Question

What is the balanced condition of Wheatstone Bridge circuit?

Answer 1

The bridge is in balance condition when no current flows through the coil or the potential difference across the galvanometer is zero. This condition occurs when the potential difference across the a to b and a to d are equal, and the potential differences across the b to c and c to d remain same.

Derivation :

Wheatstone bridge (balanced) - Let i be the current from battery E .At point A , current i1​ flows through resistance P and current i−i1​ flows through R. In balanced state , no current flows through BD , hence point B and D are at same potential .Therefore current i1​ flows through resistance Q also and current i−i1​ flows through S.

Applying Kirchhoff's loop rule in closed mesh ABDA ,

i1​P−(i−i1​)R=0

or i1​P=(i−i1​)R  ...................eq1

In closed mesh BCDB ,

i1​Q−(i−i1​)S=0

or i1​Q=(i−i1​)S  ...................eq2

Dividing eq1 from eq2 , we get

P/Q=R/S  

This is the condition for balance in a Wheatstone's bridge .