hello friends in this video we are going
to learn a behavior of AC parallel
circuit before going to this module lets
 consider a concept called as
admittance
so basically admittance is the
reciprocal of impedance lets derive
the expression of admittance for that
let's start with the RL circuit so I
have a resistance in series with the
inductor and the impedance of this is Z
is given by r plus jXL unit is ohm where
XL is inductive reactance and this
related to L with this formula XL equal
to 2 pi FL now we need to find out the
admittance for this admittance is
denoted by Y so it is the reciprocal of
impedance so y equal to 1 by Z so if I
substitute Z over here I will get Y as 1
upon R plus J Excel where XL is
inductive reactance since there is a
complex quantity obviously its
reciprocal is also complex quantity so
lets represent Y in terms of a proper
real and imaginary term for that purpose
let us multiply by complex conjugate of
the denominator and that is R minus JXL
 so I will get R minus JXl divided by
here I will use the formula a plus B a
minus B that is a square minus B Square
so it's R square minus B is jxl so if I
simplify I will get R minus JXl upon R
square if I square it I will get a J
Square and J square is minus 1 so that
minus minus will become plus over here
and it will be plus XL square so Y I can
write like this R upon R square plus XL
square minus JXL upon R square plus XL
square so this is the admittance of the
inductive circuit Here I am having two
terms one is the real and second is
imaginary
so this real term R upon R square plus
XL square is nothing but G and G is a
conductance
what is conductance it is a reciprocal
of resistance and the unit of
conductance is more second term is XL
upon R square plus XL square and that is
B B is nothing but susceptance and
susceptance is nothing but reciprocal of
reactants and the unit is once again
move so ultimately I can write Y as G
minus G B unit is move now lets
represent this with the help of a
triangle so first I will draw admittance
triangle and then I will relate this
admittance triangle with already done
impedance triangle so admittance I am
getting over here y equal to G minus JB
so if I represent this in a triangular
form it will be like this
G is the real part and minus JB
so negative direction Y axis you will
have B and this will be Y phase angle
Phi is nothing but this between y and G
corresponding impedance triangle for
that z equal to r plus jXL
it will be like this R is the real
term plus jxl will come like this and
this will be Z where phase angle Phi is
the angle between Z and R so here I can
say G is nothing but R upon R square
plus XL Square and B is nothing but XL
upon R square plus XL square same
analogy I can use for RC circuit so for
RC circuit I will have admittance
triangle for that admittance Y will be G
plus JB and it will be like this this
will be G Plus JB will come vertically
upward and third line will be this angle
Phi where G is the conductance and given
by R upon R square plus XC square and B
is nothing but XC upon R square plus XC
square where XC  is capacitive reactance
corresponding impedance triangle for
that z equal to R minus j XC and it will
be like this
so a parallel circuit instead of a
impedance we'll talk in terms of
admittances so in parallel circuit what
we will have we will have several
parallel branches whose impedances are
given let us take Z1 Z2 Z3
so all these impedances are nothing but
either series RL circuit all series RC
circuit or series RLC circuit what you
have to do you have to convert all the
impedances into corresponding
admittances and then in parallel circuit
addition of all the admittances will
give you total admittance in the circuit
and how the total admittance related to
the voltage and current it is very
simple voltage V will be nothing but
current multiplied by admittance
so rather talking in terms of impedances
for parallel circuit it will be better
if you consider there admittances so
while solving problems most of the times
we take admittance whenever we deal with
a parallel circuit thank you
