In a Wheatstone's bridge, three resistances P,Q and R connected in the three arms and the fourth arm is formed by two resistances `S_1 and S_2` connected in parallel. The condition for the bridge to be balanced will be

Options

A. `(R(s_(1) + s_(2)))/(s_(1) s_(2))`
B. `(s_(1) s_(2))/(R(s_(1) + s_(2)))`
C. `(Rs_(1) s_(2))/((s_(1) + s_(2)))`
D. `((s_(1) + s_(2)))/(R s_(1) s_(2))`

Answer

A

Explanation

Balanced condition for Wheatstone bridge
`(P)/(Q) = (R)/(S) " " … (i)`
where `(1)/(s) = (1)/(s_(1)) + (1)/(s_(2))`
`implies s = (s_(1) s_(2))/(s_(1) + s_(2)) " " … (ii)`
`therefore` From Eqs. (i) and (ii) , we get
`(P)/(Q) = (R(s_(1) + s_(2)))/(s_(1) s_(2))`