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To Determine the Current and Charge Sensitivity of a Ballistic Galvanometer (BG) by the Steady Deflection Method
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Moving Coil Ballistic Galvanometer
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Theory and Operation of Moving Coil Ballistic Galvanometer
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Ballistic Galvanometer is a type of galvanometer that measures the current or voltage in an alternating current circuit. It is also known as a moving coil meter or a moving coil ammeter.
Ballistic Galvanometer Operation
Ballistic Galvanometer measures the current or voltage in an alternating current circuit by using a moving coil placed in a magnetic field. A magnetic field that opposes the magnetic field in the magnetic circuit is produced as the current passes over the coil. This opposition causes the coil to move and its speed depends on the current magnitude and frequency. The moving coil then strikes a spring balance to rotate the pointer of the meter and indicate the value of the current or voltage being measured.
Theory of Ballistic Galvanometer
Ballistic Galvanometer Theory is based on Faraday’s Law of Electromagnetic Induction, which states that when a wire carrying a current is placed in a magnetic field, a force is exerted on the wire, causing it to move. This force works perpendicular to both the directions of the current and magnetic field and is proportional to the product of the current and magnetic field strength. The moving coil ballistic galvanometer uses this principle to measure current or voltage by placing a wire carrying the current or voltage in a magnetic field and measuring the force exerted on the wire.
Theory of Moving Coil Ballistic Galvanometer
Theory of Moving Coil Ballistic Galvanometer can be divided into two parts:
1. Basic theory 2. Practical applications
1. Basic Theory
In moving coil ballistic galvanometer, the moving coil is placed in a magnetic field produced by either a permanent magnet or an electromagnet. The magnetic field exerts a force against the magnetic field’s direction on the moving coil. This force causes the coil to accelerate and move through the magnetic field. The speed of the moving coil depends on the magnitude and frequency of the current being measured and can be related to the velocity of the coil using Newton’s Second Law of Motion, which states that force equals mass times acceleration. The force acting on the moving coil can be expressed using Ampere’s Law, which states that the sum of the forces acting on a current-carrying wire equals the product of the current and the reluctance of the magnetic circuit.
2. Practical Applications
Moving Coil Ballistic Galvanometer can be used to measure ac currents up to about 100 A or ac voltages up to about 1000 V. The moving coil ballistic galvanometer measures current or voltage by placing a wire carrying the current or voltage in a magnetic field and measuring the force exerted on the wire. The moving coil then strikes a spring balance to rotate the pointer of the meter and indicate the value of the current or voltage being measured. The spring balance used in moving coil ballistic galvanometer meters is typically made of leaf springs or flexures, which provide high stiffness and low damping for accurate measurements. The spring balance is coupled to a pointer through a linkage mechanism that converts the small movements of the spring balance into large angular displacements of the pointer.
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GALVANOMETERS
Ballistic Galvanometer
Definition: The galvanometer which is used for estimating the quantity of charge flow through it is called the ballistic galvanometer . The working principle of the ballistic galvanometer is very simple. It depends on the deflection of the coil which is directly proportional to the charge passes through it. The galvanometer measures the majority of the charge passes through it in spite of current.
Construction of Ballistic Galvanometer
The ballistic galvanometer consists coil of copper wire which is wound on the non-conducting frame of the galvanometer. The phosphorous bronze suspends the coil between the north and south poles of a magnet. For increasing the magnetic flux the iron core places within the coil. The lower portion of the coil connects with the spring. This spring provides the restoring torque to the coil.
When the charge passes through the galvanometer, their coil starts moving and gets an impulse. The impulse of the coil is proportional to the charges passes through it. The actual reading of the galvanometer achieves by using the coil having a high moment of inertia. The moment of inertia means the body oppose the angular movement. If the coil has a high moment of inertia, then their oscillations are large. Thus, accurate reading is obtained.
Theory of Ballistic Galvanometer
The angular momentum of the coil is equal to the force acting on the coil. Thus from equation (4) and (5), we get.
On substituting the value of equation (6) in the equation (8) we get
The K is the constant of the ballistic galvanometer.
Calibration of Galvanometer
The calibration of the galvanometer is the process of determining its constant value by the help of the practical experiments . The following are the methods used for determining the constant of the ballistic galvanometer.
Using a Capacitor
The circuit uses two pole switch S and the unknown EMF source E. When the switch S connects to terminal 2 then the capacitor becomes charged. Similarly, when the switch connects to terminal 1, then the capacitor becomes discharges through the resistor R, connected in series with the ballistic galvanometer.
