Laboratory work No. 6

MEASUREMENTS WITH A BALLISTIC GALVANOMETER

Part I

DETERMINATION OF CONDENSER CAPACITY
BY BALLISTIC METHOD

PURPOSE OF THE WORK:

1. Acquire practical skills in working with a ballistic galvanometer. Master the galvanometer calibration technique.
2. Master the technique of determining the capacitance of a capacitor using a ballistic galvanometer.

DEVICES:

1. Galvanometer M 17/11 1 .
2. Set of capacitors.
3. Keys.
4. IET stabilized voltage source.

5. Voltmeter.

Measuring the capacitance of a capacitor can be done in several fundamentally different ways.

In this work, the measurement of capacitances is based on the relationship between the charge of the capacitor, its capacitance C and the potential difference . For two capacitors charged to the same potential difference, we obtain the relation:

Therefore, if the value of C 1 is known, then, having defined q 1 and q 2 , we can calculate the unknown capacitance C 2 . This method of relative capacitance measurements is the basis of this laboratory work. The most important part of the problem is measuring the amount of charge q or comparing the charges of two capacitors. In this work, the comparison of the charges of two capacitors is carried out using the ballistic method, the study of which is given a central place.

THEORY OF BALLISTIC GALVANOMETER

A galvanometer designed to measure a small amount of electricity flowing through a circuit over a period of time that is small compared to the period of natural oscillation of the galvanometer frame is called ballistic. It is a special type of galvanometer of a magnetoelectric system. A ballistic galvanometer differs from a conventional mirror galvanometer in the large moment of inertia of the moving system. An increase in the moment of inertia of a moving system leads to an increase in the natural period of its oscillations. A short-term current imparts a push to the moving system (impact - hence the name ballistic), which causes torsional vibrations of the system. In order for the oscillations to be of the nature of free oscillations, it is necessary that the time of action of the current on the coil is less than the natural period of oscillations. Let us show that under this conditionthe magnitude of the first deflection of the moving system is proportional to the amount of electricity passing through the coil.

During the time of current flow, which is very short, the counteracting moment of the twisted thread can be considered equal to zero, because With a large moment of inertia, the system does not have time to move. Consequently, we can assume that the moving system during this time will only be under the influence of the torque M, caused by the interaction of the current and the magnetic field of the permanent magnet. It is known that the impulse of the moment of force is equal to the change in the angular momentum, i.e.:

M 1 dt = Id  (1),

where M 1 instantaneous value of the torque acting on the moving system of the galvanometer; I moment of inertia of the movable galvanometer system relative to its axis of rotation; d - change in the angular velocity of the system over time dt.

A frame flowing around a current and placed in a magnetic field is acted upon by a pair of forces whose torque is M 1 determined by the formula:

M 1 = B n i sin  S (2),

where B is the magnetic field induction of a permanent magnet,

n number of frame turns,

S coil area,

 - the angle between the normal to the plane of the frame and the direction of the vector.

i instantaneous current.

Since the induction lines of the magnetic field in which the frame of the device of this system rotates make an angle with the normal to the plane of the frame = 90 o for all positions of the frame, then the torque M 1 will not depend on the position of the frame and will have the greatest value equal to:

M 1 = B n S i (2  ).

Let's substitute M 1 from (2  ) into (1), we get:

B n S i d t = I d  (3).

Integrating both sides of expression (3), we will have:

B n S (4) ,

Where t is the time during which the current flowed through the coil.

Considering that:

where q the amount of electricity flowing during time t, we will have:

B n S q = I  t .

From here we get:

where  t the angular velocity that the moving system acquires at the moment the current stops.

Denoted by K 1 (constant of this device), we get:

 t = k 1 q.

Kinetic energy received by the system as a result of the action of current, m O can be found using the formula:

(5).

Substituting into (5) the expression t = k 1 q, we get:

(5  a).

The rotation of the coil will continue until all the kinetic energy of the system is converted into potential energy of the twisted suspension thread. At this moment, the moving system will stop, turning at an anglemax.

Let's calculate the potential energy of the twisted suspension thread. Counteracting moment M 2 , created by a thread when twisted at an angle will be equal to:

M 2 = k 2 . (6),

where to 2 coefficient depending on the elastic properties of the suspension thread.

Elementary work spent on twisting the thread at an angle is equal to:

dA = M 2 d  .

Total work expended in twisting the thread at an angle max , taking into account

(6), is equal to:

(7).

Obviously, (7) is an expression of the potential energy of the twisted thread of the suspension of the moving system of the device.

Equating (5  ) and (7), we get:

Where do we get:

Having designated

(8),

we get:

q = K  max (9).

Thus, we have proven that the magnitude of the first angle of deflection of the moving system of the device is proportional to the amount of electricity passing through the galvanometer.

It is easy to show that the angular displacement of the device (for small angles),

(10),

where n is the number of divisions by which the light pointer “bunny” has deviated on the galvanometer scale, D the distance from the mirror to the scale.

