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(C) Let the potential at point $A$ be $V_A$ and at point $B$ be $V_B$. By observing the circuit,the wire connecting $A$ to the node between the first

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$\frac{R}{2}$

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(C) Let the potential at point $A$ be $V_A$ and at point $B$ be $V_B$. By observing the circuit,the wire connecting $A$ to the node between the first $2R$ and $2R$ resistor makes the potential at that node equal to $V_A$. Similarly,the wire connecting the node between the $2R$ and $R$ resistor to $B$ makes the potential at that node equal to $V_B$. Effectively,all three resistors $(2R, 2R, R)$ are connected in parallel between points $A$ and $B$. The equivalent resistance $R_{eq}$ is given by: $\frac{1}{R_{eq}} = \frac{1}{2R} + \frac{1}{2R} + \frac{1}{R}$ $\frac{1}{R_{eq}} = \frac{1+1+2}{2R} = \frac{4}{2R} = \frac{2}{R}$ Therefore,$R_{eq} = \frac{R}{2}$.

What is the equivalent resistance between $A$ and $B$?

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