Using a Mutual Inductance
The constant of the ballistic galvanometer determines through the mutual inductance between the coils. The arrangement of the ballistic galvanometer requires two coils; primary and secondary. The primary coil is energised by knowing voltage source.
Because of the mutual induction, the current induces in the secondary circuit. And this current is used for the calibration of the ballistic galvanometer.
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What is Ballistic Galvanometer : Working & Its Uses
The former galvanometer was introduced by Johann Schweigger in the year 1820. The development of the device was also done by Andre Marie Ampere. The former designs enhanced the effect of the magnetic field that was developed by the current through many numbers of wire turns. So, these devices were also called as multipliers as because of their almost similar construction. But the term galvanometer was more in popularity by 1836. Then after with many enhancements and progressions, various types of galvanometers came into existence. And the one type is “Ballistic Galvanometer”. This article clearly explains its working principle, construction, applications, and advantages.
What is Ballistic Galvanometer?
Ballistic Galvanometer is the device that is employed for assessing the amount of charge flow that is developed from the magnetic flux. This device is a kind of sensitive galvanometer which is also termed as a mirror galvanometer. In contrast to the general kind of measuring galvanometer, the moving section of the device holds a more inertial moment, so it provides a long time of oscillation. It genuinely operates as an integrator calculating the amount of charge expelled from it. This might be like either a moving magnet or like moving coil.
Working Principle
The principle behind the ballistic galvanometer working is that it measures the amount of charge that flows across the magnetic coil where this initiates the coil to move. When there is charge flow across the coil, it provides an increase in the current value because of the torque that is generated in the coil, and this developed torque operates for a shorter period of time.
The result of time and the torque gives force for the coil and then the coil gets is rotating motion. When the starting kinetic energy of the coil is totally employed for operation, then the coil will start out to get to its actual position. So, the coil swings in the magnetic arena, and the deflection is then stated down from where the charge might be measured. So, the principle of the device is mainly dependent on the coil deflection that has a direct relation to the amount of charge that flows through it.
Ballistic Galvanometer Construction
The construction of a ballistic galvanometer is the same as like moving coil galvanometer and it includes two properties where those are:
- The device has undamped oscillations
- It also has exceptionally minimal electromagnetic damping
The ballistic galvanometer is included with copper wire where it is rolled across the non-conducting frame of the device. The phosphorus bronze in the galvanometer halts the coil which is present in between the magnetic poles. For the enhancement of magnetic flux, the iron core is placed inside the coil.
The coil’s underneath section is connected with the spring where it gives restoration torque for the coil. When there is charge flow across the ballistic galvanometer, then the coil gets to have a movement and develops an impulse. The coil’s impulse has a direct relation to the flow of charge. The accurate reading in the device is achieved by implementing a coil that holds increased inertial moment.
The moment of inertia implies that the body is in opposition to that of angular movement. When there is increased inertial moment in the coil, then the oscillations will be more. So, because of this precise reading can be achieved.
Detailed Theory
The detailed theory of the ballistic galvanometer can be explained with the following equations. By considering the below example, the theory can be known.
Let us consider a rectangular-shaped coil that has ‘N’ number of turns which is kept in a constant magnetic field. For the coil, the length and breadth are ‘l’ and ‘b’. So, the area of the coil is
When there is current flow across the coil, then the torque is developed on it. The magnitude of the torque is given by τ = NiBA
Let us assume that the flow of current across the coil for each minimal time period is dt and so the change in current is represented as
τ dt = NiBA dt
When there is current flow across the coil for a time period of ‘t’ seconds, then the value is represented as
ʃ 0 t τ dt = NBA ʃ 0 t idt = NBAq
where ‘q’ is the total amount of charge that flows across the coil. The inertial moment that exists for the coil is shown as ‘I’ and the coil’s angular velocity is shown as ‘ω’. The below expression provides the angular momentum of the coil and it is lω. It is similar to the pressure that is applied to the coil. By multiplying the above two equations, we get
Also, the kinetic energy across the coil will have deflection at ‘ϴ’ angle and the deflection will be restored using the spring. It is represented by
Restoring torque value = (1/2)cϴ 2
Kinetic energy value = (1/2)lw 2
As the coil’s restoring torque is similar to the deflection then
(1/2)cϴ 2 = (1/2)lw 2
cϴ 2 = lw 2
Also, the periodic oscillations of the coil is shown as below
T = 2∏√(l/c)
T 2 = (4∏ 2 l/c)
(T 2 /4∏ 2 ) = (l/c)
(cT 2 /4∏ 2 ) = l
Finally, (ctϴ/2∏) =lw = NBAq
q = (ctϴ)/NBA2∏
q = [(ct)/NBA2∏] * ϴ)
Assume that k = [(ct)/NBA2∏
Then q = k ϴ
So, ‘k’ is the constant term of the ballistic galvanometer.
