To verify the laws of combination (parallel) of resistances using a metre bridge.

AIM
To verify the laws of combination (parallel) of resistances using a metre bridge.

APPARATUS
A metre bridge, a Leclanche cell (battery eliminator), a galvanometer, a resistance box, a jockey, two resistance wires or two resistance coils known resistances, a set square, sand paper and connecting wires.

THEORY

where R is the resistance from the resistance box in the left gap and l is the length of the metre bridge wire from zero end up to balance point.

CIRCUIT DIAGRAM

PROCEDURE

1. Mark the two resistance coils as r₁ and r₂.
2. To find r₁ and r₂ proceed same way as in Experiment 1. (If r₁ and r₂ are not known.)
3. Connect the two coils r₁ and r₂ in parallel as shown in figure in the right gap of metre bridge and find the resistance of this combination. Take at least three sets of observations.
4. Record your observations.

OBSERVATIONS

Table for length(l) and Unknown resistance (x)

CALCULATIONS

RESULT
Within limits of experimental error, experimental and theoretical values of R_p are same. Hence, law of resistances in parallel is verified.

PRECAUTIONS
Same as in Experiment 1.

VIVA VOCE

ELECTRIC CURRENT
Question.1.State Ohm’s Law.
Answer.Ohm’s law states that the electric current I flowing through a conductor is directly proportional to the potential difference (voltage) V across its ends (provided that the physical conditions—temperature, pressure and dimensions of the conductor remain same).

Question.2.Give mathematical form of Ohm’s law.
Answer.Mathematical form of Ohm’s law is, V = RI.

Question.3.Define resistance.
Answer.The constant ratio of potential difference V across the ends of a conductor to the current I flowing through it, is called resistance of the conductor. It is represented by the symbol R.

Question.4.What are Ohmic and non-ohmic resistances?
Answer.Resistances which obey Ohm’s law, are called ohmic resistances e.g., metals like Cu, Al, Ag etc. at low temperature.
Resistances which do not obey Ohm’s law are called non-ohmic resistances e.g., diodes and transistors.

Question.5.Give common examples of non-ohmic resistances.
Answer.Vacuum tube diodes, semi-conductor diodes and transistors are non-ohmic resistances.

Question.6.What is effect of temperature on the resistance of a conductor?
Answer.The resistance of the conductors increases with increase in temperature.

Question.7.Name some substances whose resistance decreases with increase in temperature.
Answer.Resistance of semi-conductors (Si, Ge) decreases with increase in temperature.

Question.8.How do you conclude that the conductor used in experiment obeyed Ohm’s law?
Answer.It is done by two results :

1. The ratio of voltmeter reading (V) and the corresponding ammeter reading (J) comes to be constant.
2. A graph between V and I comes to be a straight line.

Question. 9. Why a large current is not allowed to be passed through the conductor during the experiment?
Answer. If a large current is passed (or even if a small current is passed unnecessarily for a long time), the conductor will become hot and its resistance will increase.- Then the graph will not remain a straight line.

Question.10. Why do we use thick connecting wires?
Answer. Thick connecting wires offer negligible resistance compared to given alloy wire whose resistance is to be determined.

Question.11. What is ohm? Define it.
Answer. Ohm is the S.I. unit of resistance. One ohm is the resistance offered by a conductor when one ampere current is flowing through it, when one volt P.D. is maintained across — its ends.

Question.12. What is a battery eliminator?
Answer. It is a rectifier. It converts high A.C. voltage (220 V) into low desired D.C. voltage such as 2 V, 4 V, 6 V, 8 V, 10 V, 12 V. It is a good substitute for a battery or a cell.

Question. 13. Why, unknown wire whose resistance is to be determined, is made of alloys such as manganin, Eureka?
Answer. Unknown resistance wire is made of alloy, but not of metals, because

1. The resistivity of alloys is greater than that of metals.
2. The temperature coefficient of resistance of alloys is negligible than that of metals.

Question.14. What is the effect of rheostat, range of voltmeter, ammeter on resistance of unknown wire?
Answer. No effect because resistance does not depend upon them.

Question.15. What material is chosen for rheostat wire and why?
Answer. It is constantan alloy. Because its resistivity is high and temperature coefficient of resistance is quite small.

Question.16. What is the material of the connecting wires used in the experiment?
Answer.Copper.

Question.17. Is there any advantage of battery eliminator over usual source of e.m.f.?
Answer. Main advantage of battery eliminator is that current can be drawn at desired voltages and it does not need any charging. It is easy to handle and maintain.

Question. 18. What are the factors affecting the resistance?
Answer. The resistance depends upon length, Area of cross-section, nature of material and temperature of the conductors.

Question.19. What is electric current? Define its S.I. unit.
Answer. The flow of electric charge per unit time through a conductor is called electric current. S.I. unit of current is ampere (A).
The one ampere is the amount of current flowing in a conductor which offers resistance 1 Ohm when one volts potential difference is maintained across the conductor.

Question.20. Define S.I. unit of electric potential.
Answer. Volt is the S.I. unit of electric potential. One volt is said to be the potential difference between two points if one Joule of work is done in bringing one coulomb of charge from one point to the other.

Question.21. Why is a large current not allowed to flow the circuit during the experiment.
Answer. If large current is passed or passed for a long time then wire become hot and its resistance increases. Therefore, the V-I graph will not be a straight line and Ohm’s law is not valid.

Question. 22. Can we take a metal wire in place of alloy wire whose resistance is to be measured?
Answer. No. Because large current will flow and battery will damage.

Question. 23. Why is the ammeter always connected in series to measure the current?
Answer.It is connected in series with circuit in order to measure the current without any change in magnitude.

Question. 24. Why is the voltmeter is connected in parallel?
Answer. So that it can measure the potential drop without any change in its magnitude.

Question.25. Why is the resistance wire on its self before it is wound on bobbin or reel?
Answer. To avoid induction effect.

RESISTANCE

Question.1. Define resistance.
Answer.It is the opposition offered by the material of wire to the flow of electric current, R = V/1

Question.2.How can it measured?
Answer.It can be measured by (i) Ohm’s law (ii) Metre bridge (iii) Multimeter.

Question.3.Define the unit of resistance.
Answer.The S.I. unit of resistance is Ohm (Ω) or volt per ampere. One ohm is the resistance of a conductor carrying current one ampere when unit p.d. is maintained across its ends.

Question.4.What is the cause of resistance?
Answer. Collisions of drifting electrons with the atoms.

Question.5.What is the conductance?
Answer.The reciprocal of resistance is called conductance. It is denoted by G.
G = 1/R S.I. of G is mho, or Siemen.

Question.6.How does resistance depend upon the length of a conductor?
Answer.The resistance is directly proportional to the length of a conductor (provided its area of cross-section remains constant) i.e., R ∝l. It means if length of conductor increases, then resistance increases and vice-versa.

Question.7.How does resistance depend upon the area of cross-section of a conductor?
Answer.The resistance is inversely proportional to the area of cross section of a conductor
(provided its length remains constant) i.e., R ∝=1/A. It means, if area of cross section increases then resistance decreases and vice-versa.

Question.8.What is the resistance of an open key? Explain it.
Answer.

Question.9.What is the length of resistance wire used between the gap of resistance box marked INFINITE? Explain it.
Answer.Infinite marked plug has no wire.
Explanation. We have R = Pl/A We have made R infinite by making A = 0 (rather than by making l infinite).

Question.10.What is the conductance?
Answer.

Question. 11. Define resistivity or specific resistance of the material of conductor
Answer.

Hence, resistivity is defined as the resistance of a conductor of unit length and unit cross-sectional area. The unit of resistivity is ohm-metre (Ω-m).

Question.12.Define electrical conductivity
Answer.It is reciprocal of resistivity. It is represented by the symbol σ =1/P. The unit of electrical conductivity is Siemen per metre (S m^-1).

Question.13.What is the order of magnitude of resistivity of conductors?
Answer. Resistivity of the conductors is of the order of 10^-8 Ω-m.

Question.14.What is effect of temperature on the resistance of a conductor?
Answer.Resistance of all conductors increases with increase in temperature of the conductor.

Question.15.Define temperature coefficient of resistance.
Answer.

Hence, temperature coefficient is defined as the increase in resistance of a conductor of unit resistance due to unit increase in temperature.

Question.16.Give unit of temperature coefficient of resistance.
Answer.The unit of temperature coefficient is per °C (or K) (°C^-1 or K^-1).

Question. 17. How does resistance change in series combination?
Answer. Resistance increases in series combination.

Question. 18. Explain increase of resistance in series combination.
Answer.In series combination, the effective length of resistor increases. As R∝ l, resistance increases in series combination.

Question.19. How does resistance change in parallel combination?
Answer. Resistance decreases in parallel combination.

Question. 20. Explain decrease of resistance in parallel combination.
Answer. In parallel combination, the effective area of cross-section increases. As R∝ 1/A resistance decreases in parallel combination.

Question. 21. What is Wheatstone bridge?
Answer. It is the arrangement of four resistance in quadrilateral form to determine one unknown resistance in term of other three resistances.

Question. 22. What is a metre bridge?
Answer. It is the practical form of Wheatstone bridge to determine the unknown resistance and resistivity of a given alloy wire.

Question. 23. Why is constantan used in the bridge wire?
Answer.

1. The resistivity (49 x 10^-8 Ω-m) of the constantan is high.
2. The temperature coefficient of resistance (a) is very small (0.40 x 10^-4 ) (°C^-1 ).

Question.24. How are the coils wound in a post office box or resistance box?
Answer. The resistance coil is doubly wound to avoid electromagnetic induction.

WHEATSTONE’S BRIDGE

Question. 25. When is a Wheatstone’s bridge said to be balanced?
Answer. A Wheatstone’s bridge is said to be balanced, when no current flows through the galva¬nometer and it gives zero deflection.

