6. Thirteen identical metal rods are connected as follows (see fig.). It is known that the resistance of the entire structure $R=8$ Ohms. Determine the resistance of one rod $R_{0}$, if this structure is connected to a current source at points $A$ and $B$.

$(10$ points)

![](https://cdn.mathpix.com/cropped/2024_05_06_84fc2054d2075e5d2c9fg-11.jpg?height=537&width=945&top_left_y=154&top_left_x=584)
Answer: $20 O_{m}$

Solution. The equivalent circuit looks as follows (2 points),

![](https://cdn.mathpix.com/cropped/2024_05_06_84fc2054d2075e5d2c9fg-11.jpg?height=451&width=876&top_left_y=891&top_left_x=607)

where each resistor has a resistance of $R_{0}$. As a result, the total resistance is: $R=\frac{4}{10} R_{0}$, which means the resistance of one rod $R_{0}=20$ Oм (5 points).