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One of the properties characteristic of every material is its density. We observe that a small piece of one material may be heavier than a much large piece of another material. The mass per unit volume of a substance is called its density
p = m/V
Units of density are determined by dividing the chosen unit of mass by the unit of volume, as kilogram per cubic meter, gram per cubic centimeter, or slug per cubic foot.
It is sometimes helpful to use another quantity called weight-density, or weight per unit volume:
D = W/V
Since W = mg, we have a simple relation between density and weight-density:
D = ?g
Weight-density is commonly used when we are concerned with effects depending upon force, while density is used when mass is to be considered.
Solids and liquids are only slightly compresses by even large stresses; hence their densities are almost constant under usual conditions. Gases are readily compressed; hence it is necessary to states the conditions under which the densities are measured.
In order to maintain an electric current, some agency is required to expend energy in moving the charge around a circuit. With the exception of a few metals near absolute zero, the superconductors, all conductors present some opposition to the flow of charge so that work must be done to maintain a current. An agency capable of causing such a flow by converting other forms of energy to electrical work is called a seat of electromotive force or a source of current.
It should be clearly understood that a source of current does not manufacture charge but merely moves the charge through a circuit. In most circuits this agency is concentrated in one or a few parts of this agency is concentrated in one or a few pats of the circuit. The source must create an electric field in all parts of the circuit to cause the charges to move against the various opposing effects they may encounter.
The electromotive force, or emf, of a source is the energy per unit charge transformed in a reversible process. (The term “electromotive force” is an old term now rooted in the language of physics; its choice was unfortunate, as this quaintly is not a force. Hence its abbreviation emf will be used hereafter.) In the mks system, emf will be used hereafter).
An emf causes difference of potential to exist between points in the circuit. Thus there is an intimate relation between emf and potential difference. An emf associated only with reversible conversions of energy, whereas potential difference exists not only in source of emf but also in resistors, which convert energy to heat irreversibly. The distinction is sometimes useful and will becomes clearer as we proceed.
In the simple circuit charge flow through the circuit, the cell converts chemical energy to electrical energy, giving rise to an emf. The lamp is a resistive conductor called a resistor; it converts electric energy to heat, and work done on the charge by the electric field, as the charge moves through the resistor, is evidenced by the presence of a potential difference between the ends of the resistor. A small amount of the total electric energy converted from chemical energy in the cell also produces heat inside the cell.
Electric circuits are conventionally reprinted by circuit diagrams employing standard symbols.
Man has always been curious about and often awed by the power of lightning> Benjamin Franklin’s experiment approximately 200 years ago with a kite in which showed that lightning consisted of the same type of electricity that could be produced on earth by electrostatic means is possibly the most famous study made of lightning . Although this phenomenon has been the topic of considerable research, scientists have failed to agree upon the cause and the nature of lightning.
We know that lightning is a violent example of the tremendous electrostatic charges that can occur in nature, but there are several different explanations given about the manner in which the charges that cause lightning are produced in a cold. Most of these theories are built upon the premise that because of violent air currents in cloud, and the interaction of ions and water droplets and ice [articles, positive negative charges are produced in a cloud and are then separated with the positive charges moving upward and the negative charges moving downward.
To understand this generalization, let us first look at the makeup of a thunderhead clod. In the “mature” stage the cloud top will reach up to 10,000 to 15,000 m (40,000ft) where the temperature is about -50°C. within this cloud, which may have its lower layer at a height of 5,000 ft and a temperature of around +20°C, there are strong updrafts reaching a speed of 60 mi/h. the water vapor in the cooled below its freezing immediately until it has a “seed,” or nucleus, to form upon, and as a result it becomes super cooled.
However, once ice starts to form, with crystals grow rapidly and fall through the rising air causing a down draft of cold air. When this cold air reaches the bottom of cold air. Reaches to the ground just ahead of the rain, causing the sometimes noticed chill that rain, causing the sometimes noticed chill that precedes a rainstorm.
Let us consider the most popular theory that the lighter “spray like” parts of the torn off darning falling becomes positively charged and are then carried upward into the cold upper layer of the cloud. The heavier particles become negatively charged and continue to move downward and in so doing acquire more negativity as they grow in size.
Whenever a change q moves in a magnetic field, the charge experiences a force F the magnitude of which given by
F = quB sin? = q/t lB sin?
