lets discus an important concept of division
of current in parallel resistances. say we
are given with 2 resistances connected in
parallel combination.
these are resistances r-1 and r-2. and in
this situation, if a current i is supplied
to the group of these 2 resistances.
you know that the current is divided as i-1
and i-2 in the 2 resistances. and if we wish
to calculate the value of i-1 and i-2 the
very first thing here we can see. is the total
potential difference across the terminals
ay and b of this group.
can be written as v-a-b is equal to i which
is the total current supplied multiplied by
the equivalent resistance of this group.
and for parallel combination we can write
that 1 by r-equivalent is 1 by r-1 plus 1
by r-2.
so in this situation the value of equivalent
resistance we can write as r-1 r-2 by, r-1
plus r-2.
always remember that for a group of parallel
combination of 2 resistances.
we can use the equivalent resistance as r-1
r-2 by r-1 plus r-2.
so here the potential difference will be i
r-1 r-2 upon, r-1 plus r-2 if you substitute
the value of r equivalent over here.
now this is the potential difference across
the combination which will be same across
both of these resistances.
we can directly calculate.
the current in r-1 is.
this i-1 which can be written as v-a-b upon,
r-1 that is according to ohms law current
is potential difference by resistance.
so in this situation it can be given as.
i r-2 upon r-1 plus, r-2.
similarly if we calculate, current in r-2.
this i-2 which can be given as potential difference
divided by the resistance r-2. if we substitute
the value of v-a-b over here you can see the
final value we are getting is.
i r-1 upon r-1 plus r-2.
so these are the current you just keep both
of these results as it is in your mind for
direct application time saving applications,
in different cases.
as well as one important thing here you can
see that if we take the ratio of these currents
i-1 and i-2. you can see on dividing we are
getting r-2 by r-1.
that implies the current is inversely proportional
to the resistance.
that means whichever resistance is low, more
current will flow through that.
or current will always chose the path.
more or tendency of current to choose the
path more where resistance is less because
it can be flown easily.
so you just write down a note also here.
which says that in parallel combination.
of resistances.
current is divided.
in.
inverse ratio of.
resistances.
that is wherever resistance is less more current
will flow through that path. in continuation
we can also discuss the current division among
equal resistances in parallel.
say we are given with 2 resistances which
are identical.
that is each of value r and r. now in this
situation, we can state if a current i, flows
into the combination as the 2 resistances
are equal we can see that current is equally
divided in the 2 resistances that is i by
2 and i by 2.
similarly even if we are having a group of
n resistances connected in parallel. and if
all resistances are identical like this.
then in this situation we can say.
if these all resistances are equal. and say
the total resistance say r 1 2 3 up to n.
and if a current i is supplied into the combination.
then across each resistance we can say as
the potential difference is equal the current
will be same. and here among all n resistances
current will be equally divided then we can
say that current through each resistance will
be, i by n. so we can directly state, in.
case of.
parallel combination.
of identical resistances.
current is.
equally divided.
among.
all resistances.
no mater whatever will be quantity of resistances
it’ll always be equally divided like for,
n resistances it’ll be i by n in each resistance.
