# Thirteen resistors each of resistance R are connected in the circuit as shown. What sis the effective resistance between A and B?

$\begin {array} {1 1} (A)\;2R & \quad (B)\;\large\frac{4R}{3} \\ (C)\;\large\frac{2R}{3} & \quad (D)\;R \end {array}$

The potential difference across the central resistor is zero due to symmetry of the circuit.
The circuit can be treated like a balance wheatstone bridge with all the resistors
being the equivalent resistor of the small triangle configuration at the four corners.
Thus, the effective resistance is same as the resistance of a single unit triangle shaped
resistance.
Hence, effective resistance =$\large\frac{ (R + R) \times (R)}{ ((R + R) + R)} = \large\frac{2R}{3}$