In vector form the force is given by
F = qv × B = q/t l × B
The force on the charge +q is at right angles to v and B. in the example illustrated in the force on a positive charge would be upward. A moving charge constitutes a current. The force on a charge in motion is that on the equivalent conventional current. The vectors representingv, B and F are mutually perpendicular. If the charge is free to respond to this force, it will move in the direction of F.
An electric conductor, such as a copper wire, has free electrons in it. Consider a wire moving across a magnetic field. The component B sin ? perpendicular to the velocity will exert a force on charge in the wire along the direction of the wire. Positive charges in the wire would experience a force directed toward b; electrons experience a force in the opposite direction, and the free electrons accumulate at a leaving a deficiency of electrons at b.
Equation gives F/q = vB sin ?. Thus an electric field is set up in the conductor directed from a towards b, with a magnitude E = F/q = vB sin?. The emf e induced in the wire of length l is
e = W/q = Fl/q = Eql/q = lvB sin ?
When B is expressed in webers per square meter, l in meters, and v in meters per second, the emf is in joules per coulomb, or volts.
The emf exists whether or not there is a complete circuit for current. If the moving conductor slides along stationary conducting rails a current will be establishes in the sense shown.
Quantitative measurements made by Faraday (1833) contributed to the understanding of the process occurring in electrolytic cells and showed a stinking relation between the electrolytic behavior and the chemical properties of various substance. Faraday established by experiment the following two laws of electrolysis:
First law: The mass of substance separated in electrolysis is proportional to the quantity of in electrolysis is proportional to the quantity of electricity that passes.
Second law: The mass of substance deposited is electrolysis is proportional to the quantity of electricity that passes.
Faraday’s law may be expressed by the following symbolic statements:
m ? Q (Q = It)
m ? c (c = (atomic mass)/(valence ))
m = kcQ = zQ = zIt (z = kc)
Where k is a proportionality constant, whose value depends only upon the units involved, mis the mass deposited, and z is a constant for a given substance (but different for different substance), which is known as the electrochemical equivalent of the substance under consideration. The electrochemical equivalent of a substance is the mass deposited per unit charge. In the mks system it numerically the number of kilograms deposited in one second by an unvarying current of one ampere.
Wherever a vibrating body is coupled to a second body in such a manner that energy can be transferred, the second body is made to vibrate with a frequency equal to that of the original vibrator. Such a vibration is called a forced vibration. If the base of vibrating turning fork is set against a tabletop, the tabletop is forced to vibrate. This combination radiates energy faster than the fork could alone. Similarly, a vibrating string is inefficient in transferring energy to surrounding air unless it is coupled to some sounding board.
Whenever the coupled body has a natural frequency of vibration equal to that of the sources, there is a condition of resonance. Under this condition the vibrator releases more energy per unit time, and the sound is greatly reinforced. Hence the external power supplied to a resounding system must be increased; otherwise its vibrations will be quickly damped.
The reinforcement of sound by resonance with its accompanying release of large amounts of energy has many useful and many obnoxious consequences. The resonance of the many obnoxious consequences. The resonance of the air column in an organ pipe amplifies the otherwise almost inaudible sound of the vibrating airjet. Resonance would produce objectionable distortions of speech or music.
An advantage of this law is the fact that the net number of lines of force through a surface can be expressed in terms of the electric field intensity at that surface. An alternative use of this law is the computation of the electric field intensity produced by symmetrical charge distribution in terms of the electric flux produced by these charges.
A signification relation between the net numbers of lines of force passing through any closed surface in the outward direction and the net positive charge enclosed within that surface was discord charged enclosed within that surface was discovered by Karl Friedrich Gauss (1777-1855). In the preceding sections it was shown (for the case of an isolated point charge) that the total number of lines of electric flux emerging from a charge is exactly equal to that charge (in the mks system of units). It is evident that the same net number of lines of force will pass out of any closed surface of any shape if the surface completely encloses the charge the generalization of this conclusion is known as Gauss’ law.
The net number of lines of force in an electric field that cross any closed surface in an outward direction is equal (in the msk system) to the net positive charge enclosed within that surface.
In symbols Gauss’ law may be stated by the equation previously given as ? = ?Q.