Therefore, expression (9) can be rewritten:

(11).

The value is called the ballistic constant of the galvanometer, and is usually expressed in coulombs or microcoulombs per scale division (usually per mm). Taking into account K b expression (11) will take the form:

q = K b n max (12).

Thus, the magnitude of the greatest deviation of the light indicator on the scale (rejection) is proportional to the amount of electricity passing through the galvanometer.

Expression (12) is not entirely accurate, because when deducing it, it was not taken into account that the kinetic energy obtained from the current pulse is partially spent on overcoming air resistance. However, in practice this ratio gives good results.

To quickly calm the torsional vibrations of the moving system, a small resistance and a key are often introduced parallel to the coil winding. If the key is closed at the moment when the light pointer passes through the zero of the scale, the oscillations will stop. This happens because an induced emf occurs in a coil rotating in the magnetic field of a permanent magnet. When the key is closed, an induction current arises, which, according to Lenz's rule, will counteract the movement of the coil.

In many galvanometers, a resistance without a switch (shunt) is connected in parallel to the moving system. This resistance is designed to make the motion of the moving system aperiodic. This resistance is called critical, it is on the order of several thousand ohms; connecting a critical resistance reduces the sensitivity of the galvanometer.

MEASUREMENT TECHNIQUE

I . Determination of the ballistic constant of a galvanometer

From expression (12) we have:

K b = (13),

where K b the value of the ballistic constant,

q the amount of charge flowing through the galvanometer,

n max the greatest deviation of the light indicator on the scale.

1.To determine K b assemble the circuit according to Fig. 1,

Fig.1.

where Г ballistic galvanometer;

R w galvanometer shunt;

K 0 key that turns off the galvanometer;

K key, short-circuiting the galvanometer;

K 1 two-position key (switch);

V voltmeter;

C - capacitor (first with a known capacity, then with an unknown one);

IET regulated voltage source.

According to the instructions for using the galvanometer and the horizontal reading device, prepare the galvanometer for operation and set the light indicator to the scale zero. Key K open, key K 0 close.

By moving the illuminator lens, achieve clear outlines of the “bunny”.

2. Switch K 1 short to terminals 1 and 2, feed from the IET divider to capacitor C 0 known capacitance (1 µF) voltage (potential difference) U = 0.2 V 0.5 V.

3. Throw switch K 1 to terminals 5 and 6, discharge the capacitor through the galvanometer. Note the extreme value of the scale to which the light pointer reaches during the first oscillation (first drop). If this rejection is within the scale, then you can start measuring. If the bunny goes beyond the scale, reduce the voltage.

Counting n max (the value of the first rejection), to calm the galvanometer, close the key K, then the “bunny” returns to the zero division of the scale. When the “bunny” is set to scale zero, open key K.

4. Having calculated q = C 0 U and measuring the value of the first rejection n on a scale max, according to the formula (13  ) calculate the ballistic constant:

(13  ).

Definition of nmax perform at least five times, each time recording in the table the value of the largest rejection of the “bunny” and repeating operations according to points 1, 2. Make sure that the same voltage is supplied to the capacitor. The results of measurements and calculations are included in the table. I .Find the average value of n max and calculate from it Kb.

Errors  K b and determine using error formulas obtained from formula 13 .  n max define as the root mean square error of the arithmetic mean; U instrument error, determined based on the accuracy class of the instrument; C 0 error determined by the relative error indicated in the capacitor marking.

Derivation of error formulas and calculations should be presented in the report.

5. Compare the results of K measurements b . with the galvanometer datasheet, explain the comparison results.

Table I

	n max (deeds)	 nmax (del.)	(IN)	 U (IN)	( )	 C 0 ( )	K b (Cl/ del.)	 K b (Cl/ del.)
Wed

II .Measuring the capacitance of the capacitor and checking the formulas for
calculating the capacity of capacitor banks

1.Replace the capacitor of known capacitance with the first test capacitor of unknown capacitance C 1 . Set the voltage U at the IET output 1 = 1 V-2 V, key K 1 short to terminals 1 and 2. Then switch key K 1 to terminals 5 and 6, discharging the capacitor through the galvanometer. Record the amount of “bunny” rejection on the scale. By closing key K, when the “bunny” passes through the zero of the scale, calm the galvanometer coil. Then open key K.

2.Replace capacitor C 1 another test capacitor of unknown capacitance C 2 , repeat all the operations in step 1 with it, applying voltage to the capacitor U 2 = 2V-3V.

3. Experiments to determine n max perform for each capacitor at least 5 times, get the average value n max.

4. Since, a, then find the unknown capacity using the formula:

(14),

where C determined capacity, n max average value of the “bunny” rejection on the scale, U constant voltage for each capacitor.

Errors  C and determine using the error formulas obtained from formula (14). The results of measurements and calculations are included in the table. II and similar table. III.

