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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.
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
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
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
Resistance 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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