Resistivity of the material of a given wire using Meter Bridge

Introduction

What is Wheatstone Bridge?

A kind of electrical circuit used in measuring an electrical resistance, which is unknown by balancing its two legs of the bridge circuit, where one of the legs includes an unknown component is known as a Wheatstone Bridge. In the year 1833 Samuel Hunter Christy created the first Wheatstone bridge. In today’s world the digital multimeters provide the simplest forms in measuring the resistance. Light values of resistance around the range of milli – Ohms, can still be measured using the Wheatstone bridge.

Principle of Wheatstone Bridge 

The Wheatstone Bridge works on the principle of null deflection. The ratio of the resistances is equal and hence no current flows through the circuit. In normal conditions, the Wheatstone Bridge will be in an unbalanced condition where current will flow through the galvanometer.

Formula for Wheatstone Bridge 

When no current flows through the galvanometer, the bridge will be in a balanced condition. One way to obtain this condition is by adjusting the known resistance and variable resistance.

RS= PQ

R = P SQ

Where, 

R = The unknown resistance. 

S = Standard size of the bridge. 

P and Q = Ratio of the sides of the bridge.

What is a Meter Bridge?

A meter bridge is an instrument that works on the principle of a Wheatstone bridge and is also known as a slide wire bridge. To find the unknown resistance of a conductor wire, a meter bridge is used.

It consists of a wire of length of  1 meter and of uniform cross sectional area taut clamped between two thick metallic strips that are bent at right angles having two gaps across which the resistors are to be connected. At the end points, the wire is clamped and connected to a cell through a key. The two ends of a galvanometer are connected to the metallic strip midway between 2 gaps and a jockey which moves along the wire to make electrical connection respectively. An unknown resistance R is connected across one of the gaps. We connect a standard unknown resistance S across the other gap.

The jockey is connected to some point D on the wire, a distance l1 cm from the end A. As the meter bridge works on the principle of the Wheatstone bridge. Therefore, at balance condition.

RS= l1100- l1

Null Point:

An arrangement of resistors across the arms of the meter bridge such that the deflection in the galvanometer is zero is known as the null point or the balance point.

Finding the resistance of the given wire using meter bridge

The apparatus required to find the resistance of a given conducting wire using a meter bridge are:

• Meter bridge
• Resistance box
• Galvanometer
• Unknown Resistance of a length 1 m
• Screw gauge
• Connecting Wires
• Jockey
• One – way key

The procedure to find the resistance of a given conducting wire using the meter bridge is:

1. Gather all the instruments mentioned and prepare connections. 
2. From the resistance box, set a suitable kind of resistance R.
3. Make the jockey come in contact with point A and check that there exists a deflection in the galvanometer on one of the sides, then make the jockey come in contact with point C of wire, then the deflection in the galvanometer has to be on the opposite side.
4. Find the position of the null point (the deflection in the galvanometer becomes zero). 
5. Now repeat the above process for different values of R and note down at least some 5 readings for different values of R.
6. Now, measure the length of the given wire by the use of ordinary scale and radius of the wire by utilization of a screw gauge. (take down at least five readings)
7. Calculate the mean resistance of the unknown resistance = total sum of resistance of unknown resistance of the above the five readings / 5.
8. Now, the unknown resistance can be calculated as,

X = R l100 – l

1. The specific resistance or resistivity of the material of the wire can be then calculated by using the relation,

= r2XL

 where L is the length of the wire and r is its radius.

Errors and precautions while using meter bridge

Errors

• Non-uniformity in the wire brings about different resistance per unit length, thus inducing error in unknown resistance. Moreover, there may be errors due to the heating effect, end corrections introduced due to shift of the zero of the scale.

Precautions

• The battery key should always be pressed before the galvanometer contact is made on the bridge wire to ensure that a steady current is flowing in the circuit. Otherwise, a counter e.m.f. would be self-induced somewhere in the circuit which would make it impossible to find the exact balance point.  
• The experiment should be repeated by interchanging the resistances in left and right gaps.
• The value of resistance is such that the balance condition is achieved near the center of the wire.

Conclusion

In this article, we learned about the Wheatstone bridge. A kind of electrical circuit used in measuring an electrical resistance, which is unknown by balancing its two legs of the bridge circuit, where one of the legs includes an unknown component is known as a Wheatstone Bridge. A meter bridge is an instrument that works on the principle of a Wheatstone bridge and is also known as a slide wire bridge. To find the unknown resistance of a conductor wire, a meter bridge is used. To gain a better understanding of this chapter other topics such as Ohm’s law and potentiometer are suggested to the user.