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Physics Project Name:- Dabhi Mihir Roll No:- 3 th
Class:- 12 (Science-PCB) Topic:-
Moving coil galvanometer
Moving Coil Galvanometer-Physics Project
Page 1
Certificate:This is to certify that Mihir Dabhi, a student of Class 12th (Science-PCB) has successfully completed the project on the above mentioned topic under the guidance of Mr. Rana Sir (Subject Teacher) during the year 2017-2018 in partial fulfillment of Physics Practical Examination conducted by CBSE, New Delhi.
Signature of the Examiner
Signature of subject teacher
Moving Coil Galvanometer-Physics Project
Page 2
Acknowledgement:The success and final outcome of this project required a lot of guidance and assistance from many people. I am extremely privileged to thanks Mr. Rana Sir (Subject Teacher) for providing me an opportunity to do the project work and giving me all and guidance which made me complete the project appropriately. He was always ive and inspirational for completing this project. I am also extremely thankful to all my friends for providing me all the necessary and guidance.
Mihir Dabhi Class 12th – Science-PCB Moving Coil Galvanometer-Physics Project
Page 3
Objective: To study the basic schematic structure of a moving coil galvanometer and the basic process underlying the conversion of a moving coil galvanometer into an ammeter and a voltmeter.
References: NCERT Class 12 Physics Textbook http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html http://www.brainkart.com/article/Moving-coil-galvanometer
Moving Coil Galvanometer-Physics Project
Page 4
Contents: Basics about magnetic effects of current and magnetism Torque on a current carrying coil placed in a magnetic field Brief introduction into the different types of Galvanometers along with brief description General structure of a moving coil galvanometer Conversion of a Galvanometer into an Ammeter Conversion of a Galvanometer into a Voltmeter
Moving Coil Galvanometer-Physics Project
Page 5
Basics about Magnetic Effects of Current and Magnetism: Introduction:Electromagnetism: The branch of physics which deals with interaction of electric current or fields and magnetic fields. Magnetic field: A region of space near a magnet, electric current or moving charged particle in which magnetic effects are exerted on any other magnet, electric current, or moving charged particle. It is also known as magnetic flux density or magnetic induction or magnetic field. Unit: Weber/m2 or Tesla
Dimensions: [MT-2A-1]
Oersted’s Discovery:The relation between electricity and magnetism was discovered by Oersted in 1820. Oested showed that the electric current through the conducting wire deflects the magnetic needle held near the wire. On increasing the current in conductor or bringing the needle closer to the conductor, the deflection of magnetic needle increases. Oersted discovered a magnetic field around a conductor carrying current. A magnet at rest produces a magnetic field around it while electric charge at rest produces an electric field around A current carrying conductor has a magnetic field and not electric field around it. On the other hand, a charge moving with uniform velocity has electric as well as a magnetic field around it.
The magnetic field (marked B, indicated by field lines) around wire carrying an electric current (marked I).
Moving Coil Galvanometer-Physics Project
Page 6
an it. an an
Biot-Savart’s Law:With the help of experimental results, Biot and Savart arrived at a mathematical expression that gives the magnetic field at some point in of the current that produces the field.
Magnetic Field Lines: In order to visualize a magnetic field graphically, Michael Faraday introduced the concept of field lines. Field lines of magnetic field are imaginary lines which represents direction of magnetic field continuously. o Magnetic field lines emanate from or enter in the surface of a magnetic material at any angle. o Magnetic field lines exist inside every magnetized material. o Magnetic field lines can be mapped by using iron dust or using com needle. o They are closed curves. o Tangent drawn on any point on field lines represents direction of the field at that point. o Field lines never intersect each other.
Quick Fact: Magnetic Resonance Imaging (MRI) machines generate a field 60,000 times as intense as the earth’s to vibrate the hydrogen atoms in our body; in response, the atoms emit radio waves that are analyzed to produce a map of our insides.
Moving Coil Galvanometer-Physics Project
Page 7
Magnetic Force:-
The implications of this expression include: 1. The force is perpendicular to both the velocity v of the charge q and the magnetic field B. 2. The magnitude of the force is F = qvB sinθ where θ is the angle <180 degrees between the velocity and the magnetic field. This implies that the magnetic force on a stationary charge or a charge moving parallel or antiparaller to the magnetic field is zero. 3. The direction of the force is given by the left hand rule. The force relationship above is in the form of a vector product. When current flows through a conducting wire, and an external magnetic field is applied across that flow, the conducting wire experiences a force perpendicular both to that field and to the direction of the current flow (i.e they are mutually perpendicular) . The Thumb represents the direction of Motion resulting from the force on the conductor The First finger represents the direction of the magnetic Field The Second finger represents the direction of the Current. Fleming’s Left Hand Rule to find the direction of force (movement) on a moving charged particle (or current carrying conductor) placed in Magnetic Field.
