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/(100l)]
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= Xπr^{2}/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 G_{1} and the resistance box (R) is connected in the right gap G_{2}. 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 = l_{1}] is measured. The resistances X and R are interchanged and the balancing length [BJ = l_{2}] is measured.
The mean balancing length is, l= [l_{1}+ l_{2}]/2
The value of X is calculated using the equation, X = R[l/(100l)]
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= Xπr^{2}/L.
Observations and Readings
i. To determine the resistance (X) of the wire
No: 
R 
Balance length When X is 
l = [l_{1}+l_{2}]/2 
100l 
X = R (l/[100l]) 

in left gap, l_{1} 
in right gap, l_{2} 

 
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 πr^{2}/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 X_{1} and X_{2} be the resistances of the two given wires. If the two wires are connected in series, the effective resistance
X_{S} = X_{1} + X_{2}
If X_{1} and X_{2} are connected in parallel, the effective resistance
X_{P} = X_{1} X_{2} /(X_{1} + X_{2})
The values of X_{1} and X_{2} are independently determined using metre bridge applying the equation,
X = R[l/(100—l)]
Procedure
i. To determine X_{1} and X_{2}
Connections are made as shown in figure. X_{1} is connected in the gap G_{1} and a resistance box R in gap G_{2}. 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 = l_{1} is measured. The positions of X_{1} and R are interchanged and the balancing length BJ = l_{2} is obtained. The mean balancing length, l = [l_{1} + l_{2}]/2
Therefore X1= Rl/(100— l) can be calculated.
The experiment is repeated for different values of R and the mean value of X_{1} is determined. X_{1} is removed from the circuit and X_{2} is included. As done before, mean value of X_{2} is determined.
(i) The resistances in series
The resistance wires X_{1} and X_{2} are joined end to end and connected in the gap G_{1}. As done before, mean value of the effective resistance X_{S} is calculated. The theoretical value of effective resistance of the combination is X_{1} + X_{2}.
Thus, X_{S} = X_{1} + X_{2}
(ii) The resistances in parallel
The resistance wires X_{1} and X_{2} are joined in parallel and connected in the gap G_{1}. As done before, mean value of the effective resistance X_{P}, is calculated. The theoretical value of effective resistance of the combination is
X_{P} = X_{1}X_{2}/(X_{1} + X_{2})
Series and Parallel Observations and Readings
Trial 
RΩ 
Balancing length when X is 
X = R x [l/(100l)] 
Mean X (Ω) 

In left gap, AJ = l_{1} 
In right gap, BJ = l_{2} 
l = (l_{1}+l_{2})/2 

X_{1} alone 
1 2 
1 2 
19.5 15 
29 17 
24.25 16 
0.32 0.38 
X_{1} = 0.35 
X_{2} alone 
1 2 
1 2 
49 38 
50 26 
49.5 32 
0.98 0.94 
X_{2} = 0.96 
X_{1}, X_{2} Series 
1 2 
1 2 
65.5 50.5 
54 47 
59.75 48.75 
1.48 1.90 
X_{S} = 1.69 
X_{1}, X_{2} Parallel 
1 2 
1 2 
22.5 18 
21.6 17.1 
22.05 17.55 
.2829 .4257 
X_{P} = .3543 
Resistance in Series
Experimental value of X_{S} = X_{3} = 1.69 Ω
Theoretical value of X_{S} = X_{1} + X_{2} = 1.31 Ω
Resistance in Parallel
Experimental value of X_{P} = X_{4} = 0.35 Ω
Theoretical value of X_{P} = X_{1}X_{2}/(X_{1} + X_{2}) = 0.26 Ω
Results
(i) Experimental value of X_{S} and theoretical value of X_{S} are equal and thus verifies the law of combination of resistances in series.
(ii) Experimental value of X_{P} and theoretical value of X_{P} are equal and thus verifies the law of combination of resistances in parallel.
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