Table II. (III)

	n max (del.)	 n max (del.)	(IN)	 U (IN)	(F)	 C (F)
Wed

5.Measure the capacity of batteries made up of capacitors C 1 and C 2 when connecting them in series and parallel, having completed all the operations contained in paragraphs 1, 2, 3, 4. Enter the results of measurements and calculations in the table. IV for serial connection, in table. V for parallel.

Table IV. (V).

	n max (del.)	 nmax (del.)	(IN)	 U (IN)	(F)	(F)		(F)
Wed

Compare the results of capacitance measurements for series and parallel connection of capacitors with the results of calculations of these capacitances using the formulas for series and parallel connection of capacitors.

After completing the work, key K 0 leave open

TEST QUESTIONS FOR I PARTS OF THE WORK.

1. Describe the method used in the work to determine the capacitance of the capacitor.

2. In what units is electrical capacity measured in SI and GHS? Give definitions of these units and derive the relationship between them.

3. On what values ​​does the capacitance of a flat, spherical, cylindrical capacitor depend? Know the formulas for the capacitance of these capacitors.

4.What is meant by the capacitance of a conductor or capacitor?

5.Explain the design and operating principle of a ballistic galvanometer.

6.What is the physical meaning of the ballistic constant?

Part II

MAGNETIC INDUCTION FLUX MEASUREMENT

BY BALLISTIC METHOD

PURPOSE OF THE WORK:

1) Master the technique of measuring the magnitude of magnetic induction flux and induction using the ballistic method.

1. Determine the galvanometer constant from the magnetic flux.

Determine the magnetic field induction in the measuring coil when a strip magnet is introduced into it.

DEVICES:

1. galvanometer M 17/11,

2.throttle coil,

3.magazine R 33,

4.strip magnet,

5.keys

THEORY

One of the main methods for determining the magnetic characteristics of ferromagnetic materials in constant magnetic fields is ballistic. It was first used by A.G. Stoletov to measure the magnetization of iron. The ballistic method is based on measuring the amount of electricity that occurs in a measuring coil surrounding a magnetic sample as a result of a rapid change in the magnetic flux through that coil. The same amount of electricity passes through the galvanometer frame.

In the first part of the work, the ballistic constant of the galvanometer K was determined b . We will use its value to determine the amount of electricity passing in the galvanometer circuit when the magnetic flux changes through the measuring coil. We will change the magnetic flux by introducing (or removing) a strip magnet into the measuring coil.

When the magnetic flux changes through the measuring coil, an electromotive force of induction appears in it

(1),

where N is the number of turns of the measuring coil.

Current will flow in the galvanometer circuit

(2),

where R is the total resistance of the coil and galvanometer circuit.

If the flow changes by the amount , through the galvanometer frame about th det amount of electricity

(3).

This amount of electricity can be measured by the deviation n of the gal indicator b van o meter on a scale

q = К b  n (4).

Then we determine the magnetic induction flux using formula (5)

(5).

Knowing the size of the area covered by the turns of the measuring coil, we will find the value of the magnetic induction vector

(6),

where B n =B cos  ,  - the angle between the normal to the plane of the coil and the direction of the magnetic induction vector.

MEASUREMENT TECHNIQUE

1.Assemble the circuit according to the diagram shown in Fig. 2,

Fig.2

where Г galvanometer, the frame resistance of which is R 0g =300 Ohm (passport data);

R w a shunt, the resistance of which in parts I and II of the work is the same, equal to 650 Ohms; (measured with an M 371 ohmmeter);

R cr critical resistance for a given galvanometer and a given circuit, equal to 400 Ohms (assembled on a resistance magazine R-33);

L measuring coil, the number of turns of which is N=15, ohmic resistance R L =3.2 Ohm (determined by ohmmeter M-371), coil area S=100 cm 2 ;

Purpose of keys K 0, K, K 1 indicated in Part I of the work.

1. Close key K 0 . Insert a strip magnet vertically inside the choke coil. Close key K 1 to terminals 1 - 2. Mark the starting position of the indicator light n 1 .

Quickly remove the magnet from the coil. Register new pointer position n 2 , find n=n 2 -n 1 . Take measurements 5 times, find n Wed . Error in determining n Wed find as standard deviation.

Using formula (5), find the change in the magnetic flux passing through the measuring coil when a strip magnet is introduced (or removed). It should be borne in mind that R in formula (5) is the total resistance of the circuit consisting of a measuring coil, a galvanometer frame, a shunt and a critical resistance. Using formula (6) find the magnitude of the magnetic induction vector.

The error in determining the magnetic flux can be found using the error formulas obtained from formulas (5) and (6).

1. Determine the galvanometer constant from the magnetic flux K f. As can be seen from (5),

(6).

The error in determining the galvanometer constant from the magnetic flux is determined using the error formula obtained from formula (6).

1. The results of measurements and calculations are included in the table. 6.

Compare K measurement results F. with the galvanometer datasheet, explain the comparison results.

