b
(b) As bridge is in balanced condition, no current will flow through \(BD.\)

\(R_{1}=R_{A B}+R_{B C}\)

\(=R+R=2 R\)

\(R_{2}=R_{A D}+R_{C D}=R+R=2 R\)

Also, \(R_{1}\) and \(R_{2}\) are in parallel combination

Hence, equivalent resistance between \(A\) and \(C\) will be

\(R_{e q}=\frac{R_{1} R_{2}}{R_{1}+R_{2}}=\frac{4 R^{2}}{4 R}=R\)