To Find Resistance of a Given Wire Using Metre Bridge And Hence Determine The Resistivity (Specific Resistance) of its Material.

Aim
To find resistance of a given wire using metre bridge and hence determine the resistivity (specific resistance) of its material.

Apparatus

A metre bridge (slide wire bridge), a Leclanche cell (Battery eliminator), a galvanometer, a resistance box, a jockey, a one way key, a resistance wire, a screw gauge, a metre scale, a set square, connecting wires and a piece of sand paper.

Theory

Meter bridge works based on Wheatstone bridge
(i) The unknown resistance X is given by

where, R is known resistance placed in the left gap and unknown resistance X in the right gap of metre bridge. I cm is the length of metre bridge wire from zero end upto balance point.

(ii) Specific resistance (p) of the material of the given wire is given by

                                                                                            

     

where, L is the length and D is the diameter of the given wire.

Circuit diagram

Procedure
For Resistance

1. Arrange the apparatus as shown in arrangement diagram.
2. Connect the resistance wire whose resistance is to be determined in the right gap between C and B. Take care that no part of the wire forms a loop:
3. Connect resistance box of low range in the left hand gap between A and B.
4.  Make all the other connections as shown in the circuit diagram.
5. Take out some resistance (say 2 ohm) from the resistance box, plug the key K.
6. Touch the jockey gently first at left end and then at right end of the bridge wire.
7. Note the deflections in the galvanometer. If the galvanometer shows deflections in opposite directions, the connections are correct. If the deflection is one side only, then there is some fault in the circuit. Check or take help of your teacher and rectify the fault.
8. Move (slide) the jockey gently along the wire from left to right till galvanometer gives zero deflection. The point where the jockey is touching the wire is null point D.
9. Choose an appropriate value of 12 from the resistance box such that there is no deflection in the galvanometer when the jockey is nearly in the middle of the wire (i.e.,between 45 cm to 55 cm).
10. Note position of point D (with the help of a set square) to know length AD = l.
11. Take at least four sets of observations in the same way by changing the value of 12 in steps.
12. Record your observations.
    
    For Specific Resistance
13. Cut the resistance wire at the points where it leaves the terminals, stretch it and find its length by using a metre scale.
14. Measure the diameter of the wire at least at four places, in two mutually perpendicular directions at each place with the help of screw gauge.
15. Record your observations as given in tables.

Observations
1.Length of given wire L = 100cm.

2. Table for unknown resistance (X)

                      

S No	Resistance, R (Ω)	Balancing length, AD =l (cm)	Length DB= (100-l)	Unknown resistance
1 2 3	2 4 6	54 70 85	46 30 15	1.7 1.71 1.64

                                                                                   Mean resistance, X = 1.68. Ω

3. Least count of the screw gauge

Pitch of screw gauge = 1mm

Total number of divisions on  circular scale = 100

Least count of the screw gauge (LC) = Pitch/ No.of head scale divisions = 1/100 =0.01mm

Zero error =0  and  Zero correction = 0

4. Table for diameter (D) of the wire

To find the diameter of the given wire:

Least count of the screw gauge (LC)       = 0.01 mm

Zero correction of the screw gauge (Z)   = …0…. mm

 

No.	PSR (mm)	Observed HSR, (a) (mm)	Corrected HSR, (a+Z) (mm)	Corrected HSRx LC (mm)	Total Reading, d = PSR+ (Corrected HSRx L C ) (mm)
1	0	10	10	0.1	0.1
2	0	12	12	0.12	0.12
3	0	15	15	0.15	0.15
4
5

                                                                                                                      Mean, d =0.12mm

Calculations

Calculations

Diameter of the wire, d         =…0.12……...mm =0.12X10-3 m

Length of the wire, L             = 100cm

                                          = .100X10-2 m =1 m

Resistance of the wire, X      = 1.68 Ω

Resistivity ( specific resistance) of the wire

                                                                          = .1.9X10-8Ω m

Precautions

1. The connections should be neat, clean and tight.
2. All the plugs in the resistance box should be tight.
3. Move the jockey gently over the bridge wire and do not rub it.
4. The plug in key K should be inserted only when the observations are to be taken.
5. Null point should be brought between 45 cm and 55 cm.
6. Set square should be used to note null point to avoid error of parallax.
7. At one place, diameter of wire should be measured in two mutually perpendicular directions.
8. The wire should not make a loop.

Sources of error

1. The instrument screws may be loose.
2. The plugs may not be clean.
3. The wire may not have uniform thickness.
4. The screw gauge may have faults like back lash error and wrong pitch.

Result

1. The value of unknown resistance X = 1.68
2. The specific resistance of the material of the given wire =.1.9X10-8Ω m