Hi friends in this video we are going to
see the application of mesh analysis
technique to solve a simple circuit so
lets take a circuit so in this circuit
I am having a battery of 10 volt and
number of resistances are connected so I
will have the value 5 this is 3 ohm this
is also 3 ohm 4 ohm and 1 ohm the
objective is to find out current flowing
through 1 ohm resistance using mesh
analysis technique the fourth step is to
identify how many number of loops are
there so here I can say 2 loops are
present a loop is nothing but a closed
circuit I will mention Loop Current
randomly so here I have selected both
the loop currents in a clockwise
direction I will name it  I 1 and I 2
in the direction of current let's mark
all the voltages that got develop across
number of resistances meaning for this
resistance the drop is in the direction
of current plus minus for  4 ohm it is like
this for 5 ohm it is plus minus similarly
for this loop the voltage drops will be
like this as I mentioned now there is a
one voltage source the polarity of
voltage does not depend upon the
direction of current but it will be
fixed longer arm having the positive
polarity and shorter arm will be
negative then I apply KVL to both the
loop so apply KVL
to loop 1 I will start from this point
and we'll come back to the same point
after tracing this part in a direction
of current only so in a direction of
current I am having first voltage drop
that is plus minus voltage got developed
so I will mention it minus 3  I 1
similarly for this 4 Ohm minus 4I 1 in
the direction of path I am having one
more voltage that is minus plus so the
voltage polarity it is changing from minus
to plus in this direction I will
consider that as a voltage rise so it is
plus 4 and this is because of the I 2
minus plus is again a voltage rise but
that is a DC voltage battery so 10 as it
is plus minus again a voltage drop minus
Phi I 1 equal to 0 after simplifying I
will get minus 3 minus 4 and minus 5 as
minus 12 I1 plus 4 I2 constant I will
take to other side of the equation so I
will get equation number 1 similarly I
will apply KVL to loop 2 I will start
from this point and will come back to
the same point after tracing this path
so in this path in a direction of
current this is a voltage drop so it is
a minus 3 I 2 plus minus minus 1 I 2 so I
will mention just minus I 2 plus minus
again a voltage drop minus 4 I 2 in the
direction of this current I am having
minus plus 1 more voltage but the
polarity changing from minus to plus
since a voltage rise so plus 4 and
this is because of I1 after
simplifying I will get equation 4 I 1
minus 8 I 2 equal to 0 equation number 2
after solving these two equations I will
get answer I 1 as 1 ampere and I 2 as 0.5
 ampere the objective is to find
out current flowing through the 1 ohm
if I see the circuit I will come to know
I 2 is the current which is flowing
through 1 ohm resistance so current
flowing through 1 ohm resistance will be
same as I 2 equal to 0.5 ampere
now I am getting a positive value of
this current I 2 that means whatever
direction I have assumed for these loop
currents are same meaning for this 1 ohm
I 2 will be downward so I will mention
direction of current along with a
magnitude so this will be your complete
answer so here we have taken a simple
circuit and we have seen how to use mesh
analysis technique to solve a problem in
subsequent videos you will see more
numericals based on mesh analysis thank
you
