lets discuss the concept of moving coil galvanometer.
about a moving coil galvanometer we can write
that. it is an instrument. used to measure.
current in a circuit. or to obtain. null deflection
point. in a circuit. this is common deflection
type meter which you already studied in the
previous section. a normal galvanometer meter
which is deflection type is considered as
moving coil galvanometer. and now we’ll
also study about its working. and we can write
that its working. is based on the fact. that.
a torque. is experienced. by a coil. when
a current is passed through it. that means
when a current is passed. through, a coil.
it experiences. torque if it is placed in
a magnetic field. in that situation. due to
the torque the coil will start its rotational
motion. and this is the concept which used
in construction of moving coil galvanometer.
lets discuss its internal circuit diagram.
and the construction and working mechanism.
here you can see these figure show, the internal
structure of a moving coil galvanometer. in
this galvanometer here you can see there is,
a rectangular coil. who which a current is
passed when current comes it passes through
the coil if there are n turns it circulates
and. goes out from the, other circuit. the
coil is placed between 2 . cylindrical pole
peaces of north pole and south pole in which
a magnetic field exist from north to south
pole. and at the top and bottom of the coil
on its shaft. a spiral spring, above and spiral
spring bellow is connected. this spring is
of stiffness coefficient c. which gives us
an idea that if the coil rotates by an angle
theta this. spiral coil, spiral spring will
exert a restoring torque on the. armature
coil. with magnitude c theta. now if we just
look at its top view, you can see in the top
view. the situation is like this. here when
the current is pass through the coil, you
can see. due to the circulation of current
in the coil its magnetic moment exist in the
direction perpendicular to this coil. and
here you can see, the 2 wires of coil, are
lying in the plane of this magnetic line of
force between the pole pieces. so the angle
between this magnetic induction vector and.
the magnetic moment vector here is. theta,
which is 90 degree. so, due to this it experiences
a torque which is given as m cross b. and
here you can see when the torque is applied
onto it the coil will rotate in clockwise
manner from m to b. so when the coil will
rotate in this manner you can see. when coil
is in its new position. here also you can
see its magnetic moment is. rotated to this
level if it is rotated by an angle theta.
now the coil is in the plane of this magnetic
field. which is. along the line, magnetic
line of force, through which the 2 wires of
coil are passing. so this is the new magnetic
field. which is of same magnitude because,
the same magnetic poles are used and the separation
between the magnetic poles is same. here you
can say this is crossed magnetic field. because
of which no matter whatever angle the coil
will rotate. the angle between its magnetic
moment and the final magnetic induction in
its new position will always remain 90 degree.
so here we can say that the net torque acting
on it will always be m-b. if magnetic moment
we can write as, i n-a the product of number
of turns current and the enclosed area. here
torque can be written as. b i n-a it’ll
be always independent of the angle theta by
which the coil is rotating. so in this situation
here we can see. whenever the coil rotates
in this situation. the torque acting on it
is same. but due to its rotation the spiral
spring. will exert a restoring torque onto
it which is. tau restoring which is equal
to c theta. so here as magnetic torque is
clockwise in nature. here you can see the
spiral spring will exert an anticlockwise
torque which anticlockwise in nature. and
the coil will come to rest when the. restoring
torque will be balanced by the torque of magnetic
field. so at this position the coil will be
at rest. now if a middle is connected to this
coil. we can see. based on the amount of current
passing through the coil. the needle will
be deflected which can be. placed on a. printed
scale on which we can calibrate it for the
measurement of current on which the current
can be measured. this is the way how. the
galvanometer works. lets mathematically analyze.
some. coefficients related to galvanometer.
whatever working we have discussed for a moving
coil galvanometer we can say when. coil is
in iquilibrium position. after rotation. by
an angle, theta. we can see magnetic torque.
on it is given as. b i n “ a”. and if
we calculate the restoring torque we already
discussed that restoring torque will be due
to. the spiral spring onto it that will be
c theta. and at iquilibrium we can write that
this, b i n-“ a” must be equal to c theta
that’s why the coil is in iquilibrium. and
in this situation. we can see the value of.
angle by which the coil is deflected we can
write it as. b n-a by c multiplied by i. where
b n-a and c are constant so here we can see
that theta is directly proportional to i.
now in this situation we can see whatever
amount of current we supply. there will be
a deflection in needle which is proportional
to the current. that’s why this device can
be used to measure current, on a uniform scale.
here this constant we can write as s so theta
we can write as s-i. where. s which is b n-a
by c. is called. sensitivity. of galvanometer.
this called sensitivity because if the value
of s is high. then even for a small value
of current the deflection will be large and
the galvanometer is capable to measure small
values of current. that’s why the value
b n-a by c is termed as sensitivity of galvanometer.
there is another constant we defined as k
which is 1 by s. and this called. technically
reduction factor. of galvanometer. in some
problems we are given with a reduction factor
and k we can calculate from this relation
as i is equal to. in this situation c upon
b n-“ a”. multiplied by theta and i we
can write as k theta. where, we can say if
some deflection is there using this deflection
theta we can find out the value of current
passing through galvanometer. and the proportionality
constant here we termed as reduction factor
of galvanometer.
