Introduction
Resistance measurement of an exact nature is a prerequisite in experimental physics and electrical engineering. Whereas contemporary digital tools are everywhere, including ohmmeters, multimeters, etc., classical laboratory tools, like the meter bridge, are still invaluable as a means of instruction. Besides being very easy to construct, the meter bridge is unique in that it has the ability to apply the Wheatstone bridge principles in a very elegant manner, thus measuring the unknown resistances with great accuracy.
By placing a standard resistance wire attached to a row of meters, students and researchers can balance currents and measure resistances with a great deal of accuracy. This paper discusses the construction of the meter bridge, its principle, the working principle, the balance condition, some practical considerations, and the solved problems (with reference to the Figure). More so, its applications, pros, and cons are addressed.
What is a Meter Bridge?
The meter bridge, also called a slide-wire bridge, is an experimental setup that applies the Wheatstone bridge principle for determining an unknown resistance. It consists of a uniform resistance wire of length 1 meter, clamped between two thick metallic strips. The wire is marked with a scale to allow measurements of its length.
The key idea is that the wire is treated as two resistors whose resistances are proportional to their lengths. When a jockey (sliding contact) touches a point on the wire, it divides the wire into two segments, and the galvanometer connected in the circuit helps determine whether the bridge is balanced.
Construction of a Meter Bridge
The setup of a meter bridge is illustrated in the Figure. It consists of the following components:
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A resistance wire (AC) – A 1-meter-long wire of uniform cross-sectional area is tightly fixed on a wooden base, marked with a scale for precise measurements.
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Standard resistance (S) – A known resistance connected across one of the metallic gaps.
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Unknown resistance (R) – The resistance to be measured, connected across the other metallic gap.
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Galvanometer (G) – A sensitive device used to detect current, connected between a sliding contact (jockey) and the bridge wire.
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Jockey (J) – A metallic rod with a knife-edge tip that can slide along the wire to make contact at various points.
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Battery (E) – Provides the necessary potential difference across the circuit.
Working Principle
The principle of the meter bridge is derived directly from the Wheatstone bridge.
When the jockey touches a point D on the wire, the resistance wire is divided into two parts: AD (length l1) and DC (length 100−l1). These act as two resistances in the Wheatstone bridge arms.
The condition for a balanced bridge is:
In balance, the galvanometer shows zero deflection, indicating no current flows through it.
Balance Condition of a Meter Bridge
The balance condition of the meter bridge is mathematically expressed as:
Where:
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R = Unknown resistance
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S = Standard resistance
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l1 = Balance length from end A to jockey point D
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(100−l1) = Remaining length of the wire
This equation is at the heart of the meter bridge experiment and enables accurate calculation of R.
Determination of Unknown Resistance
Once the balance length is found, the unknown resistance can be determined using the formula:
This simple relation makes the meter bridge highly effective in resistance measurement. By varying the value of the standard resistance S and adjusting the balance point, the experiment can be repeated to improve accuracy.
Practical Considerations
The accuracy of the meter bridge depends on:
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Position of Balance Point: If l1 is close to 50 cm, the percentage error is minimized.
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Uniformity of Wire: The bridge wire must have a uniform cross-sectional area and material.
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Temperature Effects: Heating of the wire due to current may change resistance, so low currents are preferred.
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Contact Resistance: Proper contact of the jockey ensures precision.
Solved Example
Let us work through a classic meter bridge problem.
Problem:
In a meter bridge, the null point is found at a distance of 33.7 cm from end A. If a resistance of 12Ω is connected in parallel with the standard resistance, the null point shifts to 51.9 cm. Determine the values of R (unknown resistance) and S (standard resistance).
Solution:
From the first balance point:
When a 12Ω resistance is connected in parallel with S, the effective resistance becomes:
Now, using the second balance point:
Substituting R = (33.7 / 66.3) * S, solving yields:
Thus, the unknown resistance is approximately 6.86Ω.
Applications of the Meter Bridge
The meter bridge is not just a textbook experiment but also a valuable tool in laboratories.
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Measurement of unknown resistances.
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Verification of Ohm’s law.
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Study of resistance variation with material, length, and temperature.
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Used in educational experiments for demonstrating Kirchhoff’s laws.
Advantages of the Meter Bridge
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High Accuracy: Provides precise results when carefully used.
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Simple Setup: Requires minimal apparatus.
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Cost-effective: Cheaper than advanced digital meters.
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Versatile: Can measure both small and medium resistances.
Limitations of the Meter Bridge
Despite its usefulness, the meter bridge has some limitations:
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Wire non-uniformity can affect accuracy.
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Temperature dependence of the wire resistance.
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Contact resistance between the jockey and wire introduces errors.
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Not suitable for measuring very high resistances.
Conclusion
This meter bridge is a simple but effective example of the Wheatstone bridge principle, according to which careful balancing of currents, combined with careful determination of the lengths of arms, is used to obtain the unknown resistances with high accuracy. The meter bridge is an essential pedagogical device even in the modernized world of digital instrumentation, which provides students with a chance to grasp the principles of resistance measurement foundations, conduct a solid error analysis, and test the laws of Kirchhoff in the real world.