CHECK QUESTIONS FOR PART II OF THE WORK.

1. Describe the method used in the work to determine the magnetic flux.
2. Does changing the position of the magnet in the coil (north pole down or up) affect the readings of the device?
3. Does the speed of movement of the magnet relative to the coil affect the readings of the device? Why?
4. The data sheet for the galvanometer M 17/11 indicates the values ​​of the device constants (K b, Kf etc.) for a distance between the illuminator and the mirror of the device equal to 1 m.

What is this distance in our setup? How does the magnitude of this distance affect I influence on the values ​​of the device constants?

Table 6

№ p/p

 n

 R

K b

 K b

 F

K f

 K f

 S

In n

 Bn

mm

mm

Ohm

Ohm

Kl/mm

Kl/mm

Wb

Wb

Wb/mm

Wb/mm

m 2

m 2

Tl

Tl

Wed

Application

The device of a galvanometer of a magnetoelectric system

Galvanometers - devices used to measure weak electric currents, are divided according to their design into two main groups: 1) with a moving coil, flowing around current and rotating in the field of a stationary magnet or electromagnet; 2) with a moving magnet and a fixed coil.

To measure the current strength, both in those and in other devices, the rotation of a moving system is used, deviating from a certain equilibrium position under the influence of the interaction of the current and the magnet. For precise measurements, only galvanometers of the first type are used.

The moving system of such a galvanometer is, in most cases, a quadrangular frame made up of rectangular turns of insulated thin wire with a cross-section of a few hundredths of a millimeter tightly laid and glued with insulating varnish. The effective cross-section of such a coil, penetrated by the magnetic field force lines, is nS, where n is the number of turns of the frame, and S is the cross-sectional area of ​​an individual rectangular turn of wire. The number of turns in such a coil ranges from several tens to hundreds. Thread E with a light mirror M attached to it (Fig. 3) serves as a suspension for frame C. The frame can rotate freely in the gap formed by two poles of a permanent magnet and a cylinder J made of soft iron, mounted on a plate P made of non-magnetic material. In this case, as shown by the dotted line at the bottom of the figure, the magnetic field in the air gap is almost radial (in the upper part of the figure, one of the magnet poles is partially removed).

The suspension thread is a thin metal (platinum) wire or a bronze ribbon with a cross-section of several microns or a thin quartz thread, sometimes platinized on the surface. The second current supply to the coil is usually a metallic silver or gold ribbon several tenths of a micron thick. In galvanometers with a quartz suspension, usually both current supplies to the frame are made in the form of such ribbons connected to the winding of the galvanometer frame (coil) in its lower part. Current supplies to the movable system of the galvanometer should not provide elastic resistance to the rotation of the movable system. Thus, the moment of elastic forces acting on the frame is only the torque of the suspension thread.

Fig.3.

Before starting work, the galvanometer must be correctly installed, which is achieved by rotating the three set screws on which the device body rests. This means that the movable system of the galvanometer, held in a fixed position before starting work by a special device (lock), must, after releasing the lock, move freely between the poles of the magnet, without touching them during rotation. The narrowness of the gap between the poles of the magnet and the central cylinder requires very precise installation of the device.

To ensure proper installation, some galvanometer systems are equipped with a level to help guide the instrument into the correct position. In other galvanometer systems, a special glued mirror is installed in the device body, which makes it easier to observe the position of the frame relative to the poles of the magnet.

Devices of the first type are installed level with a locked moving system. Devices of the second type are installed with the mobile system free. The arrester is driven by a special lever or a screw head, removed somewhere from the galvanometer and equipped with an inscription.

The release and fastening of the movable galvanometer system before operation of the device (or after its completion) should be done with great care, since the shocks of the movable galvanometer system, picked up by the arrester fork, are transmitted directly to the thin suspension thread. It is not recommended for students to perform this operation on their own in the workshop; they should seek help from the workshop laboratory assistants and take the opportunity to monitor the performance of these operations by experienced persons.

The upper end of the suspension thread is fixed in a rotating head (marked on the device body with the inscription “zero corrector”), located on the upper part of the galvanometer body. By rotating this head, you can rotate the movable galvanometer system to set it to the zero position between the poles of the magnet. In the zero position, the plane of the turns of the movable suspension system is installed approximately parallel to line ab (Fig. 3). The operation of turning the galvanometer frame (coil) requires the same precautions as releasing the device's lock. It is necessary to keep in mind that when the zero corrector head rotates, the frame follows the rotation of the head with a delay, since the transmission of torque to the frame is carried out through the suspension thread. Therefore, after turning the zero corrector by a small angle, you should wait each time until the moving system of the device is installed in a new position. Only by such intermittent rotation of the zero corrector can the moving system be brought to the desired position between the poles of the magnet. In the workshop, these operations are also performed not by students, but by laboratory assistants.