Question. 26. What is the condition for a Wheatstone’s bridge to become balanced?
Answer.

Question. 27. Will the interchange of positions of cell and galvanometer effect the balance condition?
Answer. No. The condition of balanced Wheatstone bridge remains satisfied.

Question.28. When is a Wheatstone’s bridge most sensitive?
Answer. The bridge is most sensitive when all the four resistances P, Q, R and S are of same order of magnitude.

Question.29. What are applied forms of a Wheatstone’s bridge?
Answer. The applied forms of a Wheatstone’s bridge are :

1.  Metre Bridge or Slide Wire Bridge.
2. Post Office Box.

METRE BRIDGE

Question. 30. Why is a metre bridge so called?
Answer. Since the bridge uses one metre long wire, it is called a metre bridge.

Question. 31. Why is a metre bridge also called a slide wire bridge?
Answer. Since a jockey is slided over the wire (during the experiment), it is also called a slide- wire bridge.

Question. 32. Why the jockey should not be pressed too hard on the wire when sliding over it?
Answer. Sliding the jockey with a hard press, will scratch the wire and make its thickness non¬uniform. Then the resistance per unit length of the wire will not remain constant because resistance depend upon area of cross-section.

Question. 33. What is null point?
Answer. It is a point on the ware, keeping jockey at which, the galvanometer gives zero deflec¬tion.

Question. 34. Why is it advised to keep null point between 45 cm and 55 cm?
Answer.It is done to minimise the effect of neglecting of end resistances in calculation and Wheatstone bridge is most sensitive when all four arms have same order of resistances.

Question.35. What are end resistances?
Answer. The resistances of thick copper strips which keep the two ends of the wire pressed, are called end resistances.

Question.36. What is an ideal value of null point and why?
Answer. Null point at 50 cm is an ideal null point. It makes, P/Q = 1. This ratio is not affected by neglecting end resistance of equal values at the two ends.

Question.37. How can a null point be obtained near 50 cm?
Answer. It can be done by keeping value of R very near the value of X.

Question.38. Why copper strips, used to pressed the ends of wire, are thick?
Answer. Thick Cu strips have negligible resistance over the resistance of alloy metre bridge wire and minimise effect of end resistances.

Question. 39. Why should the bridge wire have uniform thickness and material density throughout?
Answer. Because only then, the resistance per unit length (σ) will be same throughout. Then P = σ l and Q =σ (100 –l) will be correct.

Question. 40. Why the bridge method for resistance measurement is better than Ohm’s Law?
Answer. It is so because the bridge method is a null method (at null point, there is no current flowing in galvanometer) and more sensitive.

Question. 41. Under what conditions, the metre bridge is most sensitive (and hence result most accurate)?
Answer. The bridge is most sensitive when all the four resistances are of equal value. It brings null point automatically at 50 cm.

Question. 42. Why the metre bridge is suitable for measuring moderate resistances?
Answer. Because, Wheatstone bridge is suitable for moderate values of resistances. Therefore, meter bridge is more sensitive for moderate values.

Question. 43. When the sensitivity of the bridge becomes less?
Answer. Bridge has poor sensitivity when resistances P, Q, R and S (or X) are of different order.

Question. 44. Why should current be passed for a short time?
Answer. Continuous current will cause unnecessary heating and affecting values of resistances used.

Question.45. Why is Wheatstone bridge (or metre bridge) method considered unsuitable for the measurement of very low resistance?
Answer. For measuring low resistance, all resistances and resistance of galvanometer should be f low. The end resistance and connecting wires become comparable to the resistance being
measured and introduce error in the result.

Question. 46. Why is Wheatstone bridge (or metre bridge) method considered unsuitable for
the measurement of very high resistance?
Answer. The resistance forming the bridge should be high and the current in the galvanometer
reduces and it become insensitive.

Question. 47. What are the advantages of a Wheatstone bridge method of measuring
resistance over other methods?
Answer.

1. It is a null method, hence the result does not get affected from extra resistances,
2. It is easier to detect a small change in deflection than to read a deflection directly.

Question. 48. What do you mean by sensitiveness of a Wheatstone bridge?
Answer. A Wheatstone bridge is said to be sensitive if it produces more deflection in the galva- nometer for a small change of resistance in resistance arm.

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Thermal Expansion of Solids

Physics Lab ManualNCERT Solutions Class 11 Physics Sample Papers

THERMAL EXPANSION
Definition. Increase in dimensions of a solid on heating, is called thermal expansion of the solid. All dimensions increase in same proportion.
Types
(i) Linear expansion. A rod or wire has length only. When heated, its length increases. Increase in length is called linear expansion.
(ii) Superficial expansion. A sheet has area. When heated, its area increases. Increase in area is called superficial expansion.
(iii) Cubical expansion. A body has volume. When heated, its volume increases. Increase in volume is called cubical expansion.

COEFFICIENT OF LINEAR EXPANSION

COEFFICIENT OF SUPERFICIAL EXPANSION

COEFFICIENT OF CUBICAL EXPANSION
Introduction. Let a body of certain material have volume V₀ at 0°C. Let the volume become V_t at t°C.
Then, like linear and superficial expansion, cubical expansion (V_t – V₀) depends upon original volume (V₀) and rise in temperature (t). It also depends upon the material of the body.
Hence, proceeding as in linear expansion,
V_t-V₀ = γ V₀ t
where γ is constant of proportionality whose value depends upon the material of the body. It is called coefficient of cubical expansion of the material of the body.
Definition. In Eq. (1),
if V₀=1, t=1,
then, cubical expansion, V_t-V₀ = γ.
Hence, the coefficient of cubical expansion of the material of the body may be defined as the increase in volume of a body of unit volume for one degree rise in temperature.
From Eq. (1), V_t-V₀ = y V₀ t
or V_t = V₀[1+γ(t₂ -t₁)] …(2)
From Eq. (2), Vt can be found if V₀, γ and t are known.
In general, if a body has volume V₁ at t°C and V₂ at t₂°C we may prove that
V₂ = V₁[1+γ(t₂-t₁)]
Equation (3) is possible because γ has Small value and γ² is negligible.

RELATION BETWEEN α, β AND γ BY DIFFERENTIAL METHOD

VIVA VOCE

Question.1. Which part of the bimetallic strips lie outside on heating ?
Answer. The metal which has higher coefficient of linear expansion lies on the outer side.

Question.2. Where bimetallic strips are used ?
Answer. In fire alarm, thermostats, etc.

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Thermal Expansion of Liquids

THERMAL EXPANSION OF LIQUIDS
Definition. Increase in dimensions of a liquid on being heated is called thermal expansion of the liquid.
Types. Liquid has only volume. When heated, its volume increases. Increase in volume is called cubical expansion.

REAL AND APPARENT CUBICAL EXPANSION OF A LIQUID
A liquid is taken in a vessel. When the liquid is heated, the vessel is also heated. The volume of vessel increases on heating. Increase in volume of the liquid is more than the increase in volume of the vessel. On observation, the increase in volume of the liquid appears to be less than the actual increase in volume.
Actual increase in volume of the liquid (taking into account expansion of the vessel), is called real cubical expansion of the liquid.
Observed increase in volume of the liquid (excluding expansion of the vessel), is called apparent cubical expansion of the liquid.
Apparent cubical expansion of liquid is less than the real cubical expansion by the amount equal to the cubical expansion of the vessel.

COEFFICIENT OF REAL CUBICAL EXPANSION OF A LIQUID
Actual increase in volume of a liquid of unit volume for one degree rise in temperature, is called coefficient of real cubical expansion of the liquid. It is represented by the symbol γ_r.

COEFFICIENT OF APPARENT CUBICAL EXPANSION OF A LIQUID
Observed increase in volume of a liquid of unit volume for one degree rise in temperature, is called coefficient of apparent cubical expansion of the liquid. It is represented by the symbol γ_a.

RELATION BETWEEN γ_r AND γ_a
Let a glass vessel and the liquid in it have volume V₀ at 0°C. Let γ_r and γ_a be the coefficients of real and apparent cubical expansion of the liquid and let γ_g be the coefficient of cubical expansion of glass (vessel material).

VIVA VOCE

Question.1. Define real cubical expansion of a liquid.
Answer. Actual increase in volume of a liquid (taking into account expansion of the vessel), is called real cubical expansion of the liquid.

Question.2. Define apparent cubical expansion of a liquid.
Answer. Observed increase in volume of a liquid (excluding expansion of the vessel), is called apparent cubical expansion of the liquid.

Question.3. Give relation between γ_r and γ_a.
Answer. The relation is, γ_r =γ_a + γ_g.

Physics Lab ManualNCERT Solutions Class 11 Physics Sample Papers

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Thermal Radiation 

Physics Lab ManualNCERT Solutions Class 11 Physics Sample Papers

THERMAL RADIATION
A hot body emits energy. The energy emitted by a hot body in the form of radiation, by virtue of its temperature, is called thermal radiation.

RADIATION—A MODE OF HEAT TRANSMISSION
There are three modes of transmission of heat energy. They are : conduction, convection and radiation.
The radiation is the mode of transmission of heat from a hot body to a cold body or surroundings without needing an intervening medium. The speed of radiation is the speed of light in medium.

BLACK BODY
A body which completely absorbs thermal radiations of all wavelengths falling upon it, is called a black body.
When such a body is heated, it emits radiations of all possible wavelengths. The radiations emitted by a black body, are called black body radiations or full radiations.
There is no ideal black body but Ferry cavity can be considered a perfectly black body.

SOME ELEMENTARY DEFINITIONS
1. Total Emissive Power (e). The total emissive power of a body at a particular temperature is defined as the total amount of radiant energy emitted per second per unit area of the surface of the body. It is represented by the symbol e.
Its SI unit is J m^-2 s^-1. Total emissive power of a black body is represented by the symbol E.
2. Emissivity ε. Emissivity of a body is the ratio of the total emissive power of the body to the total emissive power of a black body. It is represented by the symbol ε. It means that ε =e/E  or e=εE . For a block body , ε=1.
3. Total Absorptive Power (a). The total absorptive power of a body is defined as the ratio of the total radiant energy absorbed by the body in a certain interval of time, to the total energy falling upon it in the same interval of time. It is represented by the symbol a.
Total absorptive power of a black body is represented by the symbol A. By definition A = 1.

