Hi friends in this video we are going to
use maximum power transfer theorem to
solve a problem so lets take a problem
so in this problem I am having this
resistance as a variable and I dont
know its value we will named is that RL
and a voltage sources are present 100
this polarity and told with remaining
resistances of 40 60 50 and this is also
50 ohm what is the question what should
be the value of RL to get maximum power
transfer and also calculate
maximum power so let's see how we are
going to solve we know condition for
maximum power transfer what is that
condition the load resistance RL should
be equal to R TH whenever we see our
case from these two terminals so what is
the procedure here we have two open
circuit RL and we need to short-circuit
all the voltage sources and open circuit
all the current sources
so if you say properly this is nothing
but a procedure for calculation of R TH
so thats  what the step number one is
calculation of RTH it is absolutely same
as that of a variance theorem so if I do
this modifications I will get structure
like this these are the points A and B
after removal of RL through which we
have to find out a Thevenin's  resistance
this is 40 ohm 60 ohm 50 and 50 here I am
NOT able to figure out any series and
parallel connections directly what I
will do I will redraw the circuit by
considering one more point so if I see
properly this part of the circuit is
nothing but the same point which I can
say a Point C so in all I am having
three points A B and C so lets redraw
the circuit
from A to C  I'm having 40 ohm and 60 ohm
connected so from A  I am having
resistance 40 and resistance 60
connected to point C
and from C to B I am having 50 ohm and
this is also C to B 50 Ohm
so after reading the circuit now I am
able to crack that this 40 and 60 are in
parallel because they are forming the
loop this 50/50 are also in parallel so
40 parallel 60 I will get 40 multiplied
by 60 divided by 40 plus 60 all I will
get answered as 24 Ohm same way 50
parallel 50 it will be 50 multiplied by
50 divided 50 plus 50 answer will be 25 ohm
so I will get 2 resistances 24 ohm and
25 ohm connected between points A and B so
this will be your RAB which is nothing
but 49 ohm so I can say Thevenin
equivalent resistance between points A
and B as 49 ohm and as per the condition
of maximum power transfer theorem RL
should be equal to R TH so to get a
maximum power I need to ensure RL should
have the value 49 ohm which is same as
Thevenin equivalent resistance so this
is a first part of a problem where we
answered what should be the value of RL
now lets take what is the value of P
max so the formula for P max is VDS
square divided by 4 R TH out of this I
got R TH now only thing left is
calculation of V TH
so it is absolutely same as the
procedure for calculation of V TH in 
thevenin's theorem meaning what we need to do
we need to open circuit RL keeping rest
of the elements in the circuit as it is
so I am removing this RL so leaving
behind this terminals A and B across
which we have to find out thevenin's
equivalent voltage it is a 100 volt
battery this is 2 volt battery 50 ohm 50
this is 40 this is 60 ohm now if I say
properly it is a very simple problem I
consider this as node X this node as the
reference only one potential I get and
that is nothing but 100 so I can gladly
say VX equal to 100 and this hundred
volt give rise to two currents one
through this branch another through this
branch so this branch current I will
consider as I 40 and this I will
consider as I 50 so what is I 40 it is
this voltage VX divided by total
resistance that is 40 plus 60 is 100
divided by 100 the answer I will get is
1 ampere downward because I am getting a
positive answer same way what is this I
50 is again same voltage because these
two are in parallel divided by total
resistance 50 plus 50 equal to 100
divided by 100 once again 1 ampere
downward so if I take a loop which will
consist of this A and B points which
have a 40 ohm resistance
A and B points a battery of 250 ohm
resistance this is the voltage that I am
supposed to find out which we call as a
V TH this is two old battery 50 ohm
resistance current is I 50 in this
direction I will have a voltage drop
like this 40 M resistance with current I
40 downwards and voltage drop like this
so apply KVL I will start from this
point so B to A it's V TH minus plus is
plus 40 multiplied by  I 40 plus minus minus 50
multiplied by I 50 minus plus plus 2
equal to 0 so if I substitute the value
of I 50 which is 1 I 40 once again it is
1 minus 2 if I solve I will get V TH as
8 volt here I am getting a positive
answer A positive with respect to B now
Vth be calculated Rth we know we can use
this formula and get answer so the final
step is P max P max equal to VTH square
upon 4 Rth so which is 8 square divided
by 4 multiplied by 49 I will get maximum
power transfer to the load is 0.3265 watt
 problem is over so here we
have seen how to use Thevenin's theorem in
order to get maximum power
transfer to load in subsequent videos we
will solve more numericals based on this
thank you
