TP Physique2

I - Goal :

The goal of this manipulation is to determine the value of an unknown resistance using the Wheatstone bridge and the wire bridge.

II - Theoretical reminders :

    II-1- Wheatstone Bridge :

The Wheatstone bridge consists of an electrical circuit comprising three known resistances and a fourth to be determined, powered by a direct current generator E.

Consider then the circuit below, where R₁ and R₂ are resistors of known ratio, R_V is a known adjustable resistance (rheostat) and R_X is the unknown resistance. All of these resistances thus form the so-called Wheatstone bridge. The two points C and D are connected to a galvanometer G.

To determine the value of the unknown resistance R_X, it is necessary to adjust the variable resistance R_V in the bridge until we manage to cancel the intensity of the current in the branch CD of the bridge.

Therefore, by acting on the resistors R₁, R₂ and R_V it is possible to cancel the current in the galvanometer.

In this case, we can write :   

      This makes it possible to apply Ohm's law to the terminals of R₁ and R₂  :

from where :          

On the other hand :     

Thus :      

Note that it is useless to know the resistances R₁ et R₂ ; only their report intervenes 

This report is called beachhead report.

      II-2- Wire bridge :

The wire bridge is another variant of the Wheatstone bridge. We know that for a homogeneous conducting wire, the resistance is proportional to the length. We can replace R₂ and R_V by a wire AB (of length L, section S and resistivity ρ) along which a cursor D moves.

In equilibrium, we can write, taking into account the relationship (1)

Where:

R_AD  is the resistance of the wire of length  L₁=AD :

R_DB  is the resistance of the wire of length  L₂=DB :

By replacing these two values in equation (2), we obtain :