Wheatstone bridge Principle

Wheatstone bridge

Principle:

 

1) In a Wheatstone bridge four resistors R₁, R₂, R₃ and R₄ are connected as shown in the above diagram.

2) A cell of emf e is applied with a key as shown in the diagram.

3) Now according to Wheatstone bridge principle when the key is close current starts flowing from the cell. At the junction A current separates,

4) I₁ current flows through the arm AB. & I₂  current flows through the arm AD.

5) Again at the junction B, I_g current flows along the galvanometer, So I₁ - I_g current flows along the BC arm.

6) Since I_g current meets at D, So I₂ + I_g  current flows along the DC arm

 

Now When the bridge is balanced, the galvanometer shown no deflection which means,  I_g =  0

 

7) Applying Kirchhoff’s rule in the loop ABDA

I₁R₁ +  I_gG  -  I₂R₂    = 0

When the bridge is balanced I_g =  0

then

I₁R₁  =   I₂R₂   ……….  3.63 

8) Applying Kirchhoff’s rule in the loop BCDB

(I₂ + I_g)R₄  -   (I₁ - I_g)R₃  +  I_gG   =  0

 

When the bridge is balanced I_g =  0

Then

I₂R₄  -   I₁R₃  =  0

 

I₁R₃  =   I₂R₄    .……….  3.72 

 

9) Now  

 

Which is known as Wheatstone bridge principle