This diagram illustrates how to find out the direction of force on a charged particle moving in a region of magnetic field. This method is based on the vector product of two vectors where the resultant vector is perpendicular to the plane containing both vectors.
Moving Coil Galvanometer-Physics Project
Page 8
Lorentz Force:When a charge is moving in a region, where both electric field and magnetic field having magnitudes E and B respectively exist, then electric and magnetic forces are acting on it. The resultant of these forces is called electromagnetic force or Lorentz force on charge.
Magnetic Moment:Magnetic moment of a bar magnet is defined as a vector quantity having magnitude equal to the product of pole strength (m) with effective length (l) and directed along the axis of the magnet from South to North pole. 𝑀 = 𝑚. 𝑙 Magnetic Moment of a current carrying coil (loop): A current carrying coil behaves like a magnetic dipole. The face of coil in which current appears to flow anticlockwise acts as North Pole while face of coil in which current appears to flow clock wise acts as South Pole.
Moving Coil Galvanometer-Physics Project
Page 9
A loop of geometrical area ‘A’, carries a current ‘I’, then magnetic moment of coil M=IA A coil of ‘N’ turns, geometrical area ‘A’, carries a current ‘I’, then magnetic moment M=NIA Torque on a Current carrying coil placed in Magnetic Field:-
Moving Coil Galvanometer-Physics Project
Page 10
TYPES OF GALVANOMETERS:o Tangent Galvanometer:- It works by using a com needle to compare the magnetic field generated by an unknown current to the magnetic field of the Earth. It was used earlier. It was first given by Claude Pouillet. It contains an insulated copper wire coil on a non-magnetic circular frame. o Astatic Galvanometer:- It does not use the Earth’s magnetic field for measuring the current. It was developed by Leopoldo Nobili. It contains two magnetized needles that run parallel to each other, suspended by a silk thread, with their magnetic poles reversed. The lower needle gets deflected by the ing current’s magnetic field. The second needle cancels out the dipole movement of the first one to cancel out the effects of Earth’s magnetic field. o Mirror Galvanometer:- It is used to achieve higher sensitivity for detecting extremely small currents. It contains horizontal magnets which are suspended from a fine fiber inside of the vertical coil, with an attached mirror to its magnets. A beam of light reflects from the mirror acts as a long mass-less pointer by falling on a graduated scale across the room. o Ballistic Galvanometer:- It is sensitive in mature and used to measure the quantity of charge that is discharged through it. The moving part of the galvanometer has a large moment of inertia, giving it a long oscillation period. It may be of the moving coil type or of the moving magnet type.
Moving Coil Galvanometer-Physics Project
Page 11
Moving Coil Galvanometer:-
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. Galvanometers developed from the observation that the needle of a magnetic com 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. Sensitive galvanometers have been essential for the development of science and technology in many fields. Galvanometers also had widespread use as the visualising part in other kinds of analog meters, for example in light meters, VU meters, etc., where they were used to measure and display the output of other sensors. 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:It consists of a rectangular coil of thin insulated copper wires having a large number of turns. 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. Schematic Diagram of a Moving Coil Galvanometer
Moving Coil Galvanometer-Physics Project
Page 12
Working:When a current flows through the coil, a torque acts on it. This torque is given by the equation 𝜏 = 𝑁𝑖𝐴𝐵 where the symbols have their usual meaning. Since the field is radial by design, we have taken sin 𝜃 = 1 in the above expression for the torque. The magnetic torque 𝜏 = 𝑁𝑖𝐴𝐵 tends to rotate the coil. A spring Sp provides a counter torque 𝜏 = 𝐾𝜑 that balances the magnetic torque 𝜏 = 𝑁𝑖𝐴𝐵; resulting in a steady angular deflection 𝜑. In equilibrium, 𝐾𝜑 = 𝑁𝑖𝐴𝐵 where 𝐾 is the torsional constant of the spring; i.e. the restoring torque per unit twist. The deflection 𝜑 is indicated on the scale by a pointer attached to the spring. We have 𝜑 =
𝑁𝐴𝐵 𝐾
𝑖.