KIRCHHOFF’S LAW
Statement. The law states that for a given temperature, the ratio of the emissive power to the absorptive power of a body, at a particular wavelength is a constant for all bodies and is equal to the emissive power of a perfectly black body.
Explanation. If e_λ and a_λ be the emissive and absorptive powers of a body for wave-length λ, and E_λ be the emissive power of a black body for wavelength λ, then e_λ /a_λ=Constant = E_λ
According to this law, good emitters are good absorbers and poor emitters are poor absorbers.

STEFAN’S LAW
Statement. The law states that the total amount of radiant energy emitted by unit area of a perfectly black body in one second is directly proportional to the fourth power of its absolute temperature.
Explanation. If E be the amount of radiant energy emitted by unit area in one second and T be the absolute temperature of the body, then

NEWTON’S LAW OF COOLING
Statement. The rate of cooling (i.e., heat lost per second) of a body is directly proportional to the difference of temperature of the body (T) and the surrounding (T₀), provided difference in temperature should not exceed by 30°C.

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Measurement of Electromotive Force and Potential Difference

ELECTRIC (ELECTROSTATIC) POTENTIAL AND ELECTRIC POTENTIAL DIFFERENCE
Definition. Electric potential at a point in the electric field of a charge (field charge) is defined, (or measured) as the work done in moving a unit positive charge (test charge) from infinity (i.e., from outside the field) to that point (provided that the bringing of the test charge does not effect the original field configuration.)
It is represented by the symbol V. Its S.I. unit is volt. It is scalar (being work). Electric potential difference between two points in the electric field of a field charge is defined as the work done in moving a test charge from one point to the other.

ELECTROMOTIVE FORCE AND POTENTIAL DIFFERENCE OF A CELL

1. Electromotive Force: The chemical force which makes the positive ions inside a cell to move from negative to positive terminal inside the cell, is called electromotive force (e.m.f.) of the cell. It is represented by the symbol E (or ε). Its unit is volt. It is a scalar quantity because it is the potential difference.
   It is equal to the potential difference between the two terminals of the cell, when the cell is in open circuit i.e., giving no current.
   E.M.F. is independent of
   (i) Plates (electrodes) area
   (ii)Plates separation
   (iii) Electrolyte quantity.
2. Potential Difference: It is the potential difference between the two terminals of the cell, when it is in close circuit i.e., giving current. It is represented by the symbol V. Its unit is volt.
   

INTERNAL RESISTANCE OF A CELL
The resistance offered by the electrolyte of the cell to flow of ions through it, is called internal resistance of the cell. It is represented by the symbol r. Its unit is ohm (Ω).
Internal resistance depends upon

1. Plates (electrodes) area inside the electrolyte.
2. Plates separation
3. Electrolyte nature and concentration.
4. Temperature
5. Use of cell. (Passage of time)

RELATION BETWEEN E.M.F., P.D. AND INTERNAL RESISTANCE OF A CELL
Circuit in shows a cell of e.m.f. E and internal resistance r, connected to an external resistance R. The circuit has total resistance (R + r) and current I in circuit is given by

POTENTIOMETER
(a) Potentiometer: is a device used to measure the internal resistance of cell, to com¬pare the e.m.f. of two cells and potential difference across a resistor.
(b) Principle:
It works on the principle that when a constant current flows through a wire of uniform thickness and material, potential difference between its two points is directly proportional to the length of the wire between the two points. It is a device used to measure the internal resistance of a cell, to compare the e.m.f. of two primary cells etc.
V = IR                                                                                                                        …(1)

(c) Construction:
A potentiometer consists a long wire of uniform cross-sectional area, usually 4 to 10 m long, of material having high resistivity and low temperature coefficient such as constantan or manganin. These wires are stretched parallel to each other on a broad wooden board by the side at a metre scale. The wires are joined in series by thick copper strips. A battery of constant e.m.f. (battery eliminator) is connected to the ends P and Q of wire, called driving or auxiliary cell. A jockey J, with a sensitive galvanometer G, is made to slide on the wire PQ.
Note. The number of wires can be increased to increase l and decrease k = V/l.
A lower value of k makes potentiometer more sensitive and accurate.
(d) Working:
A fully charged auxiliary battery B (Battery eliminator) having a constant and high e.m.f. is connected between terminals P and Q through an ammeter A and a rheostat (as shown in circuit diagram, experiment 5 : Section A). This provides an adjustable potential gradient along the potentiometer wire. Positive terminal of the battery is connected to terminal P. Positive terminals of other cell or cells are also connected to same terminal P.
(e) Comparison of e.m.f.’s of two cells:
With the help of a voltmeter we can measure only the terminal potential difference of a cell, but using a potentiometer we can determine the value of e.m.f. (electromotive force) of a given cell. For this purpose, we complete the circuit diagram as shown in  The e.m.f. (E) of the auxiliary battery B is constant and more than that of given cell. Insert the key K. A constant current I flows through the potentiometer wire PQ and a potential gradient k = Iσ  is set up, where a is the resistance per unit length of the potentiometer wire.
The positive terminals of the cells E₁ and E₂ are connected to the zero end terminal P of the potentiometer, whereas the negative terminals are connected through a two-way key to a galvanometer, a resistance box and a jockey. When the cell Ex is in circuit, on sliding the jockey gently along the potentiometer wire PQ a point J, say at a distance l₁ from the zero end, is obtained where the galvanometer shows zero deflection. In such a case the – ve terminal of the cell E₁ and the point J on the potentiometer wire are at the same potential. The zero end of the potentiometer wire and the + ve terminal of cell E₁ are also at the same potential. Hence, fall of potential along the length l₁ of the potentiometer wire is equal to the e.m.f. of the cell E₁ as no current is being drawn from the cell. As the fall of potential along a wire of a uniform area of cross section is proportional to its length.

For determination of internal resistance of a cell by a potentiometer, the circuit arrange¬ment used is shown in  E is the cell whose internal resistance is to be measured. By adjusting the rheostat and closing key K₁ if l₁ is the length of the potentiometer wire to the point where a balance point is obtained in an open circuit i.e., K₂ is open, then

(g) Important Precautions to be taken in Potentiometer Experiments

1. The auxiliary battery B used for producing potential gradient along the potentiometer wire should be fully charged to have a constant e.m.f. Its e.m.f. should be greater than the e.m.f. of each cell which is to be compared.
2. Positive terminals of all the cells must be connected to the terminal P where that of auxiliary battery is connected.
3. Terminal P should be taken as zero of the scale for measuring the balancing length.
4. A sensitive galvanometer should be used to find the null point. It should be protected with a resistance box (R.B.), put in series while finding approximate position of null point. Resistance in box should be made zero when exact position of the null point is to be located.
5.  The approximate position of null point must be brought in the middle of the last wire, by putting jockey J there and adjusting wire current by the rheostat.
6. Current should be passed through the wire only when taking observations, to avoid unnecessary heating of wire, which causes change of resistance changing the potential gradient, (k = Iσ).
7. In case, null point is not obtained on the potentiometer wire i.e., one-side deflection is obtained when jockey is kept at the two ends of the wires used, following checks must be made.
   (i) Connections must be correct, neat, tight and continuous (no connecting wire is broken). For correct connections, positive terminal of battery and cells be connected at one point,
   (ii) Measure the e.m.f. of the auxiliary battery. The e.m.f. must be full and stable to ensure that the battery is fully charged. The of battery must be more than the e.m.f. of either cell used.
   (iii) Make rheostat resistance in circuit zero so that maximum current passes through the potentiometer wires.
   If the above checks do not help, change the potentiometer. (It has some defect which you can not remove).

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To Study the Relationship Between the Temperature of a Hot Body and Time by Plotting a Cooling Curve

Physics Lab ManualNCERT Solutions Class 11 Physics Sample Papers

AIM
To study the relationship between the temperature of a hot body and time by plotting a cooling curve.

APPARATUS
Newton’s law of cooling apparatus (a thin-walled copper calorimeter suspended in a double walled enclosure), two thermometers, clamp and stand, stop clock/watch.

THEORY
Newton’s law of cooling, states that the rate of cooling (or rate of loss of heat) of a body is directly proportional to the temperature difference between the body and its surroundings, provided the temperature difference is small.

DIAGRAM

PROCEDURE

1. Fill the space between double wall of the enclosure with water and put the enclosure on a laboratory table.
2. Fill the calorimeter two-third with water heated to about 80°C.
3. Suspend the calorimeter inside the enclosure along with a stirrer in it. Cover it with a wooden lid having a hole in its middle.
4. Suspend from clamp and stand, one thermometer in enclosure water and the other in calorimeter water.
5. Note least count of the thermometers.
6. Set the stop clock/watch at zero and note its least count.
7. Note temperature (T₀) of water in enclosure.
8. Start stirring the water in calorimeter to make it cool uniformly.
9. Just when calorimeter water has some convenient temperature reading (say 70°C), note it and start the stop clock/watch.
10. Continue stirring and note temperature after every one minute. The temperature falls quickly in the beginning.
11. Note enclosure water temperature after every five minutes.
12. When fall of temperature becomes slow note temperature at interval of two minutes for 10 minutes and then at interval of 5 minutes.
13. Stop when fall of temperature becomes very slow.
14. Record your observations as given ahead.

OBSERVATIONS
Least count of enclosure water thermometer = ……………….°C
Least count of calorimeter water thermometer = ………..°C
Least count of stop clock/watch = …………….s.
Table for time and temperature

(Note. The ideal observations given above are as sample.)