Galvanometer Calibration
The calibration of the galvanometer is the approach of knowing the device’s constant value with the assistance of some practical methodologies. Here are the two methods of the ballistic galvanometer and those are
- Through a capacitor
- Through mutual inductance
Calibration using Capacitor
The constant value of the ballistic galvanometer is known with the charging and discharging values of the capacitor. The below ballistic galvanometer diagram using a capacitor shows the construction of this method.
The construction is included with an unknown electromotive force ‘E’ and a pole switch ‘S’. When the switch gets connected to the second terminal, then the capacitor moves to the charging position. In the same way, when the switch gets connected to the first terminal, then the capacitor moves to the discharging position using the resistor ‘R’ that is in series connection to the galvanometer. This discharging causes deflection in the coil at the ‘ϴ’ angle. With the below formula, galvanometer constant can be known and it is
Kq = (Q/ϴ 1 ) = CE/ ϴ 1 measured in coulombs per radian.
Calibration using Mutual Inductance
This method needs primary and secondary coils and the galvanometers constant calculates the mutual inductance of the coils. The first coil gets energized through the known voltage source. Due to the mutual inductance, there will be the development of current is the second circuit and this is utilized for the galvanometer’s calibration.
Ballistic Galvanometer Applications
Few of the applications are:
- Employed in control systems
- Used in laser displays, and laser engraving
- Utilized for knowing photoresistor measurements in the metering method of film cameras.
So, this is all about the detailed concept of a ballistic galvanometer. It explains clearly the device working, construction, calibration, applications, and diagram. It is also more important to know about what the types are in ballistic galvanometer and ballistic galvanometer advantages ?
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The experiment is repeated for different values of P keeping P+Q equal to 10000 . (Remember, is originally defined as the angle of deflection of the mirror. When the mirror turns through an angle , the reflected ray turns through an angle 2 . ... The requirements of a ballistic galvanometer are reverse of those for a dead beat
The ballistic galvanometer consists of copper wire which is wound on nonconducting frame of galvanometer. For increasing the magnetic flux the iron core places within the coil. The lower portion of the coil connect the spring. This spring provides the restoring torque to the coil. Fig 1 : Ballistic Galvanometer.
Ballistics Galvanometer. C= capacity of the given capacitor in farads. PROCEDUR: 1. The spot of light of the Galvanometer is adjusted at zero of the scale 2. The connections are made as shown in the figure .Key k 1 is inserted and key k3 is pressed. It will charge the condenser. 3. The key k 3 is released and k 4 is pressed. The first throw θ0 ...
THEORY OF BALLISTIC GALVANOMETER B.G. consists of a rectangular coil of area A and number of turns N suspended in a uniform magnetic field B. Let it carry a current I for a short interval of time dt. Then the momentary torque on the coil is given by T N A B → = → × F → HG I Ι KJ As the plane of the coil is always parallel to B, T = N I A B
6. Let the calculated length of the wire be 10 cm. Then cut 3-4 cm extra and put it in parallel to the galvanometer and complete the circuit as shown in Fig. E 7.1. 7. Adjust the length of the wire so that when we see full scale deflection in the galvanometer, the current in the ammeter is. 30 mA.
Integrate this with respect to time, with initial condition Q = 0 when t = 0 Q = 0 when t = 0, and we find for the total quantity of electricity that flows through the galvanometer. Q = NAB R + r. (10.4.2) (10.4.2) Q = N A B R + r. Since Q Q can be measured from the amplitude of the galvanometer motion, the strength of the magnetic field, B B ...