The quantity given in brackets is a constant for the galvanometer. Hence, Galvanometer Constant G can be expressed as:-
𝐺 =
𝑁𝐴𝐵 𝐾
∴ 𝜑 = 𝐺𝑖 ∴𝑖 ∝ 𝜑 So, the current through the coil varies linearly with the deflection and so, the current flowing through the coil can be known by measuring the deflection. The galvanometer can be used as a detector to check if a current is flowing in the circuit (this configuration is used in the Wheatstone’s bridge arrangement). In this usage the neutral position of the pointer (when no current is flowing through the galvanometer) is in the middle of the scale and not at the left end. Depending on the direction of the current, the pointer deflection is either to the right or the left.
Quick Fact: Greek scientist, Archimedes was the first person to have made use of magnets. The story goes that he enabled enemy ships to sink by using lodestone to pull out the iron nails used in the ship's body.
Moving Coil Galvanometer-Physics Project
Page 13
Current Sensitivity of Galvanometer:The current sensitivity of a galvanometer is defined as the deflection produced when unit current es through the galvanometer. A galvanometer is said to be sensitive if it produces large deflection for a small current. ∴ 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦
𝜑 𝑁𝐵𝐴 = 𝑖 𝐾
Factors increasing Current Sensitivity: Increasing the magnetic field B by using strong permanent horse shoe shaped magnet. Increasing the number of turns N. But number of turns of the coil cannot be increased beyond a certain limit. This is because the resistance of the galvanometer will increase subsequently and hence the galvanometer becomes less sensitivity. Increasing the area of the coil A. But it will make the galvanometer bulky and ultimately less sensitive. Decreasing the value of restoring force constant k by using a flat strip of phosphor – bronze instead of circular wire of phosphor – bronze. Quartz fibers can also be used for suspension of the coil because they have large tensile strength and very low value of K. Voltage Sensitivity of Galvanometer:The voltage sensitivity of a galvanometer is defined as the deflection per unit voltage.
∴ 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦
𝜑 𝑉
=
𝜑 𝐼𝐺
=
𝑁𝐵𝐴 𝐾𝐺
where G = Galvanometer Resistance
An interesting point to note is that, increasing the current sensitivity does not necessarily, increase the voltage sensitivity. When the number of turns (n) is doubled, current sensitivity is also doubled (equation 1). But increasing the number of turns correspondingly increases the resistance (G). Hence voltage sensitivity remains unchanged.
Moving Coil Galvanometer-Physics Project
Page 14
Factors increasing Voltage Sensitivity: Increasing number of turns of the coil (N) Increasing magnetic field intensity (B) Increasing area of the coil (A) Decreasing restoring torque per unit twist of the suspension (k) Decreasing resistance (G) Advantages of a Moving Coil Galvanometer: The sensitivity of the galvanometer can be increased by increasing N, B and A while decreasing the value of k. The instrument has a linear scale. Since the instrument uses high value of B, the deflection is undisturbed by the earth’s magnetic field. As the coil is wound on a nonmagnetic metallic frame, damping is produced by eddy currents. As a result the coil quickly assumes the final position.
Moving Coil Galvanometer-Physics Project
Page 15
Conversion of a Galvanometer Ammeter and a Voltmeter:-
to
an
Conversion of a Galvanometer into an Ammeter:The galvanometer cannot as such be used as an ammeter to measure the value of the current in a given circuit. This is for two reasons: (i) Galvanometer is a very sensitive device, it gives a full-scale deflection for a current of the order of µA. (ii) For measuring currents, the galvanometer has to be connected in series, and as it has a large resistance, this will change the value of the current in the circuit. To overcome these difficulties, one attaches a small resistance S, called shunt resistance, in parallel with the galvanometer coil; so that most of the current es through the shunt. The value of shunt resistance depends on the fraction of the total current required to be ed through the galvanometer. Let Ig be the maximum current that can be ed through the galvanometer. The current Ig will give full scale deflection in the galvanometer. Galvanometer Resistance = G Shunt Resistance = S Current in the circuit = I ∴ 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑡ℎ𝑒 𝑠ℎ𝑢𝑛𝑡 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐼𝑠 = 𝐼 − 𝐼𝑔 Since the galvanometer and the shunt resistance are connected in parallel, the potential difference across both of them is same. ∴ 𝐼𝑔 . 𝐺 = 𝐼 − 𝐼𝑔 . 𝑆 ∴ 𝑆 = 𝐺.
