let us discuss the, potential difference across
the battery terminals in a circuit in various
situations. lets discuss it, in 3 cases. case
1 is a situation. when. no current flows.
through the battery. in this situation say
if, we are given with a battery a real battery
in which its e m f is e and an internal resistance
r is connected in series. and externally we
are having the axis towards terminal. always
remember in a real battery we can never detach
its internal resistance from the battery e
m f it is always taken. now in this situation
if no current is flowing through the battery.
we can state the potential at terminal end
ay is v-a and if at b it is v-b. we can say
there will not be any potential drop in this
resistance because current flowing through
it is zero. so we can directly write in this
situation v-a minus v-b the potential difference
across the battery terminals will be equal
to its, e m f. that is opened circuit. terminal
voltage. now if we consider a case 2, in which
we say. when. a current, i. is supplied by
the battery. if battery supplies a current,
the situation would be like this, if we consider
the same real battery over here this terminal
ay this terminal b. this is the. e m f e of
the battery and r is the internal resistance.
and in a circuit if battery is supplying the
current it is supply the current from its
positive terminal and from the negative terminal
the current goes in. in this situation we
can see. if potential at terminal ay is v
ay, and at terminal b is v-b. so we can see
the current. is flowing from terminal b into
the resistance, so we can say if we consider
a imaginary point an imaginary point, between
the e m f and the resistance the internal
resistance of battery. then we can say at
this point the potential will be. i r less
then. the potential at terminal end b. so
we can write in this situation if at potential
b potential is v-b. then potential at the
middle terminal after passing through the
resistance r can be written as minus i r.
and at the other end it’ll be e volt higher
because this is the positive terminal this
can be written as plus e is equal to, the
potential at terminal end ay which is v-a.
so in this situation you can see the potential
difference across battery terminals v-a minus
v-b we can see it is given as e minus, i r.
so again always state, whenever. the battery
supplies a current its terminal potential
difference is always less then the. e m f
of the battery. and similarly we can discuss
about the third case when we state. when a
current i. is supplied. into the battery terminals.
or into the battery this is the situation
where we say an external voltage source which
is higher then that of battery supplying the
current into it. and here this situation would
be like this. or when, these are terminals
ay and b. this is the e m f e internal resistance
is r. and in this situation, externally a
current. i is supplied into the battery terminal.
that means in this situation. from the positive
side of the battery current is getting into
the battery. so here if we just see potential
at terminal end ay is v-a and, at point b
is v-b. then we can write. if potential here
is v-a potential right after the e m f will
be e volt less then this we can write it minus
e. and again after, this resistance r we can
say in this direction current potential decreases.
so it’ll be written as minus i r which is
equal to the potential at terminal end b which
is v-b. so here you can see that potential
difference across battery terminal v-a minus
v-b we can write as e plus i-r. which is another
important thing to be kept in mind. that.
if a current is supplied into the battery,
in that situation the terminal potential difference
of the battery is more then the battery e
m f here it is v-a minus v-b is, more then
the e m f of battery. so all these 3 cases
we are going to see soon when we’ll study
about, the circuit analysis. of various circuit
components.
