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Metre Bridge Experiment with Readings (Class 12)

Metre Bridge Experiment with Readings (Class 12) 


METRE BRIDGE EXPERIMENT - I


Aim: 


To find the resistance and hence determine the resistivity of the material of the wire.


Apparatus: 


Metre bridge, Battery (E), Key (K), Resistance box (R), Given resistance wire (X), High resistance (HR), Galvanometer (G), Jockey (J), Screw gauge etc.


Principle: 


The resistance of the given wire X = R[l/(100-l)]

where, R - Known resistance (Resistance put in the resistance box).

l - Balancing length from the side of X.

The resistivity of the material of the wire, ρ=  Xπr2/L

where, r - Radius of the given wire

X - Resistance of the given wire

L - Length of the given wire


Procedure:

Connections are made as shown in the circuit diagram. The unknown resistance (X) is connected in the left gap G1 and the resistance box (R) is connected in the right gap G2. A suitable resistance is put in the resistance box (of the same order of X) and the key (K) is closed. The jockey (J) is pressed at both ends of the wire AB. If the deflections in the galvanometer (G) are in opposite directions, the connections are correct.


The jockey (J) is moved along the metre bridge wire till the galvanometer (G) shows zero deflection. The high resistance (HR) is cut off and the correct balancing point is obtained. The balancing length [AJ = l1] is measured. The resistances X and R are interchanged and the balancing length [BJ = l2] is measured.


The mean balancing length is, l= [l1+ l2]/2


The value of X is calculated using the equation, X = R[l/(100-l)]


The experiment is repeated for different values of R and the mean value of the resistance X is determined. The radius (r) of the wire is determined using a screw gauge and the length (L) is measured using a meter scale. The resistivity is calculated using the formula, ρ=  Xπr2/L.

 

Observations and Readings


i. To determine the resistance (X) of the wire


No:

R

Balance length

When X is

l = [l1+l2]/2

100-l

X = R (l/[100-l])

in left gap, l1

in right gap, l2

-

ohm

cm

cm

cm

cm

ohm

1

1

19.5

29

24.25

75.75

0.32

2

2

15

17

16

84

0.38

3

3

12

14.2

13.1

86.9

0.45

4

4

10

11

12.5

87.5

0.469

 

Mean value of X = 0.405 ohm


ii. To find the resistivity (ρ) of the conductor,


To determine the radius of the wire (r)

Pitch = 1 mm

L.C = .01 mm

Zero correction = +10 div


Trial

PSR

Observed HSR

Corrected HSR

Corrected HSR x LC

Diameter, PSR + (HSR x LC)

1

0

49

59

.59

0.59

2

0

40

50

.50

0.5

3

0

45

55

.55

0.55

4

0

48

58

.58

0.58

 

Mean diameter of the wire = 0.56 mm = 0.56 x 10-3 m

Radius of the wire, r = 0.28 x 10-3 m

Length of the wire, L = 30 x 10-2 m

Resistivity of the material of the wire, ρ = X x πr2/L = 3.323 x 10-7 Ωm


Results:


(i) Resistance of the given wire = 0.405 ohm

(ii) Resistivity of the material of the wire = 3.323 x 10-7 ohm.m

 

METRE BRIDGE EXPERIMENT - 2

 

Aim: 


To verify both the series and parallel (laws of combination) of resistances using metre bridge.


Apparatus: 


Metre bridge, Battery (E), Resistance box (R), Key (K), Galvanometer (G), Jockey (J), Two resistance wires etc


Principle: 


Let X1 and X2 be the resistances of the two given wires. If the two wires are connected in series, the effective resistance

XS = X1 + X2

If X1 and X2 are connected in parallel, the effective resistance

XP = X1 X2 /(X1 + X2)

The values of X1 and X2 are independently determined using metre bridge applying the equation,

X = R[l/(100—l)]


Procedure


i. To determine X1 and X2


Connections are made as shown in figure. X1 is connected in the gap G1 and a resistance box R in gap G2. The circuit is closed and a suitable resistance is put in R. The jockey is moved along the wire (AB) until the galvanometer shows zero deflection. The high resistance (HR) is cut off and correct balance point is obtained. The balancing length AJ = l1 is measured. The positions of X1 and R are interchanged and the balancing length BJ = l2 is obtained. The mean balancing length, l = [l1 + l2]/2


Therefore X1= Rl/(100— l) can be calculated.


The experiment is repeated for different values of R and the mean value of X1 is determined. X1 is removed from the circuit and X2 is included. As done before, mean value of X2 is determined.


(i) The resistances in series

The resistance wires X1 and X2 are joined end to end and connected in the gap G1. As done before, mean value of the effective resistance XS is calculated. The theoretical value of effective resistance of the combination is X1 + X2.


Thus, XS = X1 + X2


(ii) The resistances in parallel

The resistance wires X1 and X2 are joined in parallel and connected in the gap G1. As done before, mean value of the effective resistance XP, is calculated. The theoretical value of effective resistance of the combination is


XP = X1X2/(X1 + X2)


Series and Parallel Observations and Readings


Trial

RΩ

Balancing length when X is

X = R x [l/(100-l)]

Mean X (Ω)

In left gap,

AJ = l1

In right gap, BJ = l2

l = (l1+l2)/2

X1 alone

1

2

1

2

19.5

15

29

17

24.25

16

0.32

0.38

X1 = 0.35

X2 alone

1

2

1

2

49

38

50

26

49.5

32

0.98

0.94

X2 = 0.96

X1, X2 Series

1

2

1

2

65.5

50.5

54

47

59.75

48.75

1.48

1.90

XS = 1.69

X1, X2

Parallel

1

2

1

2

22.5

18

21.6

17.1

22.05

17.55

.2829

.4257

XP = .3543

 

Resistance in Series


Experimental value of XS = X3 = 1.69 Ω

Theoretical value of XS = X1 + X2 = 1.31 Ω


Resistance in Parallel


Experimental value of XP = X4 = 0.35 Ω

Theoretical value of XP = X1X2/(X1 + X2) = 0.26 Ω

 

Results


(i) Experimental value of XS and theoretical value of XS are equal and thus verifies the law of combination of resistances in series.


(ii) Experimental value of XP and theoretical value of XP are equal and thus verifies the law of combination of resistances in parallel.

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