𝐼𝑔 𝐼 − 𝐼𝑔
The shunt resistance is very small because Ig is only a fraction of I.
Moving Coil Galvanometer-Physics Project
Page 16
The effective resistance of the ammeter Ra is (G in parallel with S):𝑅𝑎 =
𝐺. 𝑆 𝐺+𝑆
Ra is very low and this explains why an ammeter should be connected in series. When connected in series, the ammeter does not appreciably change the resistance and current in the circuit. Hence an ideal ammeter is one which has zero resistance. Conversion of a Galvanometer into a Voltmeter:Voltmeter is an instrument used to measure potential difference between the two ends of a current carrying conductor. A galvanometer can be converted into a voltmeter by connecting a high resistance in series with it. The scale is calibrated in volt. The value of the resistance connected in series decides the range of the voltmeter. Galvanometer Resistance = G The current required to produce full scale deflection in the galvanometer = Ig Range of Voltmeter = V Resistance to be connected in series = R Since R is connected in series with the galvanometer, the current through the galvanometer, ∴ 𝐼𝑔 =
𝑉 𝑅+𝐺
∴𝑅=
𝑉 − 𝐺 𝐼𝑔
From the equation the resistance to be connected in series with the galvanometer is calculated. The effective resistance of the voltmeter is:∴ 𝑅𝑣 = 𝑅 + 𝐺
Moving Coil Galvanometer-Physics Project
Page 17
Rv is very large, and hence a voltmeter is connected in parallel in a circuit as it draws the least current from the circuit. In other words, the resistance of the voltmeter should be very large compared to the resistance across which the voltmeter is connected to measure the potential difference. Otherwise, the voltmeter will draw a large current from the circuit and hence the current through the remaining part of the circuit decreases. In such a case the potential difference measured by the voltmeter is very much less than the actual potential difference. The error is eliminated only when the voltmeter has a high resistance. An ideal voltmeter is one which has infinite resistance.
Moving Coil Galvanometer-Physics Project
Page 18
Class:- 12 (Science-PCB) Topic:-
Moving coil galvanometer
Moving Coil Galvanometer-Physics Project
Page 1
Certificate:This is to certify that Mihir Dabhi, a student of Class 12th (Science-PCB) has successfully completed the project on the above mentioned topic under the guidance of Mr. Rana Sir (Subject Teacher) during the year 2017-2018 in partial fulfillment of Physics Practical Examination conducted by CBSE, New Delhi.
Signature of the Examiner
Signature of subject teacher
Moving Coil Galvanometer-Physics Project
Page 2
Acknowledgement:The success and final outcome of this project required a lot of guidance and assistance from many people. I am extremely privileged to thanks Mr. Rana Sir (Subject Teacher) for providing me an opportunity to do the project work and giving me all and guidance which made me complete the project appropriately. He was always ive and inspirational for completing this project. I am also extremely thankful to all my friends for providing me all the necessary and guidance.
Mihir Dabhi Class 12th – Science-PCB Moving Coil Galvanometer-Physics Project
Page 3
Objective: To study the basic schematic structure of a moving coil galvanometer and the basic process underlying the conversion of a moving coil galvanometer into an ammeter and a voltmeter.
References: NCERT Class 12 Physics Textbook http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html http://www.brainkart.com/article/Moving-coil-galvanometer
Moving Coil Galvanometer-Physics Project
Page 4
Contents: Basics about magnetic effects of current and magnetism Torque on a current carrying coil placed in a magnetic field Brief introduction into the different types of Galvanometers along with brief description General structure of a moving coil galvanometer Conversion of a Galvanometer into an Ammeter Conversion of a Galvanometer into a Voltmeter
Moving Coil Galvanometer-Physics Project
Page 5
Basics about Magnetic Effects of Current and Magnetism: Introduction:Electromagnetism: The branch of physics which deals with interaction of electric current or fields and magnetic fields. Magnetic field: A region of space near a magnet, electric current or moving charged particle in which magnetic effects are exerted on any other magnet, electric current, or moving charged particle. It is also known as magnetic flux density or magnetic induction or magnetic field. Unit: Weber/m2 or Tesla
Dimensions: [MT-2A-1]
Oersted’s Discovery:The relation between electricity and magnetism was discovered by Oersted in 1820. Oested showed that the electric current through the conducting wire deflects the magnetic needle held near the wire. On increasing the current in conductor or bringing the needle closer to the conductor, the deflection of magnetic needle increases. Oersted discovered a magnetic field around a conductor carrying current. A magnet at rest produces a magnetic field around it while electric charge at rest produces an electric field around A current carrying conductor has a magnetic field and not electric field around it. On the other hand, a charge moving with uniform velocity has electric as well as a magnetic field around it.