The measurement of current strength is based on observing the angles of rotation of the frame C. When current flows through the winding of the frame, the latter experiences a torque of forces acting on the current in a magnetic field. In this case, the frame tends to be positioned so that the magnetic moment of the current flowing through it is directed along the external magnetic field. As a result, the frame rotates at a certain angle . The modes of movement of the galvanometer frame are as follows:

1. Aperiodic mode.This is a mode in which the galvanometer frame, under the influence of current, smoothly approaches the equilibrium position without passing through it.
2. Periodic mode. The movement of the frame in this case occurs in such a way that, moving towards the equilibrium position, it passes through it and occupies it after several oscillations.
3. Critical mode. This is a mode in which the galvanometer frame, under the influence of current, approaches the equilibrium position in the shortest possible time. This mode is most beneficial for work.The parameters of the circuit elements necessary to implement the critical mode are given in the galvanometer data sheet.

1 The device of the galvanometer is described in the “Appendix” to laboratory work. The parameters of M 17/11 are indicated in the instructions for the device, which the student must read.

There are various methods capacitance measurements: ammeter-voltmeter method, bridge method, ballistic galvanometer method, by the time of discharge of a capacitor through a resistor of known resistance, resonant method, etc. Let's consider them in more detail.

One of the simplest is the ammeter-voltmeter method. It is based on measuring the capacitance of a capacitor, which is inversely proportional to capacitance and frequency electric current: ,

Therefore, to measure capacitance using this method, it is necessary to know the frequency of the voltage supplied from the power source.

Ballistic are called sensitive galvanometers, in which the period of natural oscillations of the frame is very long. Any device of a magnetoelectric system can operate in the ballistic mode if the current in the device circuit flows for a time that is many times shorter than the period of natural oscillations of its moving frame. When a capacitor is discharged through a ballistic galvanometer, the deflection of the galvanometer needle is proportional to the charge flowing through it. Let's conduct the following experiment. Let's charge the capacitor to voltage U and, having discharged it through the galvanometer, notice the amount of pointer deflection. Let's repeat the experiment, increasing the voltage by 2, 3, etc. once. Each time the ratio of the voltage to the number of divisions by which the arrow deviated will be a constant value. Then, without changing the voltage, we will conduct an experiment with capacitors of capacity C, 2C, 3C, etc. We find that the ratio of the capacitance of the capacitor to the number of divisions by which the needle has deviated is also a constant value.

The ballistic constant of a galvanometer is the ratio of the charge q flowing through the galvanometer frame to the number of divisions n by which the needle deviated: k = q/n. To determine the ballistic constant, an experiment is carried out several times with capacitors of known capacity. The charge on a capacitor is calculated by the formula q = CU, where q is the charge on one of the capacitor plates, C is the capacitance of the capacitor, and U is the voltage between the capacitor plates. Then k = CU/n. From several experiments at different voltages between the capacitor plates and different capacitance values, the average value of the ballistic constant of the galvanometer is determined.

Then a capacitor of unknown capacity is connected to the circuit and the experiment is repeated. Knowing the ballistic constant and the number of divisions by which the galvanometer needle has deflected, the capacitance is determined: Cx = kn/U.

To measure capacitance, you can use any device of the magnetoelectric system, provided that the product of the capacitance of the capacitor and the internal resistance of the device will be significantly less than the period of natural oscillations of the device's needle. In this case, the capacitor is completely discharged in a time much less than the period of its own oscillations, and a change in the resistance of the resistor connected in series with the galvanometer does not in any way affect the deflection of the galvanometer needle.

Exercise 3

Determination of the period and logarithmic decrement of the frame oscillation damping

Measurements. 1. Set the initial resistance values ​​according to the recommendations for exercise 3.

2.Using potentiometer R get a “bunny” deviation of 80-100 mm.

3.Open the switch B2(the resistance in the galvanometer circuit becomes infinitely large), the “bunny” will return to scale zero and at the same time make several damped oscillations. Use a stopwatch to determine the duration of 2-3 complete oscillations in order to determine their “period”. Repeat this procedure at least three times to be able to find the average value of the free oscillation period T 0 and their cyclic frequency  0  T 0 .

4.Measure largest deviations of two consecutive “bunny” oscillations A To And A k+1 on one side of zero (preferably on the right). Based on the measured results, determine the logarithmic decrement of oscillation damping d  frames of a galvanometer with infinite resistance.

5.Lock B2, now the galvanometer circuit contains the initially set resistance R 1 , and also R 2 And r other. Turning the current in the galvanometer on and off with a switch P, remove the dependence of the logarithmic attenuation decrement as it decreases R 1 as long as the “bunny” oscillations take place. Record the results in Table 2.