CALCULATIONS
1. Temperature of water in enclosure will be found to remain same. If not then take its mean as T₀.
2. Find temperature difference (T – T₀).
3. Plot a graph between time t and temperature T, taking t along X-axis and T along Y- axis. The graph comes to be as shown in below. It is called Cooling curve O of the liquid.

RESULT
The temperature falls quickly in the beginning and then slowly as difference of temperature goes on decreasing.
This is an agreement with Newton’s law of cooling.

PRECAUTIONS

1. Double-walled enclosure should be used to maintain surrounding at a constant temperature.
2. Stirring should remain continuous for uniform cooling.

SOURCES OF ERROR

1. Surrounding temperature may change.

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To Compare The EMF of Two Given Primary Cells Using Potentiometer.

AIM
To compare the EMF of two given primary cells using potentiometer.

APPARATUS
Potentiometer, a Leclanche cell, a Daniel cell, an ammeter, a voltmeter, a galvanometer, a battery (or battery eliminator), a rheostat of low resistance, a resistance box, a one way key, a two way key, a jockey, a set square, connecting wires and a piece of sand paper.

THEORY

where, E₁ and E₂ are the e.m.f. of two given cells and l₁ and l₂  are the corresponding balancing lengths on potentiometer wire.

CIRCUIT DIAGRAM

PROCEDURE

1. Arrange the apparatus as shown in circuit diagram figure.
2. Remove the insulation from the ends of the connecting copper wires with a sand paper.
3. Measure the e.m.f. (E) of the battery and the e.m.fs. (E₁ and E₂ ) of the cells. See that E > E₁  and also E > E₂ .
4. Connect the positive pole of the battery (a battery of constant e.m.f.) to the zero end (P) of the potentiometer and the negative pole through a one-way key, an ammeter and a low resistance rheostat to the other end (Q) of the potentiometer.
5. Connect the positive poles of the cells E₁ and E₂  to the terminal at the zero end (P) and the negative poles to the terminals a and b of the two way key.
6. Connect the common terminal c of the two-way key through a galvanometer (G) and a resistance box (R.B.) to the jockey J.
7. Take maximum current from the battery making rheostat resistance zero.
8. Insert the plug in the one-way key (K) in circuit and also in between the terminals a and c of the two-way key.
9. Take out a 2,000 ohms plug from the resistance box (R.B.).
10. Press the jockey at the zero end and note the direction of deflection in the galvanometer.
11. Press the jockey at the other end of the potentiometer wire. If the direction of deflection is opposite to that in the first case, the connections are correct. (If the deflection is in the same direction then either connections are wrong or e.m.f. of the auxiliary battery is less).
12.  Slide the jockey gently over the potentiometer wires till you obtain a point where galvanometer shows no deflection.
13. Put the 2000 ohms plug back in the resistance box and obtain the null point position accurately, using a set square.
14. Note the length l₁ of the wire for the cell E₁ Also note the current as indicated by the ammeter.
15. Disconnect the cell E₁  by removing the plug from gap ac of two-way key and connect the cell E₂  by inserting plug into gap be of two-way key.
16. Take out a 2000 ohms plug from resistance box R.B. and slide the jockey along potentiometer wire so as to obtain no deflection position.
17. Put the 2000 ohms plug back in the resistance box and obtain accurate position of null point for second cell E₂ .
18. Note the length l₂  of wire in this position for the cell E₂ . However, make sure that ammeter reading is same as in step 14.
19. Repeat the observations alternately for each cell again for the same value of current.
20. Increase the current by adjusting the rheostat and obtain at least three sets of observations in a similar way.
21. Record your observations as given below

OBSERVATIONS

CALCULATIONS

1. For each observation find mean l₁ and mean l₂  and record in column 3c and 4c.
2. Find E₁/E₂ for each set, by dividing mean l₁  (column 3c) by mean l₂  (column 4c).
3. Find mean E₁/E₂ .  

RESULT

PRECAUTIONS

1. The connections should be neat, clean and tight.
2. The plugs should be introduced in the keys only when the observations are to be taken.
3. The positive poles of the battery E and cells E₁ and E₂  should, all be connected to the terminal at the zero of the wires.
4. The jockey key should not be rubbed along the wire. It should touch the wire gently.
5. The ammeter reading should remain constant for a particular set of observation. If necessary, adjust the rheostat for this purpose.
6. The e.m.f. of the battery should be greater than the e.m.f.’s of the either of the two
   cells.
7. Some high resistance plug should always be taken out from resistance box before the jockey is moved along the wire.

SOURCES OF ERROR

1. Same as in previous experiments.
2. The auxiliary battery may not be fully charged.
3. The potentiometer wire may not be of uniform cross-section and material density throughout its length.
4. End resistances may not be zero.

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HEAT

HEAT
It is a kind of energy which produces the sensation of warmth.
It can also be defined as the internal energy of a body which is transferred from one body at higher temperature to a body at lower temperature, till their temperature become equal.
Its C.G.S. and M.K.S. units are calorie (cal) and Joule (J) respectively.

TEMPERATURE
It is the degree of hotness or coldness of a body. The temperature can be defined as the thermal state of a body gives the direction of flow of heat from one body to another when they are placed in contact.
According to kinetic theory of gases, the temperature of a body is the measure of the average kinetic energy of its molecules.
According to zeroth law of thermodynamics “the temperature is a physical quantity or parameter which has the same value for all system which are in thermal equilibrium with each other. It is measured in Celsius (°C) in C.G.S. unit and Kelvin (K) in M.K.S. units.

HEAT CAPACITY OR THERMAL CAPACITY
It is defined as the amount of heat required to raise its temperature through one degree.

SPECIFIC HEAT
It is defined as the amount of heat required to raise the temperature of unit mass of the substance through one degree.

The specific heat depend upon nature of substance and its temperature.
Molar specific heat of a substance is defined as the amount of heat required to raise the temperature of one mole of the substance through one degree. Its S.I. is J/mol K.

WATER EQUIVALENT
The water equivalent of a body is defined as the mass of water which require the same amount of heat as is required by the given body for the same rise of temperature.
Water equivalent = Mass of body x Specific heat W = me
The C.G.S. unit of water equivalent is g and the M.K.S. unit is kg.

CALORIMETRY AND PRINCIPLE
The calorimetry is the branch of physics that deals with the measuremental heat. According to the principle of calorimetry or law of mixture when a body a higher temperature is brought in contact with another body a lower temperature, the heat lost by the hot body is equal to the heat gained by the colder body, provided no heat is allowed to escape to the surroundings. Heat gained = Heat lost

CALORIMETER
It is a device in which heat measurement can be made. It consists a metallic vessel with
a stirrer of the same material like copper or aluminium. The vessel is kept inside a wooden jacket which contain heat insulating material like glass wool etc. Thus the calorimeter is thermally insulated from surroundings. The inner and outer surfaces of jacket are highly polished to reduce the radiation loss. The lid is provided with two small holes for inserting a thermometer and a strirrer into the calorimeter. When two bodies at different temperature are mixed together in the calorimeter, heat is exchanged between the bodies as well as with the calorimeter.
According to law of mixture,
Heat lost by hot bodies = Heat gained by cold bodies It is also used to determine the specific heat and latent heat.

Physics Lab ManualNCERT Solutions Class 11 Physics Sample Papers

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To Determine Specific Heat Capacity of a Given Solid by Method of Mixtures

Physics Lab ManualNCERT Solutions Class 11 Physics Sample Papers

AIM
To determine specific heat capacity of a given solid by method of mixtures.

APPARATUS
A hypsometer, calorimeter, stirrer, a lid and outer jacket, given solid in power form or in small pieces, balance, weight box, two half degree thermometer, cold water, clamp stand.

THEORY
In hypsometer, the solid is heated uniformly above room temperature up to a fixed temperature and then solid is added to cold water in calorimeter.
Heat lost by solid = Heat gain by the water and calorimeter.

DIAGRAM

PROCEDURE

1. Put two thermometer A and B in a beaker containing water and note their reading. Take one of them, say A to be standard and find the correction to be applied to the other, say B.
2. Put thermometer B in copper tube of hypsometer containing the power of given solid. Put sufficient water in hypsometer and place it on a burner.
3. Weigh the calorimeter with stirrer and lid over it by the physical balance. Record it.
4. Fill about half of calorimeter with water at about temperature 5 to 8°C below room temperature. Now, weigh it again and record it.
5. Heat the hypsometer about 10 minutes till the temperature of solid remains steady.
6. Note the temperature of water in the calorimeter. Now, transfer the solid from hypsometer to the calorimeter quickly. Stir the contents and record the final temperature of the mixture.
7. Remove the thermometer A from calorimeter and weigh the calorimeter with its contents and lid.

OBSERVATIONS

CALCULATIONS

RESULT
Specific heat of given solid by method of mixture is…………cal g^-1 °C^-1

PRECAUTIONS

1. Sufficient solid power should be taken to cover the tip of thermometer properly.
2. Sufficient water should be taken in hypsometer.
3. Solid should be dropped quickly and gently.
4. Calorimeter should be polished from outside to avoid excessive radiation losses.
5. Temperature of cold water should not be below the dew point.

SOURCES OF ERRORS

1. Some heat is lost while transferring hot solid into calorimeter.
2. Some heat is lost in conduction, convection and radiation.
3. The bulbs of the thermometer may not be well inside the solid.

Note. To determine the specific heat of given liquid by method of mixture, instead of cold water, take the liquid whose specific heat is to be determined and proceeded as in the experiment done for determining the specific heat of solid. The specific heat of solid is already calculated.

VIVA VOCE

Question. 1. What is heat ?
Answer. It is the energy which produces the sensation of warmth.

Question. 2. Define specific heat of a substance.
Answer. It is-defined as the amount of heat required to raise the temperature of unit mass of substance through 1°C.