Consider coil of wire connected to a sensitive galvanometer G. if the N pole of a bar magnet is thrust into the coil, the galvanometer will deflect, indicating a momentary current in the coil in the direction specified by the arrows. This current in called an induced current and the process of generating the emf is known as electromagnetic induction. As long as the bar magnet remains at rest within the coil, no current in induced. If, however, the magnet is quickly removed from the coil, the galvanometer will indicated a current in the direction. Opposite that at emf is induced when there is any change of magnetic flux linked by the conductor.
An emf may also be induced in a coil by the change in the magnetic field associated with a change in current in a nearby circuit. For example, a coil M connected to a battery through switch S. A second coil N connected to a galvanometer is nearby. When the switch S is closed, producing a current in the coil M in the direction shown, a momentary current is induced in coil N in a direction (arrow a) opposite to that in M. if S is now opened, a momentary current will appear in N, having the direction of arrow b. in each case there is a current in N only while the current is M is changing. A steady currents in M accompanied by a motion of M relative to N is also found to induce a current in N. we observed that, in all cases in which a currents is induced in N, the magnetic flux through N is also changing.
Lenz’s law states that, whenever an emf is induced, the induced current is in such a direction as to oppose (by its magnetic action) the change inducing the current.
Lenz’s law is a particular example of the principle of conservation of energy. An induced current can be produced heat to do chemical or mechanical work. The work energy must come from the work done to the motion of a magnet or a coil, work is done; therefore the motion must be resisted by a force. This opposing force comes from the action of the magnetic field of the induced current. When a change in current in a primary coil induces an emf in a neighboring secondary coil, the current in the secondary will be in such a direction as to require the expenditure of additional energy in the primary to maintain the current.
Two families of units are useful in the areas of electrostatics: the mks system and the system of cgs electrostatic units (esu). The electrostatic units will first be considered because of their historical significance and their simplicity.
If can be seen that there are two new concepts to be defined that have not previously been considered, namely, those represented by the electrostatic system to selected the concept represented by the symbols k and Q. it is most convenient in the electrostatic system to selected the concept represented by k as the one to be arbitrarily designated as fundamental (like length, mass, and time in mechanics). Then Q can be defined from Coulomb’s law. From this agreement, k is arbitrarily assigned the value of exactly. I dyn cm2 per unit charge2 for empty space. The esu of charge, usually called the statcoulomb (statiC), is defined as a point charge of such a magnitude that it is repelled by a force of one dyne if it is placed one centimeter away from an equal charge in empty space. The size of the statcoulomb makes it convenient for many problems in electrostatics.
The simplest possible generator is a single coil of wire rotating in a uniform magnetic field. The emf induced in such a case is an alternating emf, and hence such a generator is referred to as and hence such a generator is referred to as an ac generator. The coil in which the emf is induced is called the armature.
A high voltage may be obtained in an ac generator by having the coil wound on an iron core, the flux linked by the coil being thus increased, and also by having a large number of turns in series for each coil. Where the coil rotates, the ends of the coils are connected to circular ring called collecting rings or slip rings. Carbon (graphite) brushes bearing on these rings make connection to the outside circuit. The basic elements of an ac generator are (1) a field magnet, (2) the armature genitors the armature is made stationary and the field magnet is caused to rotate.
Several significant experiments, originally performed by Faraday with a metallic ice pail and an electroscope, are useful in illustrating some of the facts stated above. The pail is connected to the electroscope by a conducting wire.
When a charged ball, held by an insulating thread, is lowered into the pail, the leaves of the electroscope diverge, showing that they possess an induced charge. No charge in the divergence of the leaves is noticed when the charged ball is moved to various places inside the pail. This shown that the number of induced charges inside the pail is just equal to the charge on the ball. Now, if the ball is touched to a wall of the pail, no charge in the divergence of the leaves is observed. The ball is found to have lost its charge and the outside of the pail and the electroscope has gained the charge lost by the ball. When the ball touches the wall, its charge just neutralizes the charges of opposite sign that were on the inside of the pail.
If the ball is again similarly charged and reintroduced into the pail and touched to the pail, it will be found that the pail acquires an additional charge, equal in magnitude and sign to the original charge. This procedure can be continued until the pail is charged to a very high potential.
