2. Page2
CERTIFICATE
This is to certify that the project entitled “Report on
Moving Coil Galvanometer” is the bona fide work of him
the requirement of CBSE, Delhi. For the award of Senior
The original research work was carried out by him under
my supervision in the academic year 2017-2018. On the
basis of the declaration made by him I recommend
report for evaluation.
_______________ _______________
Examiner’s Signature Teacher’s Signature
submitted to Aster public school, SEC-3
for consideration in partial fulfillment of
School Certificate in Science.
3. Page3
ACKNOWLEDGEMENT
I would like to express my special thanks of gratitude to
opportunity to do this wonderful project on the topic
“Report on Moving Coil Galvanometer”, which also
helped me in doing a lot of Research and I Came to
know about so many thing I am really thankful to them.
Secondly I would also like to thank my parents and
friends who helped me a lot in finalizing this project
within the limited time frame
my teacher Mr. Pankaj sir well as our principal
Mrs.sharbari banerjee . Who gave me the golden
4. Page4
Index
S.no. Title PAGE No.
1. Certificate 2
2. Acknowledgement 3
3. Index 4
4 Introduction 5
5 Principle and
Construction
6-7
6 Theory 8-9
7 Advantages and
Disadvantages
10
8 Sensitivity and Accuracy 11-13
9 Bibliography 14
5. Page5
Introduction
A galvanometer is an electromechanical instrument for detecting and
indicating electric current. A galvanometer works as an actuator, by
producing a rotary deflection (of a "pointer"), in response to electric
current flowing through a coil in a constant magnetic field. Early
galvanometers were not calibrated, but their later developments were used
as measuring instruments, called ammeters, to measure the current
flowing through an electric circuit.
Galvanometers developed from the observation that the needle of a
magnetic compass is deflected near a wire that has electric current flowing
through it, first described by Hans Oersted in 1820. They were the first
instruments used to detect and measure small amounts of electric
currents. André-Marie Ampère, who gave mathematical expression to
Ørsted's discovery and named the instrument after the Italian electricity
researcher Luigi Galvani, who in 1791 discovered the principle of the frog
galvanoscope – that electric current would make the legs of a dead frog
jerk.
Sensitive galvanometers have been essential for the development of
science and technology in many fields. For example, they enabled long
range communication through submarine cables, such as the earliest
Transatlantic telegraph cables, and were essential to discovering the
electrical activity of the heart and brain, by their fine measurements of
current.
6. Page6
Principle
When a current carrying coil is suspended in a uniform
magnetic field it is acted upon by a torque. Under the
action of this torque, the coil rotates and the deflection in
the coil in a moving coil galvanometer is directly
proportional to the current flowing through the coil.
Construction
The suspended type consists of a rectangular coil of thin insulated copper wires
having a large number of turns.
The coil is suspended between the poles of a powerful horseshoe magnet by a
suspension fibre of phosphor-bronze. A spring is attached to the other end of the
coil. The current enters the coil through the fibre and leaves the coil through the
spring.
7. Page7
The upper end of the suspension fiber is connected to a rotating screw head so
that the plane of the coil can be adjusted in any desired position.
The horseshoe magnet has cylindrically concave pole-pieces. Due to this shape,
the magnet produces radial magnetic field so that when coil rotates in any
position its plane is always parallel to the direction of magnetic field. When
current flows through the coil it gets deflected.
A soft iron cylinder is fixed inside the coil such that the coil can rotate freely
between the poles and around the cylinder. Due to the high permittivity, the soft
iron core increases the strength of the radial magnetic field.
A small plane mirror M is fixed to the suspension fibre. This along with lamp and
scale arrangement is used to measure the deflection of the coil.
8. Page8
Theory
Consider a rectangular coil PQRS of single turn having length ‘l’ and breadth ‘b’
suspended in a uniform magnetic field of induction B such that the plane of the
coil is parallel to the magnetic field. Let ‘I’ be the current through the coil.
