in series what happens to the current
the current will depend on how much
current will flow through the circuit
that basically depends on the value of
the external resistance and the internal
resistance if the external resistance is
very high in that case the current will
be n times the current due to a single
cell but if the external resistance is
very small in that case the current
through the circuit will be same as the
current through due to a single
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