Table 2

R 1	A k	A k+1

6.Plot the dependence graph 1/ d= f(R 1 ) . One should expect a linear form of this dependence. If we extrapolate the graph 1/ d  0 , then it crosses the x-axis at R 1  R 1k, which makes it possible to determine the critical resistance (9) in another way. Indeed, at critical resistance in the galvanometer circuit, the movement of the frame to the equilibrium position occurs without oscillations, aperiodicly, which can be interpreted as “oscillations” with a very large damping decrement.

R cr = R 1k + R 2 + r.

Compare the critical resistance determined by this method and the one used in Exercise 2.

Exercise 4

Determination of the ballistic constant of the galvanometer and the electrical capacity of the capacitor

Ballistic mode of galvanometer operation (in physical jargon - ballistic galvanometer, an analogy with a ballistic pendulum is appropriate here) is used to measure the magnitude of the electric charge q, passed through the circuit during a short-term current pulse, for example, during the discharge of a capacitor. It is assumed that the pulse duration is much less than the period of free oscillations of the galvanometer frame. With this assumption, it is obvious that the entire charge will pass through the frame in such a short time that it will not have time to deflect. The frame, however, receives a push, the magnitude of which determines the angle through which it turns, which means the angle  proportional to charge q.

where is the ballistic constant at infinite resistance in the galvanometer frame circuit. Under this condition, frame braking is minimal (see exercise 3).

From formula (13) follows the definition of the ballistic constant

, (14)

G

de n– the maximum number of scale divisions by which the “bunny” deviates when “slipping” through the charge frame q (first ballistic rejection).

The ballistic constant can be determined experimentally using a capacitor with a known capacitance WITH 0 (reference) by connecting it to an electrical circuit, the diagram of which is shown in Fig. 2.

The reference capacitor is charged to the potential difference U 0 from a current source (switch P in position 1 ), then discharged through a galvanometer G(switch P in position 2 ). Electric charge

q= C 0 U 0 (15)

flows through the galvanometer frame. Substituting charge (15) into formula (14), we obtain an expression for determining the ballistic constant:

. (16)

If instead of capacitor WITH 0 turn on another capacitor with unknown capacity WITH 1 and charge it to the potential difference U 1 , then knowledge of the ballistic constant makes it possible to determine the capacity WITH 1 according to the formula

. (17)

Measurements. 1.Lock the damper IN d in order to protect the galvanometer.

2.Assemble the electrical circuit according to the diagram (Fig. 2) and invite the teacher or laboratory assistant to check it.

3.Close the switch B1 and set the voltage U 0 =0.50 V.

4.Switch P connect the capacitor to the power source (switch in position 1 ), causing it to charge to 0.50 V.

5.Open the damper IN d and check whether the light indicator is at the zero mark of the scale. If not, then achieve it. How can this be done?

6.Move the switch to position 2 and mark the greatest deviation of the “bunny” on the scale - n 0 .

7.Measurement results n 0 at three different voltages U 0 enter in table 3.

Table 3

U 0	n 0		U 1	n 1	C 1

8.Turn on instead WITH 0 capacitor of unknown capacity WITH 1 and carry out similar measurements of ballistic waste with it n 1 (item 3-6).

9.Processing the results comes down to calculating the ballistic constant using formula (16) and determining the capacity WITH 1 according to formula (17), as well as determining the width of the confidence interval according to Student.

10.Check if the following equality holds:

.

Its existence is justified in the manual, there it is formula (66). We also remind you that WITH I – current sensitivity , T 0 – period of free oscillations of the frame (see exercises 1 and 3). This check is one of the elements of monitoring the correctness of measurements and calculations of galvanometer parameters.

Exercise 5

Determination of ballistic constant

When a capacitor is connected to a galvanometer, the resistance of this circuit is indeed very high. But another situation is also possible.

P
A coil is connected to the galvanometer, in which a short pulse is excited. In this case, the pulse passes through the circuit, including through the galvanometer, but its resistance is not as high as with a capacitor, rather even small. Let's consider the circuit, the diagram of which is shown in Fig. 3. The galvanometer circuit includes a coil with inductance L 1 and active resistance r 1 , as well as resistance store R 1 . The above diagram differs from the one discussed above (Ex. 4) in that here the resistance in the galvanometer circuit, firstly, is not infinite and is so it can't be, secondly, it can be changed due to R 1 . This means that, depending on the magnitude of the resistance, the nature of the movement of the frame towards and around the equilibrium position becomes different, and this choice is in the hands of the experimenter. Under these conditions, the most favorable is a relaxation movement of a critical nature. For this, the resistance of the galvanometer circuit must be critical R cr, the value of which is determined in ex. 2 and 3. Therefore, on the store R 1 need to install

R 1 =R cr – (r+r 1 ) .

Let us consider the response of a galvanometer to a current pulse in a circuit with critical resistance. If in the reel L 1 with the number of turns w 1 for dt seconds change the magnetic flux to d , then an induced emf will be induced in the coil.

.

The induction current arising under its influence i will create in the coil L 1 Self-induced emf

.

According to Kirchhoff's second rule, the algebraic sum of the voltage drops in a closed circuit is equal to the algebraic sum of the emf.

