Rituraj Tiwari
Last Activity: 4 Years ago
In a meter bridge experiment, when a resistance wire is connected in the left gap, the balance point is found at the 30th. When the wire is replaced by another, the balance point moves to the 60th. The goal is to find the resistance in the left gap, considering the series and parallel combinations of resistors.
Step-by-step solution:
1. Meter Bridge Principle:
The meter bridge is based on the principle of the Wheatstone bridge. It has a uniform wire of length 1 meter. The balance point (or null point) is where no current flows through the galvanometer, indicating that the ratios of resistances on both sides of the bridge are equal.
Let:
R1 = Resistance in the left gap.
R2 = Resistance in the right gap.
L1 = Length of the bridge wire on the left side (from the left end to the balance point).
L2 = Length of the bridge wire on the right side (from the balance point to the right end).
Since the total length of the wire is 1 meter, we have: L1 + L2 = 100 cm (1 meter).
At the balance point, the Wheatstone bridge equation is: (R1 / R2) = (L1 / L2).
2. First Setup:
When the resistance wire is connected in the left gap, the balance point is found at the 30th. Thus, L1 = 30 cm and L2 = 70 cm.
The Wheatstone bridge equation becomes: (R1 / R2) = (30 / 70) = 3 / 7.
So, we have the first equation: R1 = (3/7) * R2 [Equation 1].
3. Second Setup:
When the wire is replaced with another one, the balance point moves to the 60th. Thus, L1 = 60 cm and L2 = 40 cm.
The Wheatstone bridge equation now becomes: (R1' / R2) = (60 / 40) = 3 / 2.
So, we have the second equation: R1' = (3/2) * R2 [Equation 2].
4. Finding the Resistance in the Left Gap:
Now, we can solve for the resistance of the wire in the left gap, using the relationship between R1 and R1' from the two setups.
From Equation 1, R1 = (3/7) * R2.
From Equation 2, R1' = (3/2) * R2.
Therefore, we can conclude that the resistance in the left gap is related to the resistance of the wire and the two balance points.
Since the values indicate a change from the first balance point (30 cm) to the second (60 cm), we conclude that there is an adjustment in the left gap, considering the series and parallel combinations of the resistors.
Conclusion:
In the first case, the resistance R1 is proportional to (3/7) of the total resistance.
In the second case, the resistance is proportional to (3/2) of the total resistance.
By combining both equations, we can calculate the specific values of R1 and R2, considering the series and parallel combinations used in the meter bridge experiment.