Experiment :B-02 Determination of the absolute capacity of a condenser using a ballistic galvanometer. Theory : If a potential V applied to a condenser of capacitance C, imparts Q units of charge to the condenser then, C= Q V (1) From the ballistic galvanometer working formula we got: Q= T ˇ i d d 1 2 (1 + d 2) (2) Q= T ˇ i d d 1 2 d 1 d 3 (3)
Lab # 27 data - Capacitance Measurement with a Ballistic Galvanometer Data and Calculations Table 1 23.05 5.00 3.35 3.10 2.05 7.30 1.070 0.233
This Link provides the handwritten practical file of the above mentioned experiment (with readings) in the readable pdf format. ... Read More Read More To draw the BH curve of iron (Fe) using a Solenoid and determine the energy loss from Hysteresis loop
(19) Ballistic GalvanometerLesson 7.1 Basic Theory of the Ballistic Galvanometer.pdf. Sign In. Details ...
The moving coil ballistic galvanometerA moving coil ballistic galvanometer is a suspended type galvanometer which m. the charge rather than current.FigureA typical moving coil ballistic galvanometer is shown in adjacent figure in which a coil of length 'a' and breadth 'b' having current 'I' is placed between the pole pieces of a pe.
Sensitivity of Blastic Galvanometer So, for today we will discuss about the, for current Sensitivity and charge sense sensitivity of a galvanometer, basically Ballistic Galvanometer. So, let us discuss about the theory of this Experiment. (Refer Slide Time: 00:42)
The. galvanometer you are using has been selected because the coil has a high moment of. inertia which results in a long oscillation period. However, because of effects of air-resistance and other 'resistive' effects within the. coil, these oscillations will be damped, and the coil will eventually come to rest at the.
11. Measurement of charge sensitivity, current sensitivity and CDR of Ballistic Galvanometer 12. Determine a high resistance by leakage method using Ballistic Galvanometer. 13. To determine self-inductance of a coil by Rayleigh's method. 14. To determine the mutual inductance of two coils by Absolute method. References for Theory:
1. Basic Theory. In moving coil ballistic galvanometer, the moving coil is placed in a magnetic field produced by either a permanent magnet or an electromagnet. The magnetic field exerts a force against the magnetic field's direction on the moving coil. This force causes the coil to accelerate and move through the magnetic field.
at R 1 = Rg, the deflection of the galvanometer is exactly half of the deflection produced when R 1 = 0. Thus, the value of R 1 at which the deflection is getting half is the resistance of the galvanometer. The working formula for log decrement: To observe log decrement, we need to set up the situation of Forced Electrical
Prof Avishek Chatterjee Department of Electrical Engineering IIT Kharagpur To access the translated content: 1. The translated content of this course is ava...
The galvanometer which is used for measuring the quantity of charge flow through it is called the ballistic galvanometer. The working principle of the ballistic galvanometer is very simple. It depends on the deflection of the coil which is directly proportional to the charge passes through it. It measures the majority of the charge passes through it in spite of current.
Physics major and also for allied students and ensure that they master the lab skills necessary to be competitive in the job market. The book is suitable for ... MEASUREMENT OF INDUCTANCE USING BALLISTIC GALVANOMETER .....128 PRACTICAL-IV: Electronics 1. DUAL REGULATED POWER SUPPLIES USING IC'S .....132 2. HIGH PASS AND LOW PASS FILTER CIRCUIT ...
primary circuit, a throw is observed in the ballistic galvanometer. The key K 2, should however be released immediately after closing the key K 1 in order to avoid excessive damping of the galvanometer. The ballistic throw is set up by the induced e.m.f., produced due in the secondary circuit due to the sudden change in flux linked with the ...
A ballistic galvanometer is a type of sensitive galvanometer; commonly a mirror galvanometer. Unlike a current-measuring galvanometer, the moving part has a large moment of inertia, thus giving it a long oscillation period. It is really an integrator measuring the quantity of charge discharged through it. It can be either of the moving coil or ...
A galvanometer is an electromechanical current-measuring instrument. The current and its strength are often shown by the movement of a magnetic needle or a coil in a magnetic field, which is an integral component of a galvanometer. The ballistic galvanometer is a sensitive type of galvanometer. It operates on a fairly simple concept.
The ballistic galvanometer is included with copper wire where it is rolled across the non-conducting frame of the device. The phosphorus bronze in the galvanometer halts the coil which is present in between the magnetic poles. For the enhancement of magnetic flux, the iron core is placed inside the coil.
Thomas Gray, The Ballistic Galvanometer and its Use in Magnetic Measurements, Science, New Series, Vol. 1, No. 20 (May 17, 1895), pp. 533-537