Find the equivalent resistances of the nerwork shown in figure between the points A and B.

Explanation

Suppose an ideal battery of emf`(epsilon)`is connected across the points A and B. The circuit is a Wheatstone bridge with the galvanometer replaced by a `50(Omega)`resistance. As the bridge is balanced `(R_(1)/R_(2)=R_(3)/R_(4))`there will be no current through the `50(Omega)`resistances. We can just remove the `50(Omega)`resistance without changing any other current. The circuit is then equivalent to two tesistances `30(Omega)`and `60(Omega)`connected in parallel. The equivalent resistance is
`R=(30(Omega))xx(60(Omega))/(30(Omega))+(60(Omega))=20(Omega).`