Determination of the specific resistance of a wire using a metre bridge



Abstract

At first, we should just connect both ends of the wire tightly. The apparatus has 5 places for the connections. All gaps for connections are found above the meter bridge wire; two on either sides and one in the middle. Then we should Connect a known resistance on one side and unknown resistance on the other this fills 4/5 gaps left for connections. In the remaining gap, we should connect a galvanometer, high resistance and jockey all in series. Then the jockey should be slide over the meter bridge wire and note down the reading for which we get zero deflection in galvanometer.[1] Using metre bridge is very useful and very easy method for determination of the specific resistance of a wire. The specific resistance of the wire is determined by this method. It returns a result of 11×10-6 Ω with an error of 15.54%  The experiment has increase practical impact in many branches of electrical engineering. So, this technique is very useful for determine the specific resistance of a wire.

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Introduction:

Resistance: When the electrons travel through wires, they experience some sort of hindrances in their way. Resistance, as the name suggests is the hindrance or the obstruction in the flow of charge. When an electron moves from one terminal to another, its way is not direct. In fact, it  is a diverted path, which includes various collisions encountered with fixed atoms within the conductor. The electric potential established across the two conductors encourages the charge, it is the resistance that discourages or disrupts it.[2] 

Fig. 01 
Specific Resistance: The Specific resistance of a material is the resistance offered by a one foot long wire of the material with a diameter of one MIL. There is a close relationship between the resistance and specific resistance of the material. The resistance of a wire is directly proportional to the specific resistance of the material. The specific resistance of a material is denoted by the letter ‘K’.[3]   
Specific resistance of materials: We discuss some of the basic facts of specific resistance:
        The specific resistance of materials is independent of length and cross-sectional area.
        Specific resistance is a constant entity. Its value remains constant for every individual substance.
        Any sort of change in length or cross-sectional area may bring about a change in the resistance of a wire as we have the relation R= pL /A, where p is the specific resistance. But, the specific resistance of the wire in all above conditions is same. Only a change in temperature can bring about a change in the specific resistance.
        Whenever there is a change in area or length, it brings about a corresponding change in R in such a way that specific resistance ‘p’ always remains constant.[4]   


Theory:

           
                                                                    Fig. 02
In the arrangement as shown in Fig. 02 if X and R be the unknown resistances respectively and l be the distance of the null point measured from the left end A of the metre bridge, then by the principle of the Wheatstone’s network we get,

Where x and y are end errors.
When the resistances X and R are interchanged, we get,
                                  

The mean of (1) and (2), after end correction, give the value of unknown resistances.
If now L be the length of the experimental wire in centimetres then 

Where ρ is the specific resistance 9f the material of the wire and r is the radius of the cross-section of the wire. Thus ρ may be determined after measuring X, r and L.[5]

Apparatus:

        Metre bridge
        Leclanche’s cell (E)
        Zero centre galvanometer (G)
        Rheostat (Rh)
        Commutator (K)
        Resistance box (R)
        The specimen wire (X)  Connecting wires  Screw-gauge etc.

Experimental Data:

 

     M.S

     V.S

     V.C

Total in cm

     d/2

   Mean

      a)

      0

     36

    0.01

    0.025

   0.125

0.01125

      b)

      0

     31

    0.01

    0.02

   0.01


Reading of the balance point:

Known

Resist-ance

R ohm

         Position of

   Balance point (for l)

             100 - l

     X

   ohms

   Mean

Unknown

Resistance

      X

Known

Resistance

     R

Direct

Reverse

Mean

0.2

Left

Right

47.5

47

47.25

52.75

0.01255

 

 

0.101885

Right

Left

38.5

39.5

39

61

7.19×10-3

0.4

Left

Right

31.05

30.6

31.05

68.95

0.02498

Right

Left

54.5

55.8

55.15

44.85

0.0138

Calculation:

 

Percentage of error:

Result:

The specific resistance of the wire measured by using the metre bridge is 11.74×10-6 ohm-cm with an error of 15,54%

Discussion:

While observing the experiment some problems were found due to some reasons. They are below,
        The wire used may not be uniform area of cross-section. So, it is essential to choose a suitable wire.
        Effect of end resistance due to copper strips, connecting screws, may affect the measurement. So, it is essential for taking proper measurement. 
        All the connections and plugs must be tight. 
        Jockey must be moved gently over the metre bridge wire. 
        Null point may be far away from the middle. 
        It is essential to take determine the diameter of the wire accurately.
        E.M.F of the cell must check before starting the experiment. The E.M.F of cell must be constant. 
        The length measurements l and l΄ may have error if the metre bridge wire taut and along the scale in the metre bridge. So, it must be ensure to taut the metre bridge along the scale.
        The resistance of end pieces/metal strips may not be negligible. The error introduced by it can be reduced by interchanging the known and unknown resistance in gaps.[6]
        The percentage of error increases if the resistance box or other materials may not be clean. So, all the materials must be clean. 
        The reading of screw gauge might be accurate.

Conclusion:

This lab effectively showed how the metre bridge based on Wheatstone bridge provides a mechanism to calculate an unknown resistance using the known relationships given through the resistivity correlation to length. It demonstrated how to set-up a Wheatstone bridge and how to manipulate a Wheatstone bridge in a laboratory setting. In addition, the lab provided a demonstration of the aforementioned linear relationships. Although significant error existed in this lab, the results still reflect the relationships governing the Wheatstone bridge sufficiently for understanding in an experimental contextual environment.
unknown resistance using the known relationships given through the resistivity correlation to length. It demonstrated how to set-up a Wheatstone bridge and how to manipulate a Wheatstone bridge in a laboratory setting. In addition, the lab provided a demonstration of the aforementioned linear relationships. Although significant error existed in this lab, the results still reflect the relationships.[7]

References

[1]  http://www.wikihow.com/Calculate-Unknown-Resistance-Using-Meter-Bridge 
[2] http://www.askiitians.com/iit-jee-electric-current/specific-resistance-of-material-of-wire-using-meter-bridge/
[3]  http://www.askiitians.com/iit-jee-electric-current/specific-resistance-of-material-of-wire-using-meter-bridge/
[4]  http://www.askiitians.com/iit-jee-electric-current/specific-resistance-of-material-of-wire-using-meter-bridge/
[5]  practical physics for degree students, Dr. Giasuddin ahmed and Md. Shahabuddin, page- 367
[6]  www.davkalinga.org/metre-bridre-experiment-discusion 
[7] http://www.answers.com/Q/What_is_the_conclusion_for_the_wheatstone_bridge_experiment

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