Having separated the variables and integrated the resulting equation, we will have the following solution:

,

Where q= i – the total electric charge passed through the circuit (including through the galvanometer) during the action of a current pulse of duration  ,

 2  1 – change in magnetic flux over time  .

From here you can find out the amount of charge,

. (19)

Passage of charge q through the galvanometer causes the frame to rotate at an angle  , proportional to the charge,

Equating expressions (19) and (20), we obtain the following formula for the ballistic constant of a galvanometer in a circuit having a critical resistance:

. (21)

The ballistic constants of a galvanometer differ from each other, since each of them is inherent in certain and incompatible operating conditions of the galvanometer, at the same time they are interconnected, since these are characteristics one device. It is proven in formula (70) that

How to find it practically? To do this, a circuit is assembled containing a galvanometer and two inductively coupled coils: one is a long single-layer solenoid L 0 , the second is a short four-section coil L 1 , placed over the solenoid.

When current passes I a magnetic field is created along the solenoid, the intensity of which on the axis of the solenoid is equal to N, induction IN and magnetic flux 

,

Where l 0 , S 0 – length and cross-sectional area of ​​the solenoid.

The same magnetic flux penetrates the second coil L 1 , let's denote it  1 . If the direction of the current in the solenoid is reversed, then the magnetic flux will change sign  2 = – B.S. 0 .

Thus, the change in magnetic flux through the second coil is

, (23)

and after substitution

. (24)

The expression for the ballistic constant (21) can be written as:

[C/(mm/m)]. (25)

The minus sign is omitted, since it determines in which direction the galvanometer frame will turn, but does not affect the magnitude of the rotation angle.

Magnitude

[Wb/(mm/m)] (26)

called ballistic constant for magnetic flux.

Measurements. 1.Assemble an electrical circuit according to the diagram in Fig. 3, including it as a coil L 1 one of four sections containing w 1 turns. Damper IN d As always, it must be closed during assembly.

2. Suggest that the teacher or laboratory assistant check the assembled circuit.

3.Install on the store R 1 critical resistance.

4. Set the solenoid circuit to a small current I, then it may have to be changed.

5.Turning the switch P from one position to another, measure the maximum ballistic throw of the “bunny” n. This must be done at three different currents I. Enter the results in Table 4.

Table 4

6.Calculate and using formulas (25), (26), find the average values ​​of each of them and the width of the Student confidence intervals as for direct measurements. Check the fulfillment of condition (22)

7.Based on the results obtained in Ex. 1...5, make a summary table of the metrological parameters of the studied galvanometer.

Summary of metrological parameters of galvanometer M17, no.………… .

Current constant	c I
Voltage constant	c U
Internal resistance
Critical Resistance	R kp
Oscillation period	T 0
Free vibration frequency
Ballistic constant
Ballistic constant
Ballist.constant. by magnetic flow

Exercise 6

Determination of the horizontal and vertical components of the Earth's magnetic field strength

In the exercise below, you can use a thoroughly researched galvanometer to solve a practical problem - determining the strength of the Earth's magnetic field using a highly sensitive galvanometer in ballistic mode. The idea behind the experience is simple. Let there be a closed circuit in the Earth’s magnetic field, which includes a galvanometer. If you change the orientation of the circuit in space so that the magnetic flux through it also changes, then an induced emf will arise in the circuit and the induced current pulse will lead to a deflection of the galvanometer pointer.

D
To carry out such an experiment, a coil is taken L 2 on a ring frame, located on a rotating stand. The Earth's magnetic field strength vector is located in the plane of the magnetic meridian at an angle  to the horizon (Fig. 4), where  – magnetic inclination (in our area can be taken approximately equal to geographic latitude).

If the coil is rotated, for example, around the axis z, then the vector flow N G through the area covered by the circuit will change, which will lead to the appearance of an induced emf equal, in accordance with Faraday’s law, E= d / dt.

2
.Install on the store R 1 resistance

.

3. Determine the plane of the magnetic meridian S–N using a compass and place the plane of the ring coil perpendicular to this direction.

4.Open the damper. Rotate the coil around the vertical axis by 180, observe the deflection of the “bunny” on the scale. This experiment must be done at least five times, noticing each time the maximum ballistic throw. Try to turn the coil so quickly that the duration of rotation is less than the period of free oscillations of the galvanometer frame, which is associated with the necessary condition for the short duration of the current pulse in the circuit. Enter the measurement results in Table 5.

5. Carry out similar measurements when rotating the coil around a horizontal axis, having first installed it horizontally.

6.Measure the diameter of the coil, this will be needed to calculate its area S 2 , and write down the number of turns w 2 the section that was included in the circuit.

Processing the results consists of calculating the horizontal and vertical components of the Earth's field strength using the formula

. (27)

Table 5

Spinning around vertical axes				Spinning around horizontal axes
n 1	N G			n 2	N V

Based on averages N G And N V Calculate the total strength of the Earth's magnetic field and compare it with the value found in the literature.

