Resistance of a Given Wire Using a Metre Bridge: Explanation

Metre bridge is an instrument that is used to determine the unknown resistance of any provided material. It is an electrical apparatus with the help of which we can measure the value of unknown resistance, and it is made using a metre long wire of uniform cross-section. The wire mentioned is either nichrome or manganin or constantan as they offer high resistance and low-temperature coefficient of resistance. Meter bridge is also known as a slide wire bridge and works under the principle of Wheatstone bridge (found by Samuel Hunter Christie). It is one of the most vital applications of a Wheatstone bridge. There is a specific way to use this method and here we will be discussing how to find the resistance of a given wire using a meter bridge and hence determine the resistivity of its material experiment. 

Keyword takeaways: Meter Bridge, Wheatstone bridge, Galvanometer, Resistance, Conductor, Screw gauge, Least count, Leclanche cell, Resistivity, Uniform cross-section

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What is a Meter Bridge?

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A Meter bridge is an apparatus that is used to determine the unknown resistance of a coil, a, or any material. The apparatus is also popularly known as the slide wire bridge. It works on the principle of the Wheatstone bridge. 

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Aim 

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The main aim of the experiments done using a meter bridge is to find the resistance of the wire and hence find the resistivity of the material of the wire. It is a wooden plank with certain electrical arrangements. 

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Materials Required

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The materials required for the arrangement are:

• A meter bridge,
• A leclanche cell,
• A galvanometer,
• A jockey,
• A resistance box,
• A resistance wire,
• A one-way key,
• A screw gauge,
• A meter scale,
• Connecting wires,
• A set square, and
• A piece of sandpaper.

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Theory 

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Metre bridge apparatus is also referred to as a slide wire bridge. It consists of a long wire with a uniform cross-sectional area and is fixed on the wooden block. It has two gaps that are formed using thick metal strips to make the Wheatstone’s bridge.

Therefore, according to Wheatstone’s principle, we have:

X/R = l/ (100-l)

The unknown resistance can be calculated as:

X = R x l/(100 -l)

Then the specific resistance of the material is calculated as:

ρ = πr² X/L

Where,

• L = the length of the wire
• r = the radius of the wire

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Circuit Diagram

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Procedure 

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• Arrange the apparatus as shown below.

• The wire, conductor, or the material whose resistance has to be calculated should be connected to the right gap between B and C without creating any loops.
• Connect the resistance box to the left gap between A and B.
• Make the other connections exactly as shown above.
• Put the plug of the key K at the 2-ohm resistance in the resistance box.
• Touch the jockey slightly, first to the left and then to the right of the bridge.
• Look at the galvanometer readings. Note them and make sure that the deflection is in the opposite direction and if it is in one direction only, there is some issue in the arrangement of the circuit.
• Consider D as the null point where the jockey touches the wire. Note: Do not move the jockey harshly over the wire, it may lead to wrong readings. Move it gently from the left direction to the right.
• Consider a value of 12 from the resistance box such that there is almost no deflection seen in the galvanometer when the jockey reaches the middle of the wire.
• Note the D position to know the value of the AD which is 'l'.
• Take a minimum of 4 readings to determine the resistance of the unknown wire by regularly changing the value of 12.
• Keep noting the readings or the observations.
• Remove the resistance wire and calculate its length by stretching it with the help of a meter scale.
• With the help of the screw gauge, measure the diameter of the wire from 3-4 different places.
• Form a table of the observations as given below.

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Observations 

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Table for the calculation of the unknown resistance

The least count of the screw gauge is calculated as follows.

Table for the calculation of diameter.

Calculation 

Note the results after the calculation has been done correctly.

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Results 

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1. The value of unknown resistance X = …….
2. The specific resistance of the material of given wire = ………
3. Percentage error = …….

Precautions 

Precautions to be taken while using a meter bridge.

• Movement of jockey should be made carefully without being harsh on the wire.
• Connect the plugs tightly to the resistance box.
• Insert the key only when the readings are to be taken.
• The least count of the wire is calculated in two mutually perpendicular directions.
• Use the set square to note the null point to avoid any kind of error, such as the error of parallax.
• The null point should be taken between 45-55cms.

Sources of Error

1. The screws of the instrument might be loose.
2. The wire can be of non-uniform diameter.
3. There can be a backlash error in the screw gauge.

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Things to Remember

• Metre bridge works on the principle of Wheatstone bridge.
• A meter bridge is used to calculate the resistance of the wire and then the resistivity of the material of the wire.
• The formula for resistance is: X = R× l/(100-l)
• The formula for the resistivity of the material: ρ = πr² X/L
• Minimum four readings should be taken for the calculation of both the resistance of the wire and for the diameter of the wire.
• Null points of the wire should be between 45-55 cms.
• The connections should be checked twice before the experiment to make the readings apt.

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