Hello friends in this video we are going
to see the application of Kirchhoff's
current law to a circuit and let's
develop a technique called as nodal
analysis lets take a simple circuit
let's have generalized value
and suppose we have to get a current
flowing through the branches where
resistances are connected
meaning current flowing through R 1
current flowing through R 2 using nodal
analysis one thing is very much
important in this is to identify how
many nodes are there so for model
analysis to solve a problem no means a
point where more than two branches are
connected so I repeat node is a point or
a junction where more than two branches
are connected so I cannot consider this
as a node for nodal analysis because one
and two branch means number of elements
present between two nodes so I can say
this is also a branch because element is
present that is resistance this is also
a branch because element voltage source
is present this is also a branch current
source is present this is a branch where
resistance R 2 is present now here two
branches are connected but here what we
are saying node is nothing but a point
where more than two branches are
connected so this cannot be a node for
me this point 1 2 3 3 branches are
vented yes so this will be a significant
node so I will name it as VA directly I
name a potential of this node is VA this
cannot be a node because two branches
rather this cannot be a branch for me
because it's just a wire just a line
there is no element present between
these two point so I cannot consider
they
as a branch so here I have only one
branch that is r2 till this point and at
this point I am having one two three
branches connected so this is also
another significant node so I will
mention it has VB once you identify how
many nodes are there one node you have
to take as a reference reference means I
will take voltage of that node is zero
so in this particular circuit I got two
nodes one of the nodes I have to take as
a reference so I will take this node as
a reference means the potential of that
node I will take as zero so I will have
only one significant node so I have to
get a voltage of that node which I have
not taken as a reference so here I have
to calculate voltage of node
which is
other than a reference in this problem
it is VA and once VA  is known I can get
all the branch currents how to get
branch currents for this purpose let's
have three simple techniques so
technique number of one if branch
consists of a current source then simply
the value of this current source which I
will take as say I which will be branch
current between point A and B so I will
mention here points A and B where
current source is present so I can say
current flowing through the branch I AB
is I second
suppose there is a resistance between
two points or two nodes having the value
R now the node potential of this a point
is VA potential of this B is V B and
based on the direction of current that
we have chosen so for example I have
consider current like this I which I
will mention as I AB  from A to B so I
can write a equation
current flowing through this branch is
nothing but potential difference between
these two points divided by resistance
so potential difference is VA minus VB
upon R see it depends upon the direction
of curve meaning suppose I take a
direction like this which I will mention
I BA so here I have consider B is at
higher potential
compared to a so I BA it was VB minus
VA divided by R so based on the
direction that we have selected as per
that this equation will change and third
most important rule suppose I am having
a voltage source and a resistance
connected in series between nodes A and
B so this is a voltage V this is a
resistance R and polarity as I mentioned
and suppose I am considering current
direction like this so the equation we
will get as since I have consider
current flowing from A to B so obviously
I am considering VA is at higher
potential compared to VB so VA minus VB
obviously that but one more voltage
source is there so in the direction of
current which is A to B I am having
voltage polarity changing plus to minus
so initially it is plus now it has
become minus in the direction of current
so there is voltage drop so it is minus
V divided by total resistance in a
branch suppose I will consider current
direction like this so I will get a
equation I BAequals now current
action is from B to A so I assume
indirectly
B as higher potential compared to A so
VB minus VA and in the direction of
current which is from B to A I have
voltage polarity changing minus to plus that
means initial it is minus in a current
it has become plus so there is a voltage
rise voltage rise I mentioned as plus
plus V divided by total resistance in a
circuit from B to A which is R so
keeping these three techniques in mind
we can write the equations for the
circuit that we have selected so let's
go back your circuit once again so I
have this circuit now where I mentioned
a significant node VA a reference
number VB having the potential zero
less mark current directions randomly so
I will consider this current source
direction as it is so it is downward now
here I assume random directions like
this so based on this direction less
write a equation now for this current it
has started from the reference so from
reference to a current is flowing so the
KCL at node A gives me first current is
starting from a reference point so zero
minus and it is ending on A potential so
zero minus VA and in the current
direction I have a voltage source so
voltage source changing this polarity
minus 2 plus or I can say in a direction
of current voltage has changed from
minus to Plus that is  the voltage
rise so voltage rise I will consider
positive V divided by total resistance
from reference to A point which is R1 in
R case so this is the incoming current
I have taken so I am applying a KCl so
total incoming current is this
outgoing this given in a circuit so
equal to total outgoing so for outgoing
I am having one current first directly
given of I value so I will write that as
it is plus second outgoing current is
this starting from A potential and
ending on reference so I am assuming A
is higher compared to be as far as
potentials are concerned so I can write
VA minus 0 divided by resistance in this
branch which is R2 so here I am having
only one unknown potential that is VA so
I will rewrite the terms V by r1 will be
the fixed
minus I again a fixed and I can take to this
side equals VA upon r2 plus VA upon R1
so this term I will get as a fixed value
VA is the only unknown 1 upon R 2 plus
1 upon R 1 it's also fixed so from this
I can get value for VA once a potential
of a node is obtained I can get any
branch current meaning current flowing
through R 1 I can get as 0 minus VA plus
V divided by R 1
because this was a term which was
telling it is a current flowing through
R1 so substituting the value of VA I can
get I R1
similarly substituting the value of VA
in this equation or in this term I will
get VA minus 0
divided by r2 if I substitute VA I will get IR 2
so here we have seen that nodal analysis
is a technique where we are supposed to
get node voltages and from the node
voltages we can get branch currents
where as in terms of a mesh analysis we
used to get loop currents and from loop
currents we used to calculate all the
branch currents so that is a difference
between mesh analysis and nodal analysis
in subsequent videos we will see how to
apply nodal analysis thank you
