L17 : Numerials: Kirchhoff law - Electric Circuits, Physics, Class 12 Video Lecture

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please make sure that you have watched
all the videos till Patt 16 before going
ahead with path 17 the last problem as
soon as you will see the problem you'll
find it very familiar because this is a
problem which I have already solved in
my previous lesson that is the lesson on
current electricity and the problem is
twelve equal wires of resistance are are
joined to form a skeleton truth this way
the current enters at one corner and
leaves at the diagonally opposite corner
find the total resistance between these
corners you remember in our previous
lesson we saw the same problem with a
different method where we first drawn
the current distribution and after that
we try to draw an equivalent circuit
depending upon the current distribution
and from there we very easily calculated
the equivalent resistance but here we
will use skills charts law and we will
find out the equivalent resistance and
you will see that the answer which you
get here is the same as the one which
you had got there right so the current
is coming through this end and leaving
through the other end that means your
battery is connected somewhere between
these two points so let us assume that
this is your battery with EMF E so now
let us mark the current distribution let
us suppose that current I is entering
here so how will I get distributed now
if you see here there are three parts
which I can take and all of them will
take the same amount of time to reach
the destination that is 1 2 3 from here
1 2 3 from here 1 2 3 so that means I
will get divided equally into these 3
parts so I by 3 I by 3 and I by 3 so
this I by 3 reaches here this I by 3
reaches here and this i betray reach a
safe so here again it gets divided into
two parts
now both of them
takes equal amount of path to reach the
destination so again it will get divided
into two equal amount to equal half so I
buy six I buy six similarly here also it
will get divided into two equal halves
that is I by 6i by 6 and from here also
it will get divided into I by six and I
buy sit now at this point I buy 6 and I
buy 6 will join together to form I buy 3
similarly at this point I buy 6 and I
buy 6 will join together and it will
from I by 3 similarly at this point I
buy 6 and I by 6 will join together and
form I by 3 so I buy 3 I by 3 and I buy
3 will join together and form I and thus
I will go back to the VAT so this is
your current distribution right I had
explained this current distribution in
the previous lesson as well now let us
name this cube so that it becomes easy
to apply Kirchhoff's law let us call
this a B C D this is e F G and H so now
we will apply the Kirchhoff's loop law
now here remember that you have each of
these resistance as small I so let us
apply the loop law to the circuit a b c
g e a that means to this circuit this
closed circuit which includes this EMF E
so we are applying it to a b c g e a and
so this is not a let us call it e 1 so
this set okay so we have to assume i
direction let us suppose I assume this
direction that means current will flow
like this right in the clockwise
direction so as per loop law what does
the EMA
in this circuit the EMF in this circuit
is e1 right and what are the resistances
involved this resistance R this
resistance R and these resistance R so
there are three resistances which are
involved in this closed loop so how much
current flows to each of them to the
first resistor it is I by three through
the second resistor R it is I by six and
to the third resistor again it is I by
three as per my assumed direction it
leaves the battery as the positive
terminal so even will be positive it
leads this act also in the same
direction so this will also be positive
for this I by sit through is also
positive and I by three also positive so
all of them will be positive so what do
you get we get e 1 is equal to I and by
3 plus I R by 6 plus I R by 3 so this is
equal to e 1 is equal to 5 I add by 6 so
from this we get 6 e 1 is equal to 5 I
add so this is one equation which I get
now let us assume that that resistance
the total resistance between corners
which we have to find out let us say
that that resistance is equal to and let
us assume so if there is an equivalent
resistance between these two corners
that is a and G is capital R in that
case what will be e1 e1 is the net EMF
so this net EMF will be equal to the
total current flowing through the
circuit that is I into R right so we can
write replace this V 1 with I and
therefore one becomes I R is equal to 5
I smaller so this I and I will get
cancelled and therefore we get capital R
so this will
six i Rho capital R will be equal to
five are by six so this is the total
resistance between the diagonally
opposite corners and that is what we
wanted to calculate right so this is one
method of calculating the equivalent
resistance between the corners and the
other method I had already shown you in
the previous lesson right so I hope now
it is clear how what is kirchoff's law
the junction law as well as the dewclaw
and how do we apply them so as you keep
practicing few more problems things will
be clearer to you thank you please visit
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