In considering thermoelectric effects, we have to realize that we are dealing with a non-equilibrium situation. A general theory of non-equilibrium is beyond our means, suffice it to say that Lars Onsager, with a paper entitled” reciprocal relations in irreversible processes” induced some fundamental insights as late as 1930; he received the Nobel Prize for his contribution to non-equilibrium thermodynamics in 1968-for chemistry, of all things. However, what we should aware of, is the essential statement of non-equilibrium theory:
As long as there is no equilibrium, we always have currents of something trying to establish equilibrium by reducing a gradient in something else that is the actual cause of the non-equilibrium. A gradient in the electrical potential, e.g., cause out well-known electrical currents, and a gradient in a concentration causes diffusion currents.
But we must abstract even more, and consider things like entropy currents as well as all kinds of combinations of gradients and currents
While Onsager discovered some quite general relations between gradients and currents, we will not delve into details here, but only look a bit more closely at what causes some thermoelectric effects of current.
See beck in 1821 found that if two wires of different metals say copper and iron are joined at their ends A and B through a low resistance galvanometer G to from a closed circuit and if one of the junctions say A is heated and the other junction B is kept cold the galvanometer shows a deflection this must be due to a current in the circuit called thermo eclectic current the current must further be due to certain called thermo the assembly of two different metals joined at their ends to have two junctions in a circuit is called a thermocouple. This phenomenon of thermo-electricity was discovered first of all by see beck. Hence it is also called see beck effect.
Thus see beck effect is the phenomenon of generation of an electric current in a thermocouple by keeping its two junctions at different temperatures.
The direction of current in Cu – Fe thermocouple is from Cu to Fe through hot junction and can be remembered by the world chl. In Sb-Bi thermocouple the direction of current is Sb to Bi through cold junction it can be recollected by ABC.
See beck found that the magnitude and direction of thermo developed in a thermo couple depends up.
The nature of metals forming the thermo couple.
Difference in temperatures of the two junctions.
The see beck effect is reversible. It means if the hot and the cold junctions are interchanged. The direction of thermoelectric current is reversed. Thus see beck effect is a reversible effect.
See beck from his experimental investigations arranged a number of metals in a series know as see beck series. Some of the metals of this series in the order see beck arranged them are given below.
Bi, Ni, Co Pd, Pt, Cu, Mn, Hg, Pb, Sn, Au, Ag, Zn, Cd, Fe, Sb, Te,.
When any two of these metals from a thermocouple current flows through the hot junction from a metal occurring earlier, to a metal occurring later, in the series.
See beck also found that for a given difference of temperatures of two junctions the larger is the gap in see beck series between the metals forming the thermo couple the greater will be the thermo emf. Generated. That is why thermo emf developed is maximum in a thermo couple of antimony and bismuth for a given difference in temperatures of the two junctions. The thermo emf is of the order of 10-3 V or less.
For a temperature difference of 100C between the two junctions the thermo produced in Cu-Fe. Thermocouple is only 0.0013V and in Sb-Bi thermocouple is 0.008V.
When two different metals are brought into contact, at the junction the free electrons tend to diffuse from the metal swath greater free electron density to the other with lower free electron density due to this diffusions a potential different is developed at the junction of the two metals called contact potential when booth the junctions are at the same temperature the contact potentials at the two junctions will be the same.
Hence no current flows in the thermocouple. But if one junction id heated up the rate of diffusion of free electrons at that junction will charge. As a result of it’s the contact potentials at the two junctions will become different and there will be an effective potential difference in the circuit called thermo.
Thus the term produced in a thermocouple is equal to the difference in contact potentials at the two junctions A and B and is given by V AB = V A – V B
A thermoelectric thermometer is used for the measurement of temperatures both low and high.
Principle: Its working is based on see beck effect thermocouples of different metals are constructed depending upon the temperature to be measured.
Construction: The wires forming the thermocouple are welded together at one end and this end forms the hot junction. The portions of the wires near the hot junction are properly insulated from each other by enclosing them in a hard-glass capillary tube C.T. the wires are passed through mice discs D, which are fitted one above the other in a porcelain tube T. the ends of these wires are connected to the terminals T1 and T2 to these terminals are connected compensating leads L1 and L2 of the same materials as those forming the thermocouple itself. By so doing the cold junction is shifted to a convenient place where a constant temperature of OC is maintained.