The magnetic field (marked B, indicated by field lines) around wire carrying an electric current (marked I).
Moving Coil Galvanometer-Physics Project
Page 6
an it. an an
Biot-Savart’s Law:With the help of experimental results, Biot and Savart arrived at a mathematical expression that gives the magnetic field at some point in of the current that produces the field.
Magnetic Field Lines: In order to visualize a magnetic field graphically, Michael Faraday introduced the concept of field lines. Field lines of magnetic field are imaginary lines which represents direction of magnetic field continuously. o Magnetic field lines emanate from or enter in the surface of a magnetic material at any angle. o Magnetic field lines exist inside every magnetized material. o Magnetic field lines can be mapped by using iron dust or using com needle. o They are closed curves. o Tangent drawn on any point on field lines represents direction of the field at that point. o Field lines never intersect each other.
Quick Fact: Magnetic Resonance Imaging (MRI) machines generate a field 60,000 times as intense as the earth’s to vibrate the hydrogen atoms in our body; in response, the atoms emit radio waves that are analyzed to produce a map of our insides.
Moving Coil Galvanometer-Physics Project
Page 7
Magnetic Force:-
The implications of this expression include: 1. The force is perpendicular to both the velocity v of the charge q and the magnetic field B. 2. The magnitude of the force is F = qvB sinθ where θ is the angle <180 degrees between the velocity and the magnetic field. This implies that the magnetic force on a stationary charge or a charge moving parallel or antiparaller to the magnetic field is zero. 3. The direction of the force is given by the left hand rule. The force relationship above is in the form of a vector product. When current flows through a conducting wire, and an external magnetic field is applied across that flow, the conducting wire experiences a force perpendicular both to that field and to the direction of the current flow (i.e they are mutually perpendicular) . The Thumb represents the direction of Motion resulting from the force on the conductor The First finger represents the direction of the magnetic Field The Second finger represents the direction of the Current. Fleming’s Left Hand Rule to find the direction of force (movement) on a moving charged particle (or current carrying conductor) placed in Magnetic Field.
This diagram illustrates how to find out the direction of force on a charged particle moving in a region of magnetic field. This method is based on the vector product of two vectors where the resultant vector is perpendicular to the plane containing both vectors.
Moving Coil Galvanometer-Physics Project
Page 8
Lorentz Force:When a charge is moving in a region, where both electric field and magnetic field having magnitudes E and B respectively exist, then electric and magnetic forces are acting on it. The resultant of these forces is called electromagnetic force or Lorentz force on charge.
Magnetic Moment:Magnetic moment of a bar magnet is defined as a vector quantity having magnitude equal to the product of pole strength (m) with effective length (l) and directed along the axis of the magnet from South to North pole. 𝑀 = 𝑚. 𝑙 Magnetic Moment of a current carrying coil (loop): A current carrying coil behaves like a magnetic dipole. The face of coil in which current appears to flow anticlockwise acts as North Pole while face of coil in which current appears to flow clock wise acts as South Pole.