The sides PS and QR being parallel to the magnetic field do not experience
any force, but the sides PQ and RS being perpendicular to the magnetic
field experience force. The force experienced by each side is given by
F = B I l
By Fleming’s left-hand rule these forces are opposite in direction. As these
two forces are equal and opposite they form what is called as a couple
and due to which a torque acts on the coil which tries to deflect the coil.
The deflection torque is given by,
Torque = Force x Perpendicular distance between the forces.
τ = F x b
∴ τ = B I l × b
But l τ b = A, the area of the coil
∴ τ = B I A
9. Page9
If the coil has ‘n’ turns, then the deflecting torque is given by
∴ τ = n BIA
Under the action of this torque, the plane of the coil rotates through an
angle θ before coming to rest. Due to the radial magnetic field, the plane
of the coil is always parallel to the direction of magnetic field. Thus at any
position, the deflecting torque has constant magnitude. The rotation of the
coil produces a twist in the fibre which produces a restoring torque which is
directly proportional to the angle of deflection θ.
τ ∝ θ
∴ τ = k θ
Where k is the torque per unit twist (or torsional constant) of the suspension fiber.
When the coil comes to rest i.e. when it attains equilibrium, the restoring
torque will balance the deflecting torque. So in equilibrium position of the
coil,
Deflecting torque = Restoring torque.
n B I A = k θ
The quantities in bracket are constant, therefore
∴ I ∝ q
Thus in a moving coil galvanometer current in the coil is directly proportional to
the angle of deflection of the coil.
10. Page10
Advantages and
Disadvantages
Advantages of Moving Coil Galvanometers:
They are not affected by strong magnetic field.
They have the high torque to weight ratio.
They are very accurate and reliable.
Their scales are uniform.
Disadvantages of Moving Coil Galvanometers:
The change in temperature causes a change in restoring torque.
Restoring torque cannot be easily changed.
There is a possibility of damage to the phosphor bronze fiber or helical
restoring spring due to severe stresses.
Such instruments can only be used for measurement of direct current
quantities and cannot be used for measurement of alternating current
quantities.
11. Page11
Sensitivity and Accuracy of
a Galvanometer
Sensitivity of Moving Coil Galvanometer:
The sensitivity of moving coil galvanometer is defined as the ratio of the
change in deflection of the galvanometer to the change in the current.
Sensitivity = dθ / di
A galvanometer is said to be sensitive if it gives larger deflection for a small
current.
The current in moving coil galvanometer is given by
Thus the sensitivity of moving coil galvanometer can be increased by
o Increasing the number turns (n) of the coil,
o Increasing the area (A) of the coil,
o increasing the magnetic induction (B) and
o Decreasing the couple per unit twist (k) of the suspension fiber.
12. Page12
Limitations to Increase in Sensitivity of Moving Coil
Galvanometer:
If the turns of the coil are increased the length of wire and hence the
resistance of the coil increases.
Increasing the area of the coil beyond limit makes the instrument bulky.
Increase in the number of turns and area of the coil increases the load on
suspension fiber. Hence spring higher value of k should be used which
decreases the sensitivity of the galvanometer.
Increasing the strength of magnetic induction leads to increase in the
weight of the apparatus.
Decreasing the couple per unit twist of the spring leads to decrease in the
strength of the spring.
Accuracy of Moving Coil Galvanometer:
The relative error in the measurement of current is given by di/i
For moving coil galvanometer, the current through it is given by
Thus the error in the measurement of current depends only on the
measurement of the deflection in the galvanometer dθ.
13. Page13
For greater accuracy of the galvanometer, the ratio di / i should be small.
It is small when the deflection is large. Thus for greater accuracy, the
deflection in the galvanometer should be large for small current in it.
As the expression of accuracy does not contain the terms n, A, B and k the
accuracy is independent of the number of turns of the coil, the area of the
coil, the magnetic induction and constant for the spring.