By keeping hot junction at different known temperatures the corresponding values of thermo are noted using distal voltmeter in the circuit of thermocouple. The digital voltmeter gives its internal resistance is very high (about 10 ?). A graph plotted between the temperature of hot junction and Themo the curve so obtained is called calibration curve.
To find the unknown temperature of a given bath the hot junction is placed in the given bath. The thermo so generated is measured. The temperature corresponding to this value of thermo is determined from the calibrations curve.
Note it is important to note that thermocouple should not be used to measure the temperature above the neutral temperature.
Thermoelectric thermometers can be used over much wide3er range of temperatures; ranging from – 200C to 1600C.
These thermometers are cheap and can be constructed easily.
These can be used to measure the temperature of small cavity.
Their thermal capacity being low they attain the temperature to be measured very quickly and are thus useful for measuring changing temperatures.
Since these thermometers are not direct riding thermometers so they cannot be used for calorimetric purposes.
There is no common relation connecting thermo and the temperature of a junction in any thermocouple. Therefore the given thermo couple has to be calibrated first.
For the measurement of temperature over different ranges, different thermocouples are to be used.
Thermo electric power is defined as the rater of charge of thermo with temperature it is also called see beck coefficient and is denoted by S.
From experimental study it was concluded that the variation of thermo e with the temperature C of the hot junction when cold junction is at OC is a parabolic curve represented by the equation
E = a ? + 1 / 2 ß ?2
Where a and ß are constants which depend upon the nature of the metals forming the thermocouple and the temperature difference of the two junction.
The thermoelectric power (called see beck coefficient) is given by
S = dE/d ? = ? + ß ?
It means S ? ?
A thermopile is a sensitive instrument used for detection of heat radiation and measurement of their intensity. It is based upon see beck effect.
A thermopile consists of a number of thermocouples of Sb –Bi all connected in series. One set of junctions on one side is coated with lamp black. The other set of junctions on the other side is well polished. The arrangement is enclosed in a funnel or horn shaped vassal. The two ends T1 and T2 of the thermopile are connected to a sensitive galvanometer.
Heat radiations coming from the funnel shaped side of the vessel are made to fall on the set of junctions coated with lampblack. These are absorbed and consequently the temperature of all the junctions in this set is raised. The other set of junctions being polished reflect these radiations and remain cold. Thermo is developed in each thermocouple. As thermocouples are connected in series, the thermoelectric current in each flow is in the same junction. The total current is therefore large and produces deflection in the galvanometer.
The deflection in the galvanometer indicates the existences of heat radiations. The deflection is calibrated to measure directly the intensity of heat radiations. This instrument is so sensitive that it can detect heat radiations from match stick lighted at a distance of 50 meters from the thermopile.
The working of thermo-electric refrigerator is based on pettier effect. According to pettier effect, if current is passed through a thermocouple heat is absorbed at one junction and evolved at the other junction of the thermocouple. If on the whole the heat is a boarded, the thermocouple acts as thermoelectric refrigerator. Such a refrigerator has no muter or compressor. Its efficiently is small in comparison to congenital refrigerator. Thermo electric refrigerator is very useful when the region to be cooled is very small and the noise is not acceptable.
The thermocouple selected for the use of thermoelectric refrigerator should have the following characteristics.
Low resistivity so that the loss of energy in the form of joule heat is minimum.
Low thermal conductivity it will help in maintaining large temperature difference between the two junctions.
High thermo electric power.
Thermocouple can be used to generate electric power using seek beck effect in remote areas. It can be achieved by heating one junction in a flame of kerosene oil lamp and keeping the other junction at room or atmospheric temperature. The thermo so developed is used to operate radio receivers or even radio transmitters.
Thomson’s effect was discovered by Thomson (later called Kelvin). According to this effect, if two parts of a single conductor are maintained at different temperatures, an e.m.f. is developed between them. The e.m.f. so produced is called Thomson’s e.m.f. If the steady current is passed through an unequally heated conductor, an absorption or evolution of heat in excess of Joule’s heat, takes place in the conductor.
Thus Thomson’s effect is the absorption or evolution of heat in excess of Joule heat when current is passed through an unequally heated conductor. Thomson effect is reversible effect.
