Metre Bridge-Resistance of a wire

 Our Objective:

To find the resistance of a given wire using a metre bridge and hence determine the specific resistance of its materials.

Theory

Wheatstone’s principle

 The metre bridge is operates under Wheatstone’s principle.  Here, four resistors P, Q, R, and S are connected to form the network ABCD. The terminals A and C are connected to a battery, and the terminals C and D are connected to a galvanometer through keys K1 and K2 respectively.                                                                                                                                                                                          In the balancing condition, there is no deflection on the galvanometer. Then,

\small \frac{P}{Q}=\frac{R}{S}

 

Metre Bridge apparatus  

The metre bridge, also known as the slide wire bridge consists of a one metre long wire of uniform cross sectional area, fixed on a wooden block. A scale is attached to the block. Two gaps are formed on it by using thick metal strips in order to make the Wheat stone’s bridge. The terminal B between the gaps is used to connect galvanometer and jockey.

              

A resistance wire is introduced in gap S and the resistance box is in gap R. One end of the galvanometer is connected to terminal D and its other end is connected to a jockey. As the jockey slides over the wire AC, it shows zero deflection at the balancing point (null point).

If the length AB is l, then the length BC is  ( 100-).

Then, according to Wheatstone’s principle; 

                                                                 \frac{X}{R}= \frac{l}{(100-l)} 

Now, the unknown resistance can be calculated as,

                                                                 X=R\frac{l}{(100-l)}

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

                                                                 \rho =\frac{\pi r^{2}X}{L} ; Where L be the length of the wire and r be its radius.


 Learning Outcomes:

  • Students understand Wheatstone’s bridge and Wheatstone’s principle.
  • Students verify Wheatstone’s principle.
  • Students correlate the principle of Wheatstone’s bridge with metre bridge experiment.

 

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