Moving Coil Galvanometer-Physics Project
Page 9
A loop of geometrical area ‘A’, carries a current ‘I’, then magnetic moment of coil M=IA A coil of ‘N’ turns, geometrical area ‘A’, carries a current ‘I’, then magnetic moment M=NIA Torque on a Current carrying coil placed in Magnetic Field:-
Moving Coil Galvanometer-Physics Project
Page 10
TYPES OF GALVANOMETERS:o Tangent Galvanometer:- It works by using a com needle to compare the magnetic field generated by an unknown current to the magnetic field of the Earth. It was used earlier. It was first given by Claude Pouillet. It contains an insulated copper wire coil on a non-magnetic circular frame. o Astatic Galvanometer:- It does not use the Earth’s magnetic field for measuring the current. It was developed by Leopoldo Nobili. It contains two magnetized needles that run parallel to each other, suspended by a silk thread, with their magnetic poles reversed. The lower needle gets deflected by the ing current’s magnetic field. The second needle cancels out the dipole movement of the first one to cancel out the effects of Earth’s magnetic field. o Mirror Galvanometer:- It is used to achieve higher sensitivity for detecting extremely small currents. It contains horizontal magnets which are suspended from a fine fiber inside of the vertical coil, with an attached mirror to its magnets. A beam of light reflects from the mirror acts as a long mass-less pointer by falling on a graduated scale across the room. o Ballistic Galvanometer:- It is sensitive in mature and used to measure the quantity of charge that is discharged through it. The moving part of the galvanometer has a large moment of inertia, giving it a long oscillation period. It may be of the moving coil type or of the moving magnet type.
Moving Coil Galvanometer-Physics Project
Page 11
Moving Coil Galvanometer:-
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. Galvanometers developed from the observation that the needle of a magnetic com 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. Sensitive galvanometers have been essential for the development of science and technology in many fields. Galvanometers also had widespread use as the visualising part in other kinds of analog meters, for example in light meters, VU meters, etc., where they were used to measure and display the output of other sensors. 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:It consists of a rectangular coil of thin insulated copper wires having a large number of turns. 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. Schematic Diagram of a Moving Coil Galvanometer
Moving Coil Galvanometer-Physics Project
Page 12
Working:When a current flows through the coil, a torque acts on it. This torque is given by the equation 𝜏 = 𝑁𝑖𝐴𝐵 where the symbols have their usual meaning. Since the field is radial by design, we have taken sin 𝜃 = 1 in the above expression for the torque. The magnetic torque 𝜏 = 𝑁𝑖𝐴𝐵 tends to rotate the coil. A spring Sp provides a counter torque 𝜏 = 𝐾𝜑 that balances the magnetic torque 𝜏 = 𝑁𝑖𝐴𝐵; resulting in a steady angular deflection 𝜑. In equilibrium, 𝐾𝜑 = 𝑁𝑖𝐴𝐵 where 𝐾 is the torsional constant of the spring; i.e. the restoring torque per unit twist. The deflection 𝜑 is indicated on the scale by a pointer attached to the spring. We have 𝜑 =
𝑁𝐴𝐵 𝐾
𝑖.
The quantity given in brackets is a constant for the galvanometer. Hence, Galvanometer Constant G can be expressed as:-
𝐺 =
𝑁𝐴𝐵 𝐾
∴ 𝜑 = 𝐺𝑖 ∴𝑖 ∝ 𝜑 So, the current through the coil varies linearly with the deflection and so, the current flowing through the coil can be known by measuring the deflection. The galvanometer can be used as a detector to check if a current is flowing in the circuit (this configuration is used in the Wheatstone’s bridge arrangement). In this usage the neutral position of the pointer (when no current is flowing through the galvanometer) is in the middle of the scale and not at the left end. Depending on the direction of the current, the pointer deflection is either to the right or the left.
Quick Fact: Greek scientist, Archimedes was the first person to have made use of magnets. The story goes that he enabled enemy ships to sink by using lodestone to pull out the iron nails used in the ship's body.
Moving Coil Galvanometer-Physics Project
Page 13
Current Sensitivity of Galvanometer:The current sensitivity of a galvanometer is defined as the deflection produced when unit current es through the galvanometer. A galvanometer is said to be sensitive if it produces large deflection for a small current. ∴ 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦
𝜑 𝑁𝐵𝐴 = 𝑖 𝐾
Factors increasing Current Sensitivity: Increasing the magnetic field B by using strong permanent horse shoe shaped magnet. Increasing the number of turns N. But number of turns of the coil cannot be increased beyond a certain limit. This is because the resistance of the galvanometer will increase subsequently and hence the galvanometer becomes less sensitivity. Increasing the area of the coil A. But it will make the galvanometer bulky and ultimately less sensitive. Decreasing the value of restoring force constant k by using a flat strip of phosphor – bronze instead of circular wire of phosphor – bronze. Quartz fibers can also be used for suspension of the coil because they have large tensile strength and very low value of K. Voltage Sensitivity of Galvanometer:The voltage sensitivity of a galvanometer is defined as the deflection per unit voltage.
