Q. What is the equivalent resistance between AB?

Dear Student ,
The equivalent resistance between the points A and B is :

$$\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{R+R}+\frac{1}{R+R}+\frac{1}{R} \\ \Rightarrow \frac{{\displaystyle 1}}{{\displaystyle R_{eq}}}=\frac{1}{2R}+\frac{{\displaystyle 1}}{{\displaystyle 2R}}+\frac{{\displaystyle 1}}{{\displaystyle R}} \\ \Rightarrow \frac{{\displaystyle 1}}{{\displaystyle R_{eq}}}=\frac{1}{R}+\frac{{\displaystyle 1}}{{\displaystyle R}} \\ \Rightarrow R_{eq}=\frac{R}{2} \end{gathered}$$
Regards