Question. 3. State the principle of calorimetery.
Answer. Whenever substances at different temperature are mixed so as to exchange the heat.
Heat lost – Heat gained.

Question. 4. Why do we use calorimeter made of copper ?
Answer. Copper has very low value of specific heat. Due to this a large size in temperature takes place,
when some quantity of heat is supplied to it.

Question. 5. Is heat gained always equal to heat lost ?
Answer. No, it is only correct if there is no chemical reaction takes place between its components.

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To Determine The Internal Resistance of a Given Primary Cell Using Potentiometer

AIM
To determine the internal resistance of given primary cell using potentiometer.

APPARATUS
A potentiometer, a battery (or battery eliminator), two one-way keys, a rheostat of low resistance, a galvanometer, a high resistance box, a fractional resistance box, an ammeter, a voltmeter, a cell (say Leclanche cell), a jockey, a set square, connecting wires and a piece of sand paper.
THEORY
The internal resistance of a cell is given by

where and l₂ are the balancing lengths without shunt and with shunt, respectively, and R is the shunt resistance in parallel with the given cell.

CIRCUIT DIAGRAM

PROCEDURE

1. Make the connections accordingly, as shown in circuit diagram.
2. Clean the ends of the connecting wires with sand paper and make tight connections according to the circuit diagram.
3. Tight the plugs of the resistance box.
4. Check the e.m.f. of the battery and cell and see that e.m.f. of the battery is more than that of the given cell, otherwise null or balance point will not be obtained (E’ > E).
5. Take maximum current from the battery, making rheostat resistance small.
6. To test the correctness of the connections. (Insert the plug in the key K₁ and note the ammeter reading. Take out 2000 Ω resistance plug from the resistance box. Place the jockey first at the end P of the wire and then at the end Q. If the galvanometer shows deflection in opposite directions in the two cases, the connections are correct).
7. Without inserting the plug in the key K₂ adjust the rheostat so that a null point is obtained on the fourth wire of potentiometer.
8. Insert the 2000 ohm plug back in its position in resistance box and by slightly adjusting the jockey near the previously obtained position of null point, obtain the null point position accurately, using a set square.
9. Measure the balancing length l₁ between this point and the end P of the wire.
10. Take out the 2000 ohms plug again from the resistance box R.B. Introduce the plugs in key K₁, as well as in key K₂. Take out a small resistance (1-5 Ω) from the resistance box R connected in parallel with the cell.
11. Slide the jockey along the potentiometer wire and obtain null point.
12. Insert 2000 ohms plug back in its position in R.B. and if necessary make further adjustment for sharp null point.
13. Measure the balancing length l₁ from end P.
14. Remove the plug keys at K₁ and K₂. Wait for sometime and for the same value of current (as shown by the ammeter), repeat the steps 7 to 13.
15. Repeat the observations for different values of R repeating each observation twice.
16. Record your observations as given below.

OBSERVATIONS

1. Range of voltmeter =………
   Least count of voltmeter = ………
   E.M.F. of battery (or battery eleminator) = ………
   E.M.F. of cell = ………
2.                                                                                           Table for Lengths
   

CALCULATIONS

1. For each set of observation find mean and l₂ and write in column 3c and 3f.
2. Calculate value of r for each set and write it in column 5.
3. Take mean of values of r recorded in column 5.

RESULT
The internal resistance of the given cell is………

PRECAUTIONS
Same as in Experiment 4 and other precautions are as:

1. The e.m.f. of the battery should be greater than that of the cell.
2. For one set of observation the ammeter reading should remain constant.
3. Current should be passed for short time only, while finding the null point.
4. Rheostat should be adjusted so that initial null point lies on last wire of the potentiometer.
5. Cell should not be disturbed during experiment.
6. Jockey should not be rubbed against the potentiometer wire.

VIVA VOCE

Question. 1. What do you understand by the e.m.f. of a cell?
Answer. Electromotive force i.e., e.m.f. of a cell is the potential difference across the terminals of the cell when the cell is in an open circuit i.e., when no current is drawn from the cell.

Question. 2. What is a potentiometer?
Answer. It is an instrument used to measure potential difference or e.m.f. of a cell.

Question. 3. Why is it called a potentiometer? ,
Answer. Because it measures potential difference between any two points of electric circuits.

Question. 4. What is the principle of a potentiometer?
Answer. It works On the principle that for a constant current, fall of potential along a uniform wire is directly proportional to its length.

Question. 5. What is potential gradient?
Answer.It is the fall of potential per unit length of the potentiometer wire. K =V/l.

Question. 6. How does the potential gradient vary along the length of the wire from end P to end Q?
Answer. Potential gradient is same throughout if the wire has uniform cross-section and material density.

Question. 7. What kind of source of e.m.f. should be used as auxiliary battery?
Answer. The e.m.f. of the source must be steady. A freshly charged accumulator should be used for this purpose.

Question. 8. What should be the order of magnitude of the e.m.f. of the auxiliary battery?
Answer. The e.m.f. of the auxiliary battery should be slightly greater than the e.m.f. of the individual cells.
(With battery of lesser e.m.f., null point will not be obtained on the potentiometer wire).

Question. 9. Why do we use a rheostat in the battery circuit?
Answer. To vary the potential gradient.

Question. 10. What purpose is served by varying the potential gradient?
Answer. A lower potential gradient gives more length of wire upto null point. Accuracy becomes more.

Question. 11. On what factors does the potential gradient depend?
Answer. Potential gradient depends directly on the strength of the current and resistance per cm
of the wire. K = Ip/A.

Question. 12. What is the preferred material used for making potentiometer wires?
Answer. Manganin. It is characterised by a low temperature coefficient of resistance and a high resistivity.

Question. 13. Why do we want the material of the potentiometer wire to have a low temperature coefficient of resistance?
Answer. There is invariably some heating of the potentiometer wire when a current flows through it. A material with a low temperature coefficient ensures that its resistance does not change much because of this heating.

Question. 14. Why don’t we use a copper wire as a potentiometer wire?
Answer. Copper has a high temperature coefficient of resistance and low resistivity and hence a copper wire will have a low resistance. There would then be no appreciable potential drop across the ends of the potentiometer wire.

Question. 15. Which materials can be used for making potentiometer wire?
Answer. The alloys like manganin, constantan etc.

Question. 16. What do you mean with sensitivity of a potentiometer?
Answer. Sensitivity of a potentiometer is the smallest potential difference that it can measure.

Question. 17.Why is a ten-wire potentiometer more sensitive than a four-wire one?
Answer.The potential gradient, under same conditions, decreases with an increase in the length of the potentiometer wire. Hence, a 10-wire potentiometer (having a smaller potential gradient) is more sensitive than a 4-wire one.

Question. 18.How will you know that the apparatus can give a null point?
Answer.The jockey is put at the two ends of the potentiometer wire. The deflection in the galvanometer must be in opposite directions.

Question. 19.What will you conclude if the deflection of the galvanometer is in same direction at both the ends?
Answer.The reasons may be

1. the positive terminals of all the cells are not connected at one point.
2. the potential difference between the ends of the wire is less than the e.m.f. of the cell which is to be measured.
3. the e.m.f. of driving cell is less than the e.m.f. of each cells whose e.m.f. to be com¬pared or measured.

Question. 20. How are above situations corrected?
Answer.

1. Connections of positive terminals are checked.
2. Current in potentiometer wire is increased.
3. E > E₁ or E >E₂.

Question. 21. Under what conditions galvanometer will give no deflection when jockey is put on the wire?
Answer. The reason may be

1. the cell whose e.m.f. is being measured, is totally damaged to have infinite internal resistance.
2. connecting wire in the galvanometer circuit may be broken.

Question. 22. Under what conditions deflection in the galvanometer is shaky?
Answer. The reason may be

1. the e.m.f. of the battery or the cells may be fluctuating.
2. the circuit has a loose contact somewhere.

Question. 23. Why should we use a sensitive galvanometer?
Answer. A sensitive galvanometer will respond to even a small departure from the exact balance point and will hence enable us to locate the balance point with greater precision.

Question. 24. Why do we need a protective series resistance/shunt along with a sensitive galvanometer?
Answer. To prevent it from damage from the flow of excessive currents that may exist when the jockey is far from the balance point.

Question. 25. Does the use of a series protective resistance/shunt effect the location of the balance point?
Answer. No; however, it makes the galvanometer less sensitive. We therefore, remove it once we are near the balance point.

Question. 26. Why do we not want the balance point to be on the first wire, say?
Answer. The smaller is the balancing length, the greater is the relative uncertainty in its location.

Question. 27.What is the merit of a potentiometer over a voltmeter in measurement of e.m.f. of a cell?
Answer.E.M.F. measured by potentiometer is more accurate because the cell is in open circuit, giving no current.

Question. 28.How will you determine specific resistance of potentiometer wire material?
Answer.We measure V across a known length l of the wire. We measure diameter D of wire and

Question. 29.What do you mean by internal resistance of a cell?
Answer.It is the resistance offered by the electrolyte to the flow of ions to their respective electrodes.

Question. 30.Is there any change in the internal resistance of cell in open and closed circuit?
Answer.

Question. 31.On what factors does the internal resistance of a cell depend?
Answer.Internal resistance of a cell depends upon :

1. Distance between electrodes and is directly proportional to its
2. Facing surface area of the electrodes in electrolyte and is inversely proportional to it
3. Nature of electrolyte and is inversely proportional to its specific conductivity
4. Temperature increases, the internal resistance decreases and vice-versa.
5. Internal resistance increases with the use of cell.

Question. 32.Does the internal resistance depend on the current drawn from the cell?
Answer.Yes, the internal resistance usually increases as more current is drawn from the cell.

Question. 33.Can we find the internal resistance of an accumulator or secondary cell?
Answer.No. the internal resistance of an accumulator is so small (= 0.01 Q) that this method cannot be used.

Question. 34.Why a cell should not be disturbed during experiment?
Answer.Disturbing of the cell may change the factors (Q. 31 above) on which the internal resistance of the cell depends.