∴ 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦
𝜑 𝑉
=
𝜑 𝐼𝐺
=
𝑁𝐵𝐴 𝐾𝐺
where G = Galvanometer Resistance
An interesting point to note is that, increasing the current sensitivity does not necessarily, increase the voltage sensitivity. When the number of turns (n) is doubled, current sensitivity is also doubled (equation 1). But increasing the number of turns correspondingly increases the resistance (G). Hence voltage sensitivity remains unchanged.
Moving Coil Galvanometer-Physics Project
Page 14
Factors increasing Voltage Sensitivity: Increasing number of turns of the coil (N) Increasing magnetic field intensity (B) Increasing area of the coil (A) Decreasing restoring torque per unit twist of the suspension (k) Decreasing resistance (G) Advantages of a Moving Coil Galvanometer: The sensitivity of the galvanometer can be increased by increasing N, B and A while decreasing the value of k. The instrument has a linear scale. Since the instrument uses high value of B, the deflection is undisturbed by the earth’s magnetic field. As the coil is wound on a nonmagnetic metallic frame, damping is produced by eddy currents. As a result the coil quickly assumes the final position.
Moving Coil Galvanometer-Physics Project
Page 15
Conversion of a Galvanometer Ammeter and a Voltmeter:-
to
an
Conversion of a Galvanometer into an Ammeter:The galvanometer cannot as such be used as an ammeter to measure the value of the current in a given circuit. This is for two reasons: (i) Galvanometer is a very sensitive device, it gives a full-scale deflection for a current of the order of µA. (ii) For measuring currents, the galvanometer has to be connected in series, and as it has a large resistance, this will change the value of the current in the circuit. To overcome these difficulties, one attaches a small resistance S, called shunt resistance, in parallel with the galvanometer coil; so that most of the current es through the shunt. The value of shunt resistance depends on the fraction of the total current required to be ed through the galvanometer. Let Ig be the maximum current that can be ed through the galvanometer. The current Ig will give full scale deflection in the galvanometer. Galvanometer Resistance = G Shunt Resistance = S Current in the circuit = I ∴ 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑡ℎ𝑒 𝑠ℎ𝑢𝑛𝑡 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐼𝑠 = 𝐼 − 𝐼𝑔 Since the galvanometer and the shunt resistance are connected in parallel, the potential difference across both of them is same. ∴ 𝐼𝑔 . 𝐺 = 𝐼 − 𝐼𝑔 . 𝑆 ∴ 𝑆 = 𝐺.
𝐼𝑔 𝐼 − 𝐼𝑔
The shunt resistance is very small because Ig is only a fraction of I.
Moving Coil Galvanometer-Physics Project
Page 16
The effective resistance of the ammeter Ra is (G in parallel with S):𝑅𝑎 =
𝐺. 𝑆 𝐺+𝑆
Ra is very low and this explains why an ammeter should be connected in series. When connected in series, the ammeter does not appreciably change the resistance and current in the circuit. Hence an ideal ammeter is one which has zero resistance. Conversion of a Galvanometer into a Voltmeter:Voltmeter is an instrument used to measure potential difference between the two ends of a current carrying conductor. A galvanometer can be converted into a voltmeter by connecting a high resistance in series with it. The scale is calibrated in volt. The value of the resistance connected in series decides the range of the voltmeter. Galvanometer Resistance = G The current required to produce full scale deflection in the galvanometer = Ig Range of Voltmeter = V Resistance to be connected in series = R Since R is connected in series with the galvanometer, the current through the galvanometer, ∴ 𝐼𝑔 =
𝑉 𝑅+𝐺
∴𝑅=
𝑉 − 𝐺 𝐼𝑔
From the equation the resistance to be connected in series with the galvanometer is calculated. The effective resistance of the voltmeter is:∴ 𝑅𝑣 = 𝑅 + 𝐺
Moving Coil Galvanometer-Physics Project
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Rv is very large, and hence a voltmeter is connected in parallel in a circuit as it draws the least current from the circuit. In other words, the resistance of the voltmeter should be very large compared to the resistance across which the voltmeter is connected to measure the potential difference. Otherwise, the voltmeter will draw a large current from the circuit and hence the current through the remaining part of the circuit decreases. In such a case the potential difference measured by the voltmeter is very much less than the actual potential difference. The error is eliminated only when the voltmeter has a high resistance. An ideal voltmeter is one which has infinite resistance.
Moving Coil Galvanometer-Physics Project
Page 18
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