Metre Bridge

The metre bridge contains a wire of length 1 metre of the uniform cross-section which is fixed between two metallic bands. So, it is known as the metre bridge. It is used to find an unknown resistance of a wire.

Metre bridge wire is made of some alloy wires like Manganin or Constantan as the resistance of such wires is almost temperature independent. Another metallic band is fixed between the metal bands, so that in one chamber the unknown resistance is connected and, in another chamber, a known resistance is fixed.

An object made of metal is attached with the metal band, fixed in between the metre bridge. It is called a Jockey. Another end of the Jockey is fixed with a centre zero galvanometer to check the point of zero deflection while the unknown resistance is connected.

A metre scale is kept parallel to the apparatus to measure the length of the wire in a particular position where the galvanometer scale shows zero deflection. Both sides of the wire fixed with the metre bridge are connected through a battery source(E) through a key.

Principle of Metre Bridge

• Metre bridge work is based on the principle of the Wheatstone bridge
• In the Wheatstone bridge, P, Q, R and S are four resistances and G is the galvanometer

• Now, applying Kirchhoff’s law at the terminals of the Wheatstone bridge we can obtain in balanced condition i.e., when there is no current flow through the galvanometer, we obtain,

P/Q=R/S

This condition can be also considered as the principle of a metre bridge

• To obtain the balanced condition, consider that the jockey B, is moved randomly towards the fixed-point A and C of the bridge
• For both conditions, the galvanometer arrow will move in the opposite direction
• If we start moving the jockey from one terminal and gradually move towards terminal C, we can obtain a point on the wire where the galvanometer arrow shows no deflection
• The arrow should be fixed at a zero point 
• If there is no such point in the metre bridge wire, the variable resistance from the resistance box should be changed so that the ratio of two resistances is equal to the ratio of another two resistances
• Now, repeat the same procedure after connecting the new wire and consider at a point B, the zero or null deflection is obtained
• This point on the wire is known as the null point
• In the given metre bridge, a zero deflection in the galvanometer scale is obtained at a point B
• The length of AB is given as l1 and the length of BC is given as l2
• The length of the wire is 1 metre = 100 cm. So, the length l2 = 100 – l1

Calculation of Resistance of Wire S: (Metre Bridge Formula)

Considering the principle of metre bridge, for no deflection through the galvanometer we can write,

Resistance through AB=SResistance through BC

 i.e., 

Rl1=Sl2

 Or,

Rl1=S100-l1

So,                                                  

S=Rl1(100-l1)

The last equation can be considered as the metre bridge formula.

For example, let us consider a resistor of 10 Ohm is connected through the left band of the metre bridge, also an unknown resistance is fixed in the right band of the same. Now, if the zero-deflection point is shifted by a distance of 60 cm when the wires change its position with one another. So, we can find the value of the unknown resistance by using the metre bridge formula as,

l1-l2=60 and l1+l2=100 i.e., l1=80 .

Also, R=10 Ohm

Now, S=Rl1(100-l1)

Or, S=1080(100-80)

  Therefore,   

      S=2.5 Ohm

Now, at the time of winding the wire with the metre bridge, the length of the wire may vary at different positions. It may cause an error while shifting the jockey to calculate the zero-deflection condition. To remove this error, we should take the value of the unknown resistance at different times. We can take the mean value of the obtained values of the resistor.

In balanced conditions, if the ratio of both the known and unknown resistances seem to be unity, then the metre bridge sensitivity gets increased. Which means the metre bridge can detect small changes in the resistance or due to a small emf change in the battery source, the galvanometer scale can show the deflection. So, the sensitivity of the metre bridge shows the measurement accuracy of a metre bridge.

Conclusion

A metre bridge is an apparatus that is used to measure unknown resistance of a wire or a metallic coil by finding a zero deflection in a galvanometer coil when no electric current is passing through the circuit. It can be also used to compare two unknown resistances. There is a wire of 1 metre length which is fixed with the two ends of the bridge. Sliding the jockey at different positions of the wire, the null point is obtained. It works on the principle of Wheatstone bridge. So, the unknown resistance is obtained by applying the metre bridge formula,  S=Rl1(100-l1) , where l1 is the distance of the wire from one end where the balanced position is obtained.