To understand Thomson’s effect, consider an unequally heated rod AB of copper. Let the end A of the be at higher temperature than its end B. on passing the current from A to B in the rod, heat is evolved along the length of the rod. In case, the current is passed in the rod from end B to A, the heat is absorbed along the length of the rod. It is accounted due to the fact that in case of copper, the hot end of the rod is at higher potential and its cold end is at lower potential.
When current flows from hot end to cold end of copper rod i.e. from higher potential to lower potential, the energy is produced which is radiated out in the form of heat. When current is flowing from cold end to hot end of the copper rod i.e. from lower potential to higher potential, the energy required which accounts for the absorption of heat energy. Thomson’s effect for copper is positive. Other substances showing positive Thomson’s effect are Sb, Ag, Zn etc.
There are some other substances like Fe, Co, Bi, Pt etc. for which Thomson’s effect is negative. It means for such metals, Thomson’s effect is just reverse as that for copper. It means, according to Thomson’s effect for iron rod, heat is absorbed when current is passed from hot end to cold end and heat is evolved when current is passed from cold end to hot end of the rod.
For lead, Thomson’s effect is nil. It means no heat is evolved or absorbed when current is passed through an unequally heated rod of lead. It is due this reason that lead is used as a reference metal in thermoelectricity.
Area is a scalar quantity. But in some of the problems it is convenient to treat it a a vector. The question is how to associate a vector to the area of a curved surface. Let us divide the given closed area into a large number of very small area elements. Each small area element may be treated as planar. As normal to the plane specifies the orientation of the place, therefore, the direction of a planar area vector is along its normal. But a normal can point in two directions, inwards or outwards. By convention the vector associated with every area element of a closed surface is taken to be in the direction of the outward normal.
Thus, an area element vector S at a point on a closed surface can be written as
? = (? )
where S in magnitude of the area element and is a unit vector in the direction of outward normal at that point.
Electric flux over an area in an electric field represents the total number of field lines crossing this area.
We know that the number of field lines crossing a unit area placed normal to the field at a point is a measure of strength of electric field E at that point. If we place a small planar element of area ?S normal to E at this point, number of electric filed lines crossing this area element is proportional to E (?S) note that it is not proper to say that number of field lines crossing the area is equal to E (?S). The number of field lines is after all a matter of how many field lines we choose to draw. What is physically significant is the relative number of field lines crossing a given area at different points.
If we tilt the area element by angle ? [or we tilt E w. area element by angle ?, the number of field lines crossing the area will be smaller. As projection of area element normal to E is ?S cos ? (or component of E normal of electric filed lines crossing area ?S is proportional to E?S cos ?.
To obtain relation between electric intensity E and electric potential V, let us consider two equipotential surfaces A and B spaced closely as shown in fig. 1 (c) let the potential of A be VA = V and potential of B be VB = (V + dV) where dV is increase in potential in the direction of electric intensity E normal to A and B.
Suppose dr is perpendicular distance between the two equipotential surfaces. When a unit positive charge is taken along this perpendicular distance from the surface B to the surface A against the electric field.
Work done WBA = | E | dr
WBA = VA – VB = V – (V + dV) = - dV
|E| dr = – dV
Like the potential energy of a mass in a gravitational field we can define electrostatic potential energy of a charge in an electrostatic field.
For the sake of simplicity, let us assume that electrostatic field is due to charge + Q placed at the origin. Let a small test charge + q be brought from a point A to a point B, against the repulsive force on it due to charge + Q we shall assume that the test charge +q is so small that it does not disturb the original configuration of charge + q at the origin further we assume that an external force ext applied is just sufficient to counter the repulsive electric force on the test charge q so that net force on test charge q is zero and it maces from A to B without any acceleration.
In this situation, work done by external force is evasive of work done by the electric force and gets fully stored in the charge q in the form of its potential energy.
On reaching B, if the external force applied on q were removed, the electric force will take the test charge + q away from source charge + Q. the strode potential energy at B is used to provide kinetic energy to the charge q in such a way that the sum of kinetic and potential energies at every point is conserved.
Basically electrostatic potential of a body represents the degree of electrification of the body it determines the direction o flow of charge between two charged bodies placed in contact with each other. The charge always flows from a body at higher potential to another body at lower potential the flow of charge stops as soon as the potentials of the two bodies become equal.
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