Question. 35.What other measurements can be made by a potentiometer?
Answer.A potentiometer can be used for measuring small thermo e.m.f. It can also be used for calibrating voltmeter and ammeter. It can be used to measure and control stress, temperature, radiation, pH, frequency etc.

Question. 36.Can you measure e.m.f. by a voltmeter?
Answer.No. The voltmeter measure the terminal potential difference of a cell because it draw some current
V = E -Ir, when  I≠0, then V < E.

Question. 37.Which voltmeters can be used to measure the e.m.f. of the cells?
Answer.Electric voltmeter. Vaccum tube volt meter (VTVM) afters nearly infinite resistance. So the current drawn is minimum, nearly zero. These two voltmeter are act as ideal voltmeter.

Question. 38. Is the terminal potential difference (V) and e.m.f. (E) of a cell different? Explain.
Answer.

Question. 39. Does the at position of balance point (null point) mean no current through the potentiometer?
Answer. No. the current always flow in potentiometer wire. These is no current in galvanometer f because there is no current drawn from the cell whose e.m.f. is to be measured or compared.

Question. 40. Does the potentiometer is used to determine the internal resistance of
(i) primary cell (ii) secondary cell?
Answer. The potentiometer is used to determine the internal resistance of primary cell only but not secondary cell because of very small resistance (0.02 Q).

Question. 41. What are the factors on which the e.m.f. of a cell depends?
Answer.

1. Nature of electrodes,
2. Nature of electrolyte,
3. concentration of electrolyte,
4. Temperature of electrolyte.

Question. 42. Why is a potentiometer preferred over a voltmeter for measuring the e.m.f. of cell?
Answer. A potentiometer draws no current from the cell whose e.m.f. is to be measured. On the other hand, the voltmeter always some current. Thus e.m.f. measured by voltmeter will be slightly less than the e.m.f. measured by potentiometer.
V = E -Ir

Question. 43. Why do we prefer a potentiometer with a longer bridge wire?
Answer. When the bridge wire is longer, the potential gradient is smaller. Smaller the potential gradient, more is the sensitivity of potentiometer wire.

Question. 44. What are the factors on which internal resistance of a cell depends.
Answer.

1. Nature of electrodes
2. Nature of electrolyte
3. Concentration of electrolyte
4. Temperature of electrolyte
5. Distance between the electrodes
6. The area of electrodes immered in electrolyte.

Question. 45. Can we consider the potentiometer as an ideal voltmeter?
Answer. Yes. At null point, the potentiometer does not draw any current. Hence it measure the emf. The potentiometer is equivalent to an ideal voltmeter.

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Wave Motion and Velocity of Waves

WAVE MOTION
It is a disturbance which travels in a material medium through the repeated periodic motion of the particles of the medium about their mean position. The disturbance being handed over from one particle to the next, resulting in a phase difference between their motion through which energy and momentum is transferred.

CHARACTERISTICS OF A WAVE MOTION
The important characteristics of a wave motion are :
1. In wave motion, only the disturbance or energy spreads out from the source through the repeated periodic oscillation of the particles of medium about their mean position, without any bodily movement of the particles of the medium.
2. There is a definite phase difference between every two consecutive particles.
3. The velocity of wave motion is different from velocity of the particle. The wave moves ahead with a constant velocity in a homogeneous medium—whereas the particles vibrate about mean position simple harmonically.
4. For the propagation of mechanical wave, the medium must possess the properties of inertia, elasticity, uniform density and minimum friction amongst its particles.

TYPES OF WAVE MOTION
Wave motion has two types :
1. Transverse wave motion
2. Longitudinal wave motion.
1. Transverse Wave Motion. In transverse wave motion, particles of the medium vibrate perpendicular to the direction of propagation of the wave (Fig).

Examples: waves in strings, light waves, etc. Mechanical transverse waves are produced only in solids and on liquid surfaces.
2. Longitudinal Wave Motion. In longitudinal wave motion, particles of the medium vibrate along the direction of propagation of the wave (Fig).

Examples : waves in springs, sound waves, etc.
Longitudinal wave are produced in solids, in liquids and also in gases.

SOME USEFUL TERMS AND THEIR DEFINITIONS
The following terms are commonly used in description of a wave motion :
Amplitude. The maximum displacement of a vibrating particle, on either side of its mean position, is called its amplitude.
Vibration. The motion of the vibrating particle from its mean position to one extreme, then to other extreme (through its mean position) and back to mean position, is called one vibration.
Time period (or period). The time taken by a particle to complete one vibration, is called its time period. It is represented by the symbol T.
Frequency. The number of vibrations made by a particle in a unit time (one second), is called its frequency. It is represented by the symbol v. (nu)
By definition, v = 1/T or vT = 1.
Phase. Phase of a vibrating particle at any instant is the state of the particle, as regards its position and direction of motion at that instant. It is represented in terms of angle or time.
Phase difference. Two vibrating particles, having different positions and directions of motion at same instant, are said to have a phase difference.
Crest. The region of maximum displacement on the positive side (upper side) of a transverse wave, is called crest. In Fig. C denotes the crest in a transverse wave.
Trough. The region of maximum displacement on the negative side (lower side) of a transverse wave, is called trough. In Fig, T denotes the trough in a transverse wave.

Compression. The region of maximum density of the medium in a longitudinal wave, is called a compression. In Fig, C denotes the compression in a longitudinal wave.
Rarefaction. The region of minimum density of medium in a longitudinal wave, is called rarefaction. In Fig, R denotes the rarefaction in a longitudinal wave.

Wavelength. The distance travelled by the disturbance during the time period of the vibrating particle, is called wavelength (length of the wave). It is denoted by the Greek symbol X.
The wavelength is also equal to the distance between two consecutive crests or troughs in a transverse wave (Fig) or between two consecutive compression’s or rarefaction’s in a longitudinal wave (Fig).
In general, wavelength is the distance between any two consecutive particles of the medium vibrating in the same phase.

RELATION BETWEEN FREQUENCY AND WAVELENGTH OF A WAVE
Wave frequency is the number of waves produced per second. It is equal to the frequency of the particle (or the body) whose vibrations produce the waves.
If a vibrating body has time period T and frequency v, then wave frequency also becomes v. Let this body produce waves of length λ .

VELOCITY OF TRANSVERSE WAVE ALONG A STRETCHED SPRING (DERIVATION BY METHOD OF DIMENSIONS)
Let a string having mass m per unit length (linear mass density) be stretched by a force of tension T. Let a transverse wave travel along the string with a velocity υ.

VELOCITY OF LONGITUDINAL WAVES THROUGH AN ELASTIC MEDIUM
Let an elastic medium have density ρ and elastic constant E. Let a longitudinal wave travel through it with a velocity υ.

VARIATION OF VELOCITY OF SOUND DUE TO CHANGE IN DIFFERENT FACTORS
Variation of velocity due to change in temperature
The velocity of sound in air varies directly as the square root of the absolute temperature of air.

It means that the velocity of sound varies inversely as the square root of the density of the medium.
Since density of oxygen is 16 times the density of hydrogen, velocity of sound in oxygen is one-fourth of that in hydrogen.
Variation of velocity due to humidity of the medium
Density of water vapours (humidity) is 0.625 of the density of the dry air. Hence humidity decreases density of the air.
It is due to this reason that after calmness during rains, every sound heard appears loud due to increased velocity.
Variation of velocity due to wind
When sound waves travel in air, air molecules do not move (characteristic of wave motion). When wind blows, air molecules move. This produces variation in velocity of sound waves.
If wind has velocity w, velocity of sound waves in direction of wind becomes, υ + w and the same in opposite direction becomes υ – w. (It is assumed that w < υ).

VIVA VOCE

Question. 1. Define transverse wave motion.
Answer. In transverse wave motion, particles of the medium vibrate perpendicular to the direction of the propagation of the wave.

Question. 2. Give examples of transverse wave motion.
Answer. Examples are : waves produced in strings, light waves, waves on surface of water, E.M.W.

Question. 3. In which type of medium transverse waves are produced ?
Answer. Transverse waves are produced only in solids and on liquid surfaces.

Question. 4. Define longitudinal wave motion.
Answer. In longitudinal wave motion, particles of the medium vibrate along the direction of propagation of the wave.

Question. 5. Give examples of longitudinal wave motion.
Answer. Examples are : waves produced in springs, sound waves.

Question. 6. In which type of medium longitudinal waves are produced ?
Answer. Longitudinal waves are produced in solids, in liquids and also in gases.

Question. 7. Define amplitude.
Answer. The maximum displacement of a vibrating particle, on either side of its mean position, is called its amplitude.

Question. 8. Define vibration.
Answer. The motion of the vibrating particle from its mean position to one extreme, then to other extreme (through its mean position and back to mean position), is called one vibration.

Question. 9. Define time period (or period).
Answer. The time taken by a particle to complete one vibration, is called its time period. It is denoted by T.

Question. 10. Define frequency.
Answer. The number of vibrations made by a particle in a unit time (one second), is called its frequency. It is denoted by v.

Question. 11. Define phase.
Answer. Phase of a vibrating particle at any instant is the state of the particle, as regards its position and direction of motion at that instant.

Question. 12. How is the phase represented ?
Answer. The phase is represented in terms of angle or time.

Question. 13. How are phase angle and phase time related ?
Answer. A phase angle of 2n is equal to a phase time T.

Question. 14. What is phase difference ?
Answer. Two vibrating particles having different positions and directions of motion at same instant, are said to have a phase difference.

Question. 15. Define a crest.
Answer. The region of maximum displacement on the positive side of a transverse wave, is called crest.

Question. 16. Define a trough.
Answer. The region of maximum displacement on the negative side of a transverse wave, is called trough.

Question. 17. Define a compression or condensation.
Answer. The region of maximum density of the medium in a longitudinal wave, is called a compression or a condensation.

