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)))/(Rs_(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))rArr 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))`