1.Course of electrical measurements. /Ed. V.G. Prytkov, A.V. Talitsky. M.-L.: State. energetic ed., 1960. Part 1, ch. 5.

2. Electrical laboratory equipment. Ed. Perm. Univ., 1976. §15-16.

3. Guide to laboratory classes in physics./Ed. L.L. Goldina. M.: Nauka, 1973. P.274.

4. Sivukhin D.V. General physics course. M.: Nauka, 1977. T.3, p.556.

5. Kortnev A.V., Rublev Yu.V., Kutsenko A.N. Physics workshop. M.: Higher School, 1963. P.232.

Research Coursework >> Chemistry

Replace with another. Main areas applications chromium – decorative protection, ... electrodes; beam of rays reflected mirrored galvanometer, installed near the left edge... components of the chrome plating process Object research: solid waste from galvanic...

1.4. We quickly switch to K 1 and count the first maximum deviation of the light spot b on the scale. (To quiet the ballistic galvanometer frame, you must turn on the K key).

1.5. Then repeat the same experiment for two other currents I 2 = 0.2A and

1.6. Using formula (8), we determine C, and then its average value:

Table 1 - Determination of the ballistic constant setting

			C c r, Wb/m

2. Demagnetization of a torus.

2.1. Open the measuring circuit with key K so as not to burn the galvanometer during demagnetization.

2.2. Connect the output ends of the LATR (“Load”) to the “Demagnetization” terminals located on the panel.

2.3. Set the LATR voltage regulator to the zero position.

2.4. Connect the LATR to a 220 V alternating voltage network.

2.5. Smoothly change the output voltage of the LATR from 0 to 100 V, and then from 100 to 0. Repeat this 5 times.

2.6. Disable LATR.

3. Study of the dependence of B on H.

3.1. Using switch K 2, close the circuit to the torus.

3.2. Using rheostats R 1 and R 2, set the current to 0.1A.

3.3. Quickly change the direction of the current in the torus by switching key K 1 in the opposite direction and record the deviation of the light spot of the ballistic galvanometer a.

3.4. At given value current, repeat the experiment at least 3 times and determine the average value a avg.

3.5. Consistently, each time increasing the current in the torus by DI = 0.1A, carry out experiments in paragraphs 3.1-3.4 until the maximum current value that can be obtained in the installation is reached.

3.6. For each current value in the torus winding, calculate the magnetic field strength H using formula (6), determining

3.7. For each current value, determine B using formula (5).

3.8. Plot a graph of B = f(H).

3.9. Using formula (7), calculate m and plot the dependence m=f(H).

3.11. Draw a conclusion about the nature of the dependencies B = f(H) and m=f(H).

Table 2 – Results of studying the magnetic field of the torus core

			V,T

SAFETY RULES

1. Connect the stand to a 220 V alternating voltage network only with the permission of the teacher.

2. Carefully demagnetize the torus. When demagnetizing, be sure to open the ballistic galvanometer circuit with key K (to the “Off” position).

CHECK QUESTIONS FOR PERMISSION TO WORK

1. What is the purpose of the work?

2. What is the order of the work?

3. How is the installation’s ballistic constant determined?

4. How is B determined?

5. How is H determined?

6. How is m determined?

7. What is the installation diagram? Tell us about her.

TEST QUESTIONS TO PROTECT YOUR WORK

1. What phenomenon underlies the performance of work?

2. What is characteristic of the class of substances - ferromagnets?

3. What are diamagnetic and paramagnetic materials?

4. What is the physical meaning of the ballistic constant installation?

5. What is the amount of charge flowing through a ballistic galvanometer when the magnetic flux changes?

6. Explain the dependence B = f(H) for a ferromagnet.

7. Why was the torus demagnetized?

8. Explain the dependence m=f(H).

1. Trofimova T.I. Physics course. - M.: Higher School, 1999. - 542 p.

2. Zisman G.A., Todes O.D. General physics course. T.2.-M.: Science, 1969.-

3. Doroshenko N.K., Voronov I.N. Magnetic properties of matter. - SibGGMA: Novokuznetsk, 1997. - 27 p.

Plan 2002

Compiled by:

Doroshenko Nadezhda Kuzminichna

Voronov Ivan Nikolaevich

Konovalov Sergey Valerievich

Bokova Tatyana Grigorievna

Martusevich Elena Vladimirovna

STUDY OF MAGNETIC INDUCTION IN IRON

BY BALLISTIC METHOD

Guidelines for performing laboratory work on the course

“General Physics”

Editor N.P. Lavrenyuk

Publisher No. 01439 dated 04/05/2000 Signed for seal

Paper format 60x84 1/16 Writing paper Offset printing

Cond.bake.l. 0.58 Academic-ed.l. 0.65 Circulation 100 copies. Order

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