Question. 18. Define a rarefaction.
Answer. The region of minimum density of the medium in a longitudinal wave, is called rarefaction.

Question. 19. Define a wavelength.
Answer. The distance travelled by the disturbance dining the time period of the vibrating particle, is called wavelength (length of the wave). It is denoted by symbol X.

Question. 20.Give definition of wavelength.
Answer.The distance between two consecutive crests or troughs in a transverse wave or between two consecutive compression’s or rarefaction’s in a longitudinal wave, is also called a wavelength.
Or
The distance between any two consecutive particles of the medium in same vibrating phase, is also called a wavelength.

Question. 21. Define wave frequency.
Answer. The number of waves produced per second, is called wave frequency. It is equal to the frequency of the particle or the body, whose vibrations produce the waves.

Question. 22. Give relation between wave velocity, wave frequency and the wavelength.
Answer. The relation is,
Wave velocity = Wave frequency x Wavelength.

Question. 23.What was the reason for Newton’s formula to be wrong ?
Answer. Newton’s assumption for isothermal changes in the medium (air) was wrong. Actually changes are adiabatic.

Question. 24.What is an isothermal change ?
Answer. A change in pressure and volume of a gas at the same temperature, is called an isothermal change.

Question. 25.What are the conditions for a change to be isothermal ?
Answer. The change must be slow and in conducting surroundings.

Question. 26.What is an adiabatic change ?
Answer. A change in pressure and volume of a gas, without any heat exchange with surrounding, is called an adiabatic change.

Question. 27.What are the conditions for a change to be adiabatic ?
Answer.The changes must be quick and in non-conducting surroundings.

Question. 28.What mistake of Newton was pointed out by Laplace ?
Answer. Laplace pointed out the changes in medium are adiabatic and not isothermal as assumed by Newton.

Question. 29.How does velocity of sound vary with pressure of medium (air) ?
Answer. There is no variation of velocity of sound in air due to change in pressure of medium (air).

Question. 30.How does velocity of sound vary with density of medium (air) ?
Answer. Velocity of sound varies inversely as the square root of the density of the medium (air).

Question. 31.What is the ratio of velocity of sound in hydrogen to that in oxygen under similar conditions ?
Answer. The velocity of sound in hydrogen is four times of that in oxygen.

Question. 32.How does velocity of sound vary with humidity ?
Answer. Velocity of sound increases with increase in humidity in air. Sound travels faster after rains, hence it appears louder.

Question. 33.How does velocity of sound vary with wind velocity ?
Answer. Velocity of sound increases in direction of wind and decreases in opposite direction.

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NCERT Solutions for Class 8th Sanskrit Chapter 11 सावित्री भाई फुले 

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NCERT Solutions for Class 8th Sanskrit Chapter 12 कः रक्षति कः रक्षितः 

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NCERT Solutions for Class 8th Sanskrit Chapter 13 हिमालयः 

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NCERT Solutions for Class 8th Sanskrit Chapter 14 आर्यभटः 

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NCERT Solutions for Class 8th Sanskrit Chapter 15 प्रहेलिकाः  

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Galvanometer, Ammeter and Voltmeter

GALVANOMETER
A galvanometer is a device (instrument) used for detecting feeble electric voltage, currents in a circuit. It has a coil pivoted (or suspended) between concave pole faces of a strong laminated horse shoe magnet. When an electric current passes through the coil it deflects. Its deflection is noted by attaching a pointer to the coil (or by using a lamp and scale arrangement). The deflection is proportional to the current passed.
The galvanometer coil has a moderate resistance (about 100 ohms) and the galvanometer itself has a small current carrying capacity (1 mA).

MOVING COIL (POINTER TYPE) GALVANOMETER
(a) Construction: (Refer Section 2.13).
(b) Theory: Let,

where G = K/NAB and is called galvanometer constant. Knowing G and observing θ,I can be calculated.
(c) Figure of merit: If is defined as the current required to produce unit deflection in the galvanometer. It is represented by the symbol k.

(d) Current sensitivity: Deflection produced due to flow of unit current in its coil, is called current sensitivity of the galvanometer. It is represented by the symbol S_I

(e) Voltage sensitivity: Deflection produced due to current produced by unit potential difference between ends of the galvanometer coil, is called voltage sensitivity of the galvanometer. It is represented by the symbol S_v.

AMMETER (AMPERE METERE)
An ammeter is a device (instrument) used for measuring large electric currents in ‘ circuits. For this purpose, it is put in series with the circuit in which the current is to be measured.
For accurate measurement, an ammeter must have following two properties:

1. A very small resistance (zero in ideal case).
2. A very large current carrying capacity.

It is done by connecting low resistance in parallel with the coil of the galvanometer. This parallel low resistance is called shunt. The shunt reduces the overall resistance of the ammeter and increases its current carrying capacity.

VOLTMETER
A voltmeter is a device (instrument) used for measuring electric potential difference between two points in a circuit. For this purpose, it is put in parallel with that branch of circuit, at the ends of which the potential difference is to be measured.
For accurate measurements a voltmeter must have following two properties:

1. A very large resistance (infinite in ideal case).
2. A very small current carrying capacity.

It is done by connecting a high resistance in series with the coil of the galvanometer. The series high resistance increases the overall resistance of the voltmeter and reduces its current carrying capacity.

RESISTANCE OF A GALVANOMETER BY HALF DEFLECTION METHOD
The connections for finding the resistance of a galvanometer by half deflection method are shown in  When key K₁ is closed and K₂ open, then current flowing through the galvanometer is given by

where E is the E.M.F. of the cell, R is resistance from the resistance box, G is the galvanometer resistance and 0 is the deflection in galvanometer for current I, k is proportionality constant (called figure of merit).
When key Kg is also closed and the value of shunt resistance S is so adjusted that deflection in the galvanometer becomes θ/2 then resistance of the parallel combination of G and S is GS/G+S
and current in the circuit is

FIGURE OF MERIT OF A GALVANOMETER
It is defined as the current required to produce a deflection of one division in the scale of galvanometer. It is represented by the symbol k. (It is reciprocal of current sensitivity).
When current I produces a deflection 0 in the galvanometer, then figure of merit is given by using Eq. (1),

CONVERSION OF A GALVANOMETER INTO AN AMMETER
A galvanometer can detect only small currents.
For measuring large currents (to convert into ammeter), a small resistance called shunt resistance (S) is connected in parallel across the galvanometer. Out of total current I only a small current I_g flows through the galvanometer for full scale deflection and remaining I-I_gby passes through the shunt S. Since G and S are parallel to each other therefore, potential difference across both is same.

CONVERSION OF A GALVANOMETER INTO A VOLTMETER
(a) Introduction: A voltmeter is a high resistance galvanometer, used for measuring the potential difference between two points of an electric circuit. It is always connected in parallel with those two points. The resistance of a galvanometer is made very large so that its measuring range increases and when connected in parallel to a circuit, it draws a feeble current and does not change the magnitude of current flowing in the main circuit. Hence to convert a galvanometer into a voltmeter a suitable high resistance is connected in series with the galvanometer, as resistance of a galvanometer, is very low .

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Vibration of Strings and Air Columns

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SUPERPOSITION OF WAVES AND SUPERPOSITION PRINCIPLE
When two or more waves arrive simultaneously in certain region of a medium, the particles of the medium are subjected to two or more simultaneous displacements, one due to each wave. The resultant displacement is the vector sum of full the displacements (because ( displacement is a vector) and a new wave motion is produced.
(a) Superposition of waves. The phenomena of intermixing of two or more waves to produce a new wave, is called superposition of waves.
(b) Superposition principle. The superposition principle states that the resultant displacement of a particle is equal to the vector sum of the individual displacements given to it by the superposing waves.

STATIONARY WAVES
Definition. Superposition of two travelling waves of same frequency and same amplitude and travelling with same velocity in opposite directions, produces stationary waves.
Nodes and Antinodes. In some regions, particles of medium have zero displacement and maximum strain. These regions are called nodes. They are denoted by N in Fig.

In some other regions, particles of medium have maximum displacement and zero strain. These regions are called antinodes. They are denoted by A in Fig. They are situated between nodes.
The distance between two consecutive nodes or two consecutive antinodes is equal to half the wavelength of the stationary wave. The distance between a node and the nearest antinode, is equal to one-quarter of the wavelength of the stationary wave. (i.e., NN = AA = λ/2, NA = λ/4).

PRODUCTION OF TRANSVERSE STATIONARY WAVES IN STRETCHED STRING
Let a string be fixed at its ends A and B [Fig.]. Let it be plucked at C in the middle [Fig]. A disturbance is produced.
When the string is left free, it moves downward and disturbances move towards ends A and B. These disturbances are reflected from the fixed ends A and B and travel back in the string. Along the string, incident and reflected disturbances (waves) get superposed. Their superposition produces stationary waves in the string. The stationary waves are transverse because the string moves from C to D and back from D to C, whereas waves travel along the string from A to B and B to A.

Nodes are produced at the fixed ends A and B, where displacement is zero and strain is maximum. Antinode is produced in the middle (where the string was plucked) because there the displacement is maximum and strain is zero.
If the string be held at C and plucked at E—middle point of C and B [Fig. (c)] and then left free, it vibrates in two segments. Similarly, it can be made to vibrate in three segments [Fig. (d)]. Figs. (b), (c) and (d) represent different modes of vibration of a string.

FUNDAMENTAL, HARMONICS AND OVERTONES
When a body is vibrated, it vibrates with more than one frequencies. All the frequencies are an integral multiple of some least frequency.
The least frequency is called first harmonic or fundamental. Frequency double than the fundamental is called second harmonic, triple the fundamental is called third harmonic and so on. In general, a frequency n times the fundamental is called nth harmonic.
All frequencies, other than the fundamental are called overtones. They are called first, second, third overtones in order of their increasing frequency after the fundamental. Thus second harmonic becomes first overtone and third harmonic becomes second overtone. In absence of second harmonic, third harmonic becomes first overtone.

