Hi friends in this video we are going to
see how we can develop a technique
called as mesh analysis by using
Kirchhoff's voltage law I will take one
general Network
having 2 loops I will consider all
generalized value that means for this
battery EMF is e 1 here e 2 and these
resistances will have the values r1 r2
and r3 and objective is that we have to
find out current flowing through all of
them meaning let's find out what is IR 1
IR 2 and IR 3 to get these values let's
start how we are going to solve this
using mesh analysis which is ultimately
a application of Kirchhoff's voltage law so
the first step I will consider number of
loops present in a circuit so loop means
a closed path so here I am having these
two loops I will mark loop currents
randomly so I will consider direction of
loop current clockwise so this will be I
1 this will be I 2 you could take any
random directions but let's stick to the
basics I will always consider clockwise
direction for a loop current then based
on this direction of currents I am going
to mark voltage drops that got developed
across all the resistances so the
concept is that whenever I am having a
resistance like this and current I is
flowing lets take  in this direction then
voltage drop developed across a
resistance will be in the direction of
current in
this manner plus-minus and that is
considered as a drop so let's mark all
the voltage drops for these three
resistances so in the direction of
current I will get this polarity now R3
is a common resistance between loop 1
and 2 so obviously it will have two
voltage drops so as per the I1 it will
have the voltage drop of this polarity
and as per the I2 it will have the
voltage drop of the mention polarity now
once you have done this let's go back to
the batteries Batteries as we discussed
earlier the voltage or a potential of a
battery does not depend upon direction
of current it will be fixed polarity and
the polarities  longer arm plus shorter
arm
- so same way I mark the polarities  for
e2 next I need to trace a
loop now so I will trace loop in the
direction of current only that means in
a clockwise direction for both the loops
so whenever I will press a loop in the
direction of current I may come across
two voltage drops or two voltages
meaning I could have voltage changing
from plus to minus or I could have
voltage changing from minus to plus if
in the direction of a current voltage is
getting developed like this plus minus
then I will consider that as voltage
drop and I will consider negative value
for that while analyzing similarly if in
the direction of current voltage is
changing from minus to plus I will
consider that as voltage rise
and analysis purpose I will take that as
positive now keeping this in mind I may
write let's apply KVL to Loop 1 so I
will apply KVL like this so I will start
from this point and we'll come back to
the same point after tracing these many
elements so plus minus plus minus is a
voltage drop so it is minus and voltage
developed across a resistance will be
current flowing through it multiplied by
resistance value same way here plus
minus so minus I1 R3 but in the
direction of this current I have one
more voltage drop minus plus and that is
developed because of the I 2 so minus
plus is voltage rise so it's plus and it
is developed because of I 2 so it's I 2
R 3 and the third element is minus plus
a potential difference of a battery
minus plus means it's a voltage right so
it is a plus constant value even equal
to 0 now I will simplify
I will club all I want together so I
will get like this I will take this
constant on another side of equation
minus e1 equation number 1 similarly I
can apply KVL to loop 2 so looked I
will start from this point and we'll
come back to the same point after
tracing these many elements along with
the polarities of a voltage drop so lets
apply KVL to loop 2 so I will get
minus I 2 R 2 minus E 2 minus I 2 R 3 plus
I 1 R 3 equal to 0 let me go back to a
circuit once again so I am considering
this loop starting from this point and
coming back to the same point plus minus is
a voltage drop so minus I 2 R 2 plus
minus is again a voltage drop but this
is a potential difference of a battery
so I will take that as it is minus E2 here
again two drops are there one is because
of the I 2 so in the direction of I 2
it is plus minus voltage drop and that
is because of I 2 so minus I 2 R 3 and
in the direction of I 2 one more drop is
there minus plus minus plus is voltage
side so I will take that as positive and
that is because of I 1 so I 1 R 3 so that
I will get finally this equation and
after simplifying this that means I will
rearrange the term I will get this
equation number 2 the objective is to
find out value of current flowing
through all the resistances for that I
should know all loop currents so by
solving equation 1 and 2 obviously
whenever we solve a numerical we will
have the value instead of R 1 R 2 R 3 E
1 and E 2
so obviously you will have a number and
then you can get a value of I 1 and
value of I 2 now using these two loop
currents I am supposed to get the value
of I R 1 R 2 and I R 3 so lets go
back to the circuit once again so
so if I see properly the current flowing
through the R 1 is nothing but I 1
only current flowing through the R 2 is
I 2 only but current flowing through the
R 3 it may be I 1 and I 2 but not
necessarily that will be I 1 plus I 2 it
all depends upon the direction of
current meaning I 1 is flowing like this
downward and I 2 is flowing upward so
different directions meaning the value
of current flowing through the R 3 will
be the subtraction of I 1 and I 2 and
whoever having the more value that
particular current Direction ultimately
the current through R 3 will have so I
can write here current flowing through
the R 1 is nothing but I 1 current
flowing through the R 2 is nothing but I
2 and current flowing through the R 3 it
may be I 1 minus I 2 or I 2 minus I 1
depends upon whichever value is more so
here we have seen that we can use the
KVL in a different manner and develop a
technique which we call as a mesh
analysis which is simpler than than
that of a KVL and KCL  in further videos
we will see application of this mesh
analysis for solving certain numericals
thank you
