When two known resistances R and S are connected in the left and right gaps of a metre bridge, the - Physics - Current Electricity

Question

When two known resistances R and S are connected in the left and
right gaps of a metre bridge, the balance point is found at a
distance l1from zero end of the metre bridge wire An unknown
resistance X is now connected in parallel to the resistance S and
the balance point is now found at distance l2 from the zero end of
the metre bridge wire Obtain a formula for X in terms of l1 ,l2 and
S

Dinesh Pandey · Accepted Answer

Dear Student,

(a) When resistance R and S are connected :Since balance point is found at a distance l1 from the zero end,R α l1and, S α 100-l1Therefore, RS=l1 100-l1  
 (1)(b) When unknown resistance X is connected in parallel to S :The effective resistance in the right gap,S'=SXS+X  
(2)Since balance point is obtained at a distance l2 from the zero end,R α l2S' α 100-l2Therefore, RS'=l2 100-l2  
(3)substituting the value of S' from (2),RS+XSX=l2 100-l2 
(4)Dividing equation (4) by (1),S+XX=l2 100-l2× 100-l1l1SX+1=l2100-l1l1100-l2SX=l2100-l1l1100-l2-1SX=100l2-l1l2-100l1+l1l2l1100-l2X=l1100-l2100l2-l1S