TIME PERIOD AND FREQUENCY OF TRANSVERSE VIBRATIONS OF A STRETCHED STRING
Let a string of length l and mass per unit length m be fixed at its two ends and stretched by a tension T [Fig.(a)]. Let it be plucked in the middle at C and left free [Fig.(b)]. Transverse stationary waves are produced in it and they travel along the length of the string. The velocity of these transverse waves is given by the formula,

LAWS OF TRANSVERSE VIBRATIONS OF A STRETCHED STRING
We know that a string of length l having mass per unit length m and stretched with a tension T, has fundamental frequency of vibration v given by

PRODUCTION OF LONGITUDINAL STATIONARY WAVES IN CLAMPED RODS
Introduction. When a clamped rod is rubbed along its length by a resined cloth, longitudinal waves are produced in it. These waves reflect from clamped r region and get superposed with the incident waves. As a result, longitudinal stationary waves are produced in the clamped rod.
Different Cases
1. Rod clamped at one end. The clamped end becomes node (N) and free end becomes antinode (A) as shown in Fig.

The length (l) of the rod is equal to quarter wavelength of the longitudinal waves

2. Rod clamped in the middle. The clamped part becomes node (N) and both the free ends antinode (A, A), as shown in Fig.

The length (l) of the rod is equal to half wavelength of the longitudinal waves

3. Rod clamped at both the ends. The clamped ends become node (N, N) and the middle point becomes antinode (A), as shown in Fig.
The length (l) of the rod is equal to half wavelength of the longitudinal waves.

4. Rod clamped at a point at quarter length from one end. The clamped point becomes node (N), and the two free ends become antinodes (A, A). Besides one more antinode is formed in the middle and one more node is formed at a point one quarter length away from the other end. It is shown in Fig.
The length (l) of the rod is equal to the wavelength of the longitudinal wave i.e., l=λ .

TUNING FORK
Introduction. It is a source of a standard frequency very useful in sound experiment where a frequency standard is needed.
Principle. It works on the principle of vibration of a clamped (or supported) rod.
Diagram.

Construction. It is a U-shaped bar ABODE made of steel with a handle CF attached at the bend (C). Thus, it has a shape of letter Y. Its free ends A and E are called prongs. Its frequency is written near the bend.
Working. When one of the prong is struck with a soft rubber pad, the prongs begin to vibrate. This sets the whole tuning fork into vibrations as shown in Fig.
From Fig., it is quite clear that vibrations of prongs A and E are transverse (perpendicular to AC to EC), whereas vibrations of handle CF are longitudinal (along CF). It is for this reason that vibrations of prongs stop just by touching them by a finger, whereas vibrations of handle continue even when it is held tightly in hand.
Application. When vibrated, tuning fork vibrates with its frequency (written near the bend). It then produces in air sound waves of same frequency as its own frequency.
These vibrations of known frequency can be used either with a sonometer for verifying laws of transverse vibrations of a stretched string or with a resonance tube for determination of velocity of sound in air.

SONOMETER
Diagram.

Construction. It is a hollow and rectangular wooden box of length more than a metre. It has a hook fixed over its board at one end and a friction less pulley at the other end. A string has one end tied to the hook and passes over the pulley. From other end of the string is suspended a hanger in which slotted weights can be added. The weights give tension to the string. Two wooden prisms (bridges) P, P are put over the board. The length of the string is adjusted between edges of these two prisms. Two holes are provided in one of the long vertical wall. These holes allow the vibrations in the air inside the sonometer to outside air to be received by the experiementer.
Working. A known weight is suspended from the hanger to give a known tension T to the string. The tuning fork (T) of unknown frequency v is vibrated and put over sonometer board. The length of string between edges is so adjusted that it vibrates in resonance with tuning fork. (When this happens, a paper rider R kept over the string in the middle of the edges falls down). The length l of the string between the edges is noted.
Calculation. If m be the mass per unit length of the string, then velocity of transverse waves through string is given by

The length l of the string is equal to half the wavelength of stationary waves having frequency equal to frequency (v) of the timing fork.

FREE, FORCED AND RESONANT VIBRATIONS
(a) Free vibrations. Vibrations of a vibrating body, continued by itself, are called free vibrations. In this case, the body vibrates with its own frequency, called natural frequency.
Example. In sonometer experiment, vibrations of tuning fork are free vibrations.
(b) Forced vibrations. Vibrations of a vibrating body under a periodic force, are called forced vibrations. In this case the body vibrates with the frequency of the applied periodic force and only so long as the force acts. Once the periodic force is withdrawn, the body either stops vibrating or vibrates with its own frequency.
Example. In sonometer experiment, vibrations of sonometer board are forced vibrations.
(c) Resonant vibrations. Vibrations of a vibrating body, under the influence of a second vibrating body of same frequency kept near it, are called resonant vibrations. The phenomena is called resonance. In this case, the first vibrating body will continue vibrating even when the second body is removed.
Example. In sonometer experiment, vibrations of sonometer wire, when paper rider falls, are resonant vibrations. (The wire is in resonance with the tuning fork. Both have same frequency).

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To Study the Relation Between Frequency and Length of a Given Wire Under Constant Tension Using Sonometer

AIM
To study the relation between frequency and length of a given wire under constant tension using sonometer.

APPARATUS
A sonometer, a set of eight tuning forks, 1\2 kg hanger, seven 1\2 kg slotted weights, rubber pad, paper rider, metre scale, screw gauge.

THEORY
If stretched wire (string) vibrates in resonance with a tuning fork of frequency v, then the string also has same frequency v.
If the string has a length l, diameter D, material of density p and tension T, then

DIAGRAM

PROCEDURE (To find the relation between frequency and length)

1. Place the sonometer on the table as shown in Fig.
2. Test the pulley and make it frictionless by oiling (if necessary).
3. Put suitable maximum weight in the hanger.
4. Move wooden bridges P, outward to include maximum length of wire (AB) between them.
5. Take a tuning fork of least frequency from among the set. Strike its prong with a rubber pad to make it vibrate. Bring the tuning fork near your ear.
6. Pluck the wire AB from the middle and leave it to vibrate.
7. Listen sound produced by tuning fork and wire and judge which has less frequency (sound which is grave and has low pitch, has less frequency).
8. Since the long wire may have less frequency, decrease its length by moving the bridges inwardly. Check the frequencies again.
9. Go on decreasing the length till frequency of vibrating wire AB becomes equal to the frequency of the tuning fork.
10. Put an inverted V shape paper rider R on the wire AB in its middle. Vibrate the tuning fork and touch the lower end of its handle with sonometer board. The wire AB vibrates due to resonance and paper rider falls.
11. Note the length of the wire AB between the edges of the two bridges and record it in ‘length decreasing’ column.
12. Bring the two bridges closer and then adjust the length of the wire by increasing it little by little till rider falls.
13. Note the length of the wire and record it in ‘length increasing’ column.
14. Take the remaining five tuning forks, one by one, in order of increasing frequency and repeat steps 5 to 13.
15. Record your observations as given below.

OBSERVATIONS
Constant tension on the wires, T =………….kg.
Table for frequency and length

CALCULATIONS

RESULT

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To Determine Resistance of a Galvanometer By Half-deflection Method And to Find its Figure of Merit

AIM
To determine resistance of a galvanometer by half-deflection method and to find its figure of merit.

APPARATUS
A weston type galvanometer, a voltmeter, a battery or battery eliminator, two (10,000 Ω and 200 Ω) resistance boxes, two one-way keys, a rheostat, a screw gauge, a metre scale, an ammeter of given range, connecting wires and a piece of sand paper.

THEORY

CIRCUIT DIAGRAM

PROCEDURE
(a) Resistance of galvanometer by half deflection method

1. Make the connections accordingly as shown in circuit diagram.
2. See that all plugs of the resistance boxes are tight.
3. Take out the high resistance (say 2000 Ω) from the resistance box R and insert the key K₁ only.
4. Adjust the value of R so that deflection is maximum, even in number and within the scale.
5. Note the deflection. Let it be θ.
6. Insert the key also and without changing the value of R, adjust the value of S, such that deflection in the galvanometer reduces to exactly half the value obtained in step 5 i.e., θ/2.
7. Note the value of resistance S.
8. Repeat steps 4 to 7 three times taking out different values of R and adjusting S every time.
   (b) Figure of merit
9. Take one cell of the battery (battery eliminator) and find its E.M.F. by a voltmeter by connecting +ve of the voltmeter with +ve of the cell and -ve of voltmeter with -ve of the cell. Let it be E.
10. Make connections as in circuit diagram.
11. Adjust the value of R to obtain a certain deflection 0 (say 30 divisions) when the circuit is closed.
12. Note the values of resistance R and deflection θ.
13. Now change the value of R and note the galvanometer deflection again.
14. Repeat the steps 9 to 13 with both cells of the battery with different voltages like 2, 4, 6, 8, volts from battery eliminator.
15. Find the figure of merit k using the formula.

OBSERVATION AND CALCULATION

1.                                    Table for resistance of the galvanometer by half deflection method
   
2.                                                                                    Table for figure of merit
   
   

RESULT

1. Resistance of given galvanometer = …….. Ω
2. Figure of merit of given galvanometer = A/dn.

PRECAUTIONS

1. All the connections should be neat, clean and tight.
2. All the plugs in resistance boxes should be tight.
3. The e.m.f. of cell or battery should be constant.
4. Initially a high resistance from the resistance box (R) should be introduced in the circuit (otherwise for small resistance an excessive current will flow through the galvanometer or ammeter can be damaged).

SOURCES OF ERROR

1. The screws of the instruments may be loose.
2. The plugs of resistance boxes may not be clean.
3. The e.m.f. of battery may not be constant.
4. The galvanometer divisions may not be of equal size.

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