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

For ballanced Wheatstone's network,
`(R_(1))/(R_(2))=(R_(3))/(R_(4))`
i.e., `(P)/(Q)=(R)/((S_(1)S_(2))/(S_( 1)+S_(2)))`
i.e., `(P)/(Q)=R((S_(1)+S_(2